Beginning of Section HOSetConstr
Theorem. (
conj_HOSetConstr_TMZDFW6pMNWz7vpxXhhZwdjfnM6K7Yz1czg )
∀X0 : (((((set → set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → prop ∀X2 : ((set → set → set → set → ((set → set → (set → set → set → prop ∀X3 : (set → set → ((set → (set → set → set → set → set → (set → set → set → set → (((set → set → set → set → (set → set → set → ((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum (X6 (λX9 : (set → set → set → set λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (λX8 : set → set setsum X7 ∅ ) X3 (λX8 : set ⇒ X6 (λX9 : (set → set → set → set λX10 : set ⇒ ∅ ) ) (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj1 (setsum ∅ (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum ∅ ∅ ) (λX8 : set → set setsum (setsum (setsum (setsum ∅ ∅ X7 (Inj1 (Inj1 ∅ (Inj1 (setsum (X5 ∅ ∅ ) (setsum (X5 (Inj0 X4 ∅ X4 ) → (∀X4 : (((set → set → set → set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (X10 (Inj0 (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum ∅ X7 ) (λX8 : set → set ∅ ) (X6 ∅ (setsum (Inj1 (X6 ∅ ∅ X7 (X6 (setsum ∅ (Inj1 (X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 (setsum (X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 ∅ ∅ ∅ X0 (λX8 : (((set → set → set → set → set → set setsum (Inj0 (Inj0 ∅ ∅ ) (X6 ∅ (Inj0 (Inj1 (setsum ∅ ∅ (λX8 : set → set → set X5 (Inj1 (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : (((set → set → set → (set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set (setsum ∅ (Inj0 X5 ∈ Inj1 (setsum (setsum (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 ∅ ∅ → X3 (λX8 : set ⇒ X8 ) (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (setsum ∅ ∅ ∅ ) (λX8 : set → set setsum (X7 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (X8 ∅ (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ∅ ) (setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ X9 ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ X2 (λX8 : set → set → set setsum (X6 ∅ (X7 (λX9 : set ⇒ X9 ) ∅ (X6 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set → set ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set ∀X7 : set , (setsum (setsum ∅ (Inj0 (Inj0 ∅ ∅ ∈ Inj1 (Inj0 ∅ → X2 (λX8 : set → set → set Inj1 (setsum (Inj0 (X5 ∅ (X6 (λX9 : set → set X9 ∅ ) ) (λX8 : set → set λX9 : set → set setsum (setsum (setsum ∅ ∅ ∅ (setsum ∅ (Inj1 ∅ ) X3 (λX8 : set ⇒ X5 ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (Inj1 (X8 (setsum ∅ ∅ (λX12 : set ⇒ Inj0 ∅ ) ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set X6 (λX9 : set → set X6 (λX10 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) ) (setsum (setsum (Inj0 (Inj1 ∅ (X5 ∅ (setsum (X6 (λX8 : set → set setsum ∅ ∅ ) (setsum (Inj0 ∅ (X6 (λX8 : set → set ∅ ) (X6 (λX8 : set → set Inj0 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 (X10 X11 (λX12 : set ⇒ X10 ∅ ) (Inj1 (setsum (Inj0 ∅ (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set X7 ) (λX8 : set → set Inj1 X7 ) (Inj1 ∅ (Inj1 ∅ X1 (λX8 : set ⇒ X7 ) (λX8 : set → set setsum ∅ ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set → set Inj0 (X5 (Inj1 (setsum ∅ ∅ ) X2 (λX8 : set → set → set X6 ) (λX8 : set → set λX9 : set → set setsum (Inj0 (Inj0 X6 (setsum (Inj1 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set setsum ∅ ∅ ) (setsum ∅ (setsum X4 (Inj0 (setsum ∅ ∅ (λX8 : set → set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set Inj1 (X6 (setsum (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ ∅ (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (setsum X5 (setsum (Inj0 ∅ (setsum (X6 ∅ ∅ (λX8 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set → set → set ∅ ) (Inj0 (Inj1 ∅ ∈ Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPXt2PFGaBVBw96AxuKTHhMDmzAeescogP )
∀X0 : (set → set → set → (set → (set → set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : ((set → set → set → set → (((set → set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → ((set → set → set → set → set → set → set → set → (set → set → set → (set → set → prop (∀X4 : (((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set → set → set (Inj1 ∅ ∈ setsum (setsum (setsum (X5 ∅ (X5 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ → X3 (λX8 : set → ((set → set → set → set λX9 : set ⇒ X9 ) (setsum (Inj1 X6 ∅ (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum (setsum (Inj0 ∅ X8 (Inj1 (setsum (setsum ∅ ∅ (X5 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X6 ∈ X5 → X3 (λX8 : set → ((set → set → set → set λX9 : set ⇒ ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ setsum X5 X5 ) X3 (λX8 : set → ((set → set → set → set λX9 : set ⇒ X7 (setsum ∅ ∅ ) (Inj0 ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum X8 X8 ) (λX8 : set ⇒ Inj1 (Inj1 X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set → set ∀X7 : set , (setsum X7 ∅ ∈ Inj0 X7 → X2 (λX8 : set → set → set → set λX9 : ((set → set → set → set → set setsum (setsum (X6 (λX10 : (set → set → set → set X9 (λX11 : set → set λX12 : set ⇒ ∅ ) ) ∅ (setsum ∅ ∅ (Inj1 ∅ ∅ ∅ ) (X6 (λX8 : (set → set → set → set Inj1 (Inj1 (Inj0 ∅ ) (Inj1 X4 X4 (X6 (λX8 : (set → set → set → set Inj1 (X8 (λX9 : set ⇒ ∅ ) ∅ ) (Inj1 (setsum ∅ ∅ X7 ∅ (setsum (X6 (λX8 : (set → set → set → set setsum ∅ ∅ ) X5 (Inj1 X4 (Inj0 ∅ (setsum (setsum X7 ∅ (Inj0 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : (((set → set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set → set → set → set λX9 : ((set → set → set → set → set X9 (λX10 : set → set λX11 : set ⇒ setsum (setsum ∅ (Inj0 ∅ (setsum ∅ (setsum ∅ ∅ ) ) X7 ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ ) False ) → (∀X4 : set → set ∀X5 : set → set → set → set → set ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (setsum X10 (setsum ∅ ∅ (Inj1 (X7 (λX11 : set ⇒ Inj1 ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set , (setsum ∅ (X6 (Inj1 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∈ Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ X3 (λX8 : set → ((set → set → set → set λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj0 ∅ (setsum ∅ (Inj1 X8 ) (λX8 : set ⇒ setsum (setsum (Inj0 X7 (setsum (Inj1 ∅ (Inj1 ∅ (setsum X8 (Inj0 (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X9 X8 ) (Inj0 (Inj0 ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 (setsum (X9 ∅ (setsum ∅ ∅ ) (setsum X6 X5 ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTuHoaZc2WyCb9fegGap3pDffefQsYofjW )
∀X0 : ((set → set → (set → set → set → set → (set → set → set → set → set → (set → set → set → set → (set → (set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → (set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : ((set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (X4 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X10 ) (setsum (Inj0 X7 (X4 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X9 X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → set → set → set → set X3 (λX8 : set ⇒ ∅ ) X5 ∅ (setsum ∅ ∅ ∈ Inj1 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ Inj1 X7 ) (Inj1 (Inj0 ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj1 X7 ) ∅ (Inj0 ∅ ∈ Inj1 ∅ ) → (∀X4 : set → (set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : set , (setsum ∅ (Inj1 X7 ∈ Inj0 X7 → X3 (λX8 : set ⇒ X8 ) (setsum X7 (setsum (setsum (Inj0 ∅ ∅ (setsum (X4 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (setsum X7 (Inj1 X5 X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 X6 ) (λX8 : set ⇒ X7 (Inj0 ∅ ) X0 (λX8 : set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj0 X10 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set X7 ∅ ) (setsum (Inj1 ∅ (setsum (setsum (setsum ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set X7 ) (Inj1 (setsum X4 ∅ X0 (λX8 : set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj0 ∅ (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set X9 ∅ (X9 (Inj1 ∅ X7 ) (setsum (setsum (Inj0 X7 (setsum (Inj1 ∅ ∅ (X6 X4 ) → (∀X4 : (((set → set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X0 (λX8 : set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X10 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set ∅ ) (Inj1 (setsum (X5 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ ∅ X0 (λX8 : set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set ∅ ) X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGtUexTLvLJiRGYCY4LFPabYdbXwj9gEP1 )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : ((set → set → set → set → (set → (set → set → set → set → set → prop ∀X3 : ((set → set → set → set → set → ((set → set → set → set → set → set → set → (((set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 ∈ Inj1 (Inj1 ∅ X3 (λX8 : set → set → set → set → set λX9 : (set → set → set → set → set setsum (Inj0 (Inj1 (X8 ∅ ∅ ∅ ∅ (setsum X6 X7 ) (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : set → set → set → set → set λX9 : (set → set → set → set → set ∅ ) (Inj0 (Inj0 (Inj0 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj0 (Inj1 (setsum ∅ ∅ ) False ) → (∀X4 : set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X1 (λX8 : set ⇒ ∅ ) (Inj1 (setsum (Inj1 (Inj1 ∅ ∅ X2 (λX8 : set → set → set X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set → (set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ X9 (Inj0 ∅ ) X0 (λX8 : set ⇒ X6 ) X6 (Inj0 (X4 (setsum (Inj1 ∅ ∅ (λX8 : set ⇒ ∅ ) (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum (setsum (X5 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ (Inj0 X7 ∈ X5 ∅ → X3 (λX8 : set → set → set → set → set λX9 : (set → set → set → set → set ∅ ) (setsum ∅ (setsum (X4 (setsum ∅ ∅ (setsum (setsum ∅ ∅ (X5 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ setsum (Inj0 X8 (Inj1 X7 ) ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 (X6 (X4 (λX8 : (set → set → set ∅ ) X1 (λX8 : set ⇒ ∅ ) (X6 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set → set → (set → set → set (Inj0 ∅ ∈ Inj1 ∅ → X0 (λX8 : set ⇒ ∅ ) ∅ (X5 (λX8 : set → set → set λX9 : set → set Inj1 (X8 (X9 ∅ (Inj1 ∅ ) (Inj1 (Inj0 (setsum ∅ ∅ X4 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set → (set → set → set → set → set (Inj1 (X5 (Inj0 ∅ ∈ Inj1 ∅ → X0 (λX8 : set ⇒ setsum ∅ ∅ ) (X5 (setsum (setsum (setsum ∅ ∅ ∅ X4 (setsum (setsum (setsum (Inj0 ∅ X4 ∅ (setsum X4 (X5 (X7 ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ (X6 (λX8 : set ⇒ X6 (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (X7 ∅ (λX11 : set ⇒ ∅ ) ∅ ∅ (Inj0 ∅ ) ) (λX8 : set → set λX9 : set ⇒ setsum (X7 (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ∅ (X6 (λX10 : set ⇒ X9 ) (λX10 : set → set λX11 : set ⇒ ∅ ) ) X1 (λX8 : set ⇒ X6 (λX9 : set ⇒ X7 ∅ (λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) (setsum ∅ (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (X7 ∅ (λX11 : set ⇒ ∅ ) ∅ ∅ ) ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKmD6gTQTBvmYaD4WiJBkmDrzH7DjRDYen )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → set → (set → set → set → set → prop ∀X2 : ((set → set → (set → set → set → ((set → set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → set → set → set → set → prop (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : (set → set → set → set ∀X6 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set → ((set → set → set → (set → set → set → set X3 (λX8 : ((set → set → set → set Inj0 (setsum (setsum ∅ (X8 (λX9 : set → set ∅ ) (X7 ∅ (λX9 : set → set Inj0 ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ) (setsum (Inj1 (Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (Inj0 (Inj0 ∅ (Inj0 ∅ (X6 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ X9 ) (Inj0 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (X6 (λX9 : (set → set → set → set X9 (λX10 : set ⇒ ∅ ) ∅ ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : ((set → set → set → set Inj1 ∅ ) X4 (Inj1 (setsum (Inj1 X5 (Inj1 (setsum ∅ ∅ (Inj1 ∅ (Inj0 (Inj0 X6 ∈ Inj0 (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → (set → set → set ∀X6 : ((set → set → set → set → (set → set → set ∀X7 : set , (Inj1 (Inj0 (Inj1 ∅ ∈ X5 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (Inj0 ∅ X9 ) (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X8 ) → X3 (λX8 : ((set → set → set → set Inj1 (X5 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum X11 (setsum ∅ ∅ ) (λX9 : set ⇒ X7 ) ) (setsum (X5 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) X7 X4 (setsum (setsum ∅ ∅ (Inj0 (Inj1 (Inj1 ∅ X2 (λX8 : set → set λX9 : set → set → set λX10 : (set → set → set → set X8 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum (X6 (λX8 : set → set setsum (X6 (λX9 : set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) X4 (λX8 : set ⇒ X7 ) (Inj1 (Inj1 ∅ ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → set λX9 : set → set → set λX10 : (set → set → set → set setsum (X10 (λX11 : set ⇒ Inj1 ∅ ) ∅ (X9 ∅ ∅ ) ∅ X2 (λX8 : set → set λX9 : set → set → set λX10 : (set → set → set → set setsum (Inj1 (X9 (setsum ∅ ∅ ∅ (Inj1 ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , (Inj1 ∅ ∈ setsum ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ ∅ ) ) (setsum ∅ (setsum (Inj1 (setsum ∅ ∅ X4 (X6 (λX8 : set ⇒ X7 ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set ∀X7 : set → (set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (setsum ∅ X9 (X7 ∅ (λX11 : set ⇒ Inj1 X11 ) ) ∅ X2 (λX8 : set → set λX9 : set → set → set λX10 : (set → set → set → set setsum (X9 ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ (X8 (Inj0 ∅ ) (Inj1 (setsum (X5 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ X6 ) ∅ X4 ) → (∀X4 : ((set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (Inj0 (setsum (Inj1 ∅ (Inj0 ∅ (X4 (λX8 : set → set X6 (X8 ∅ (Inj1 (X5 (λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 (Inj1 ∅ ) ∅ ) (Inj0 (Inj0 (setsum (Inj0 ∅ (Inj1 ∅ ∈ X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum (Inj0 (setsum ∅ ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWhvSB3qF4baQJU9Yo9ibyVK2NZAmare6G )
∀X0 : ((((set → set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → (set → set → set → set → set → set → set → set → set → (((set → set → set → set → prop ∀X2 : ((set → set → set → set → (set → set → prop ∀X3 : (((((set → set → set → set → set → set → set → set → set → (((set → set → set → (set → set → set → prop (∀X4 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X6 ∈ Inj0 (setsum X6 X6 → X3 (λX8 : (((set → set → set → set → set → set → set setsum (setsum (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (X7 (Inj0 ∅ ) (Inj1 (X7 X5 (λX8 : (set → set → set λX9 : set → set ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → set → set Inj0 (setsum ∅ X5 ) X7 (λX8 : (set → set → set λX9 : set → set X6 ) (X7 ∈ setsum (setsum (Inj0 (X4 ∅ (X4 ∅ (setsum (X4 ∅ X7 ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X6 ∈ Inj1 X6 → X2 (λX8 : set → set λX9 : set ⇒ Inj0 (Inj1 X7 ) (λX8 : set ⇒ setsum X7 (setsum X6 (setsum ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : (((set → set → set → set → (set → set → set → set → set → set ∀X7 : (((set → set → set → set → set → (set → set → set → set (Inj0 (Inj0 (X5 (λX8 : set ⇒ setsum ∅ ∅ ) (X7 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∈ X6 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 (setsum (setsum ∅ ∅ ∅ ) (Inj0 (Inj1 ∅ → X2 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) X3 (λX8 : (((set → set → set → set → set → set → set ∅ ) X4 (λX8 : (set → set → set λX9 : set → set setsum ∅ (Inj1 (Inj0 (X8 (λX10 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (setsum (setsum (Inj0 (setsum ∅ ∅ (Inj0 X6 ∅ ∈ setsum (Inj0 ∅ ∅ → X1 (λX8 : (((set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum (setsum (X5 (setsum ∅ ∅ ∅ (setsum (setsum ∅ ∅ (Inj0 X4 (λX8 : (set → set → set Inj1 (setsum (setsum ∅ ∅ (X5 (X8 (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : (set → set → set → (set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : (((set → set → set → set → set → set → set X1 (λX8 : (((set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ (λX8 : (set → set → set X8 (λX9 : set ⇒ Inj1 (X8 (λX10 : set ⇒ Inj1 ∅ ) ) ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : (set → set → set → (set → set → set X0 (λX8 : ((set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) (setsum ∅ (X4 (Inj1 X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : ((set → set → set → set λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum ∅ (X10 ∅ ) ∅ (Inj1 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWE93ZpcqnHqZub1f6mZhZZ9kRg25xrd6i )
∀X0 : (set → set → set → set → ((((set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X1 : (set → set → set → (set → set → prop ∀X2 : (set → set → (((set → set → (set → set → set → (set → set → (set → set → set → prop ∀X3 : (set → set → set → set → set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum X5 ∅ ∈ X6 → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) ∅ (setsum (Inj1 ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) (Inj0 (Inj1 ∅ ∅ ) → (∀X4 : set → set → set → set ∀X5 : (set → (set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , (X4 (X4 ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) X7 (Inj1 ∅ (X4 (Inj0 ∅ (Inj1 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ X7 ∈ setsum (X4 (setsum (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (X6 ∅ ∅ (Inj1 (Inj0 ∅ (setsum ∅ (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum X10 (setsum ∅ ∅ ) X7 (setsum (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 ∅ (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 X10 ) ∅ (setsum (X4 (setsum (X4 ∅ ∅ ∅ (Inj0 ∅ (setsum (Inj1 ∅ (X4 ∅ ∅ ∅ (Inj1 (setsum ∅ ∅ (setsum (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (X4 ∅ ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : (((set → set → set → set → set X2 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set λX10 : set → set setsum (setsum ∅ (X8 (λX11 : set ⇒ setsum ∅ ∅ ) (λX11 : set ⇒ Inj1 ∅ ) (Inj1 (X9 (X9 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (Inj1 ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set λX10 : set → set setsum (setsum ∅ (X7 (setsum ∅ ∅ (X7 (Inj0 (Inj0 ∅ ) (X7 ∅ ∈ X5 ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set → set → set → set X2 (λX8 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set λX10 : set → set ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (Inj0 (setsum ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj1 X5 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (setsum (setsum ∅ ∅ ∅ X7 ) (λX8 : set ⇒ X8 ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set X6 ) (λX8 : set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set λX10 : set → set ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 (Inj0 (Inj0 ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set → set ∅ ) (λX8 : set → set → set λX9 : set ⇒ X9 ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set → ((set → set → set → (set → set → set ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (X7 (λX11 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) ) (λX8 : ((set → set → set → set → set X6 ∅ (λX9 : set ⇒ λX10 : set ⇒ setsum (X7 (λX11 : set ⇒ X9 ) (Inj1 (Inj1 ∅ ) (λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ Inj1 (X10 ∅ ) (λX9 : set → set Inj1 ∅ ) (λX9 : set ⇒ X9 ) ) (λX8 : set → set → set λX9 : set ⇒ Inj0 (X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ setsum X9 (setsum ∅ ∅ ) (λX10 : set ⇒ X10 ) (X7 (λX10 : set ⇒ X9 ) ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMT5ViaVjArL2yg8MLKXNAawcgcxfeETKBc )
∀X0 : (set → set → set → (set → set → prop ∀X1 : (((((set → set → set → set → set → set → set → set → ((set → set → set → set → set → set → (set → set → prop ∀X2 : (set → set → set → (set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → ((((set → set → set → set → set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → (set → set → set → set (X6 ∈ X5 (λX8 : set → set X6 ) (Inj1 (Inj0 ∅ → X3 (λX8 : set → set Inj1 (Inj1 (X7 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set X9 ) X3 (λX8 : set → set setsum ∅ (Inj0 (X8 X6 ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set setsum (Inj1 (Inj1 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set (setsum (Inj1 (setsum (Inj0 ∅ (Inj1 ∅ (Inj0 (setsum (X6 ∅ ∅ (setsum ∅ ∅ ∈ Inj1 ∅ → X3 (λX8 : set → set Inj1 (setsum X5 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) X2 (λX8 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ ∅ X5 ) (Inj1 (Inj1 (X6 (setsum ∅ ∅ (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (X7 (setsum (Inj0 ∅ X10 X10 ) (λX8 : set → set λX9 : set ⇒ setsum X9 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : (set → set → set → (set → set → set → set → set ∀X7 : ((set → set → set → set X3 (λX8 : set → set Inj0 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set Inj1 (X10 ∅ ) X2 (λX8 : set ⇒ ∅ ) (setsum ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ Inj0 X9 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj0 ∅ X8 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set ⇒ X11 ) (λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum (setsum ∅ ∅ X9 ) (setsum ∅ (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ X11 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (Inj0 (setsum ∅ (X5 (X4 ∅ ∅ ∈ Inj1 (Inj0 ∅ → X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum X12 (Inj0 (Inj0 (X10 (λX13 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set X2 (λX8 : set ⇒ ∅ ) (setsum X6 (Inj1 (Inj1 X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : (set → set → set → set Inj1 (X11 (λX12 : set ⇒ setsum ∅ ∅ ) ∅ ) (λX11 : set → set ∅ ) (λX11 : set ⇒ setsum (setsum (Inj0 ∅ (Inj1 ∅ ∅ ) (Inj1 (setsum (Inj1 ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj1 (X8 (setsum ∅ ∅ X6 ) X0 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) X4 (λX8 : set ⇒ X7 (Inj1 (setsum (X7 ∅ (setsum ∅ ∅ ) (X6 X4 (setsum (X6 ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj0 ∅ ∈ setsum (X6 X5 (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGLBUhQJAMk6MwnU5sMCtXcYg5hWCAfU6x )
∀X0 : (((set → (set → set → set → (set → set → set → set → set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → (set → set → prop ∀X2 : ((set → ((set → set → set → set → set → (set → set → set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set → set X3 (λX8 : set ⇒ Inj0 (Inj0 X5 ) (setsum (Inj0 (Inj0 (X7 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ ∅ (X4 ∈ Inj0 ∅ ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X2 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set ∅ ) (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set X2 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set Inj1 ∅ ) (setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ (X5 (λX8 : set → set λX9 : set → set Inj0 (Inj0 (X9 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ ∅ X6 ) False ) → (∀X4 : (((set → set → set → (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set → set X2 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set setsum (X8 (Inj1 (X8 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ setsum X11 (Inj0 ∅ ) (setsum (Inj0 ∅ (Inj1 ∅ ) (Inj0 ∅ X5 X1 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (X6 (X6 (setsum (Inj0 ∅ (X4 (λX8 : (set → set → set λX9 : set → set ∅ ) ∅ ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X6 (λX8 : set ⇒ Inj0 ∅ ) (Inj1 (Inj0 ∅ ∈ Inj0 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set X0 (λX8 : (set → (set → set → set → (set → set → set → set → set λX9 : set ⇒ setsum (Inj0 (X7 (λX10 : set ⇒ λX11 : set → set X11 ∅ ) (Inj0 X6 ) ∅ (X7 (λX8 : set ⇒ λX9 : set → set X9 (X9 ∅ ) (setsum X6 (Inj1 (Inj1 (X5 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ (X7 (λX8 : set ⇒ λX9 : set → set X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 ∈ Inj1 (setsum X4 (X6 (setsum ∅ ∅ X0 (λX8 : (set → (set → set → set → (set → set → set → set → set λX9 : set ⇒ X7 ) (X6 (setsum ∅ ∅ (setsum ∅ (setsum ∅ (Inj0 X4 X7 (setsum ∅ (setsum ∅ (setsum (setsum ∅ ∅ ∅ X2 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set X7 ) (Inj0 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMpw1cahFCGBnSbYzoj7W2HZN87XVfQZu9 )
∀X0 : ((set → ((set → set → set → set → (((set → set → set → set → set → set → set → set → prop ∀X1 : ((set → (set → set → set → (((set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → set → prop ∀X3 : ((((set → set → (set → set → set → set → set → set → (((set → set → set → set → set → set → set → prop (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → (set → set → set → set Inj1 (setsum (Inj1 X5 (X8 (λX9 : set → set λX10 : set → set setsum ∅ ∅ ) ) (Inj1 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X3 (λX8 : ((set → set → (set → set → set → set setsum ∅ (X8 (λX9 : set → set λX10 : set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) ) ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj1 X7 ∅ (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → (set → set → set → set ∅ ) (Inj0 (setsum ∅ (setsum ∅ (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X3 (λX8 : ((set → set → (set → set → set → set X6 ) ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (X8 (λX11 : set ⇒ X8 (λX12 : set ⇒ ∅ ) (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ (Inj1 X4 ) → (∀X4 : (set → set → set ∀X5 : ((set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj0 X8 ) (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) (X5 (λX8 : set → set λX9 : set ⇒ setsum ∅ X6 ) (λX8 : set → set setsum X6 (Inj0 ∅ ) ∈ Inj1 (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ ∅ ∈ setsum ∅ (setsum (setsum (Inj1 ∅ ∅ (Inj0 (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) → X3 (λX8 : ((set → set → (set → set → set → set Inj1 (setsum (setsum ∅ (Inj1 ∅ (setsum ∅ (Inj1 ∅ ) (Inj0 (Inj0 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X1 (λX8 : set → (set → set → set λX9 : ((set → set → set → (set → set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → (set → set → set λX9 : ((set → set → set → (set → set → set → set setsum ∅ ∅ ) X6 X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) ∅ ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set X0 (λX8 : set → ((set → set → set → set λX9 : ((set → set → set → set → set setsum (Inj1 ∅ (Inj0 (X7 (X7 ∅ (λX10 : set → set ∅ ) (λX10 : set → set X10 ∅ ) ) ∅ X6 ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → ((set → set → set → set λX9 : ((set → set → set → set → set ∅ ) (setsum (Inj1 (Inj1 (Inj0 ∅ (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (X8 (λX11 : set ⇒ ∅ ) ) X7 (Inj1 (Inj0 X5 ∈ Inj0 (Inj0 (Inj1 (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYPz39QW4votLZ7KnocjX65EJHAEn6ikHJ )
∀X0 : ((((set → set → set → set → set → ((((set → set → set → set → (set → set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → (((set → set → set → set → set → set → (set → set → prop ∀X2 : (set → set → set → ((set → set → set → set → set → set → prop ∀X3 : ((set → set → ((set → set → set → set → set → set → prop (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set , (X6 (λX8 : set ⇒ X7 ) (λX8 : set → set λX9 : set ⇒ X7 ) ∈ X5 → X3 (λX8 : set → set λX9 : (set → set → set ∅ ) (setsum (setsum (X6 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ X5 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set λX9 : (set → set → set Inj1 ∅ ) (Inj1 (setsum ∅ (Inj0 X7 (setsum ∅ (Inj0 ∅ False ) → (∀X4 : (set → set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : (set → set → set X0 (λX8 : ((set → set → set → set Inj0 (setsum ∅ (X7 (λX9 : set ⇒ setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set → (set → set → set → set Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ) (setsum (Inj0 (X5 ∅ (λX8 : set → set λX9 : set ⇒ X6 ∅ ∅ (λX10 : set ⇒ ∅ ) ∅ ) (Inj0 (setsum ∅ ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (X7 (λX10 : set ⇒ ∅ ) X8 (setsum (X7 (λX10 : set ⇒ ∅ ) X8 ) (λX8 : set → set → set λX9 : set ⇒ Inj1 (Inj1 (X7 (λX10 : set ⇒ setsum ∅ ∅ ) ) (setsum (setsum (Inj1 (Inj0 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : (((set → set → set → set → (set → set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set → set → set λX9 : set ⇒ ∅ ) (Inj0 (Inj0 (Inj1 ∅ X3 (λX8 : set → set λX9 : (set → set → set ∅ ) (setsum (X6 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 (X9 ∅ ) ∅ ∅ (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : ((set → set → set → set → ((set → set → set → set → set ∀X6 : set → set → set ∀X7 : ((set → set → set → set → set (Inj1 (setsum (setsum (setsum ∅ ∅ (X6 ∅ ∅ (setsum (X7 (λX8 : set → set → set ∅ ) (setsum ∅ ∅ ∈ Inj0 (setsum (Inj1 ∅ (X6 (Inj0 ∅ (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set → set → set λX9 : set ⇒ setsum ∅ (Inj1 (X6 X9 (setsum ∅ ∅ ) (Inj0 (setsum ∅ (X4 (λX8 : (set → set → set setsum ∅ ∅ ) X1 (λX8 : (((set → set → set → set → set λX9 : ((set → set → set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set X1 (λX8 : (((set → set → set → set → set λX9 : ((set → set → set → set → set setsum ∅ (setsum ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set → set ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → ((set → set → set → set → set → set X0 (λX8 : ((set → set → set → set X8 (λX9 : set → set setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set → (set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ X9 (setsum (setsum ∅ ∅ (X8 (λX11 : set → set λX12 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (λX9 : set ⇒ setsum ∅ (Inj0 X6 ) (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X8 (λX9 : set → set λX10 : set ⇒ X8 (λX11 : set → set λX12 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (λX9 : set ⇒ X8 (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ ) (setsum ∅ ∅ ) (X7 (λX8 : set ⇒ X8 ) (λX8 : set → set setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) (Inj1 ∅ (Inj1 (X4 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : ((set → set → set → set ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set setsum X6 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) ∅ X3 (λX8 : set → set λX9 : (set → set → set X7 ) X6 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGTiEh8A7bLEe1RwuEQLduo2pJGA5k6Dy1 )
∀X0 : (set → set → ((((set → set → set → (set → set → set → set → set → set → set → set → set → prop ∀X1 : ((set → ((set → set → set → set → set → (set → set → set → set → set → set → set → prop ∀X2 : ((set → (set → set → (set → set → set → set → set → ((set → (set → set → set → set → (set → set → set → set → prop ∀X3 : ((set → set → set → ((set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → ((set → set → set → set X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set ∅ ) ∅ (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ X8 (Inj1 (setsum X9 ∅ ) ) → (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set Inj0 ∅ ) (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj1 X7 ) X1 (λX8 : set → ((set → set → set → set → set λX9 : set → set Inj1 ∅ ) (X6 X5 (setsum X7 X7 ∅ (setsum (setsum (Inj0 ∅ X5 (setsum ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (setsum (X5 (λX8 : set → set → set λX9 : set → set ∅ ) (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ∈ setsum ∅ (setsum ∅ ∅ → X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set setsum X9 (X10 (λX11 : set ⇒ setsum (Inj1 ∅ (Inj0 ∅ ) ) ∅ (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) X2 (λX8 : set → (set → set → (set → set → set → set X6 ) (λX8 : set → (set → set → set → set λX9 : set → set → set X9 ∅ (X7 (X8 (Inj1 ∅ (λX10 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj1 (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) ∈ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ X7 → X2 (λX8 : set → (set → set → (set → set → set → set ∅ ) (λX8 : set → (set → set → set → set λX9 : set → set → set Inj0 (X9 (Inj0 (setsum ∅ ∅ X7 ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set Inj1 X7 ) (Inj0 (Inj1 ∅ (setsum (Inj0 X4 X4 (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set ∀X7 : set , (setsum (X6 (λX8 : set ⇒ setsum (X6 (λX9 : set ⇒ ∅ ) (λX9 : set → set ∅ ) ∅ ) (λX8 : set → set ∅ ) (setsum (X6 (λX8 : set ⇒ X6 (λX9 : set ⇒ ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set → set ∅ ) (setsum ∅ (setsum ∅ ∅ ∈ Inj1 (setsum X7 X7 → X1 (λX8 : set → ((set → set → set → set → set λX9 : set → set Inj1 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ X7 ) (Inj0 X5 (Inj1 ∅ (setsum X7 (X4 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ (X6 (λX8 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) (λX8 : set → set setsum X7 (Inj1 ∅ ) ) → (∀X4 : (set → set → ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → set λX9 : set → set ∅ ) (setsum (Inj0 (Inj0 (setsum ∅ ∅ X7 (setsum (Inj0 ∅ X7 X7 (Inj1 (setsum (X4 (λX8 : set ⇒ X7 ) (λX8 : set → set Inj1 ∅ ) (X4 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ ∅ X6 (X5 (setsum ∅ ∅ False ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj1 X7 ) (λX8 : ((set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X7 (setsum ∅ (setsum (Inj0 ∅ (Inj1 ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set → set → set ∀X7 : set → set (X5 ∈ X4 (λX8 : set → set → set X5 ) → X0 (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) (setsum (setsum (Inj0 (setsum ∅ ∅ (Inj0 (Inj0 ∅ (Inj0 ∅ (X4 (λX8 : set → set → set X5 ) X2 (λX8 : set → (set → set → (set → set → set → set Inj0 (Inj0 (setsum (Inj1 ∅ (Inj1 ∅ ) (λX8 : set → (set → set → set → set λX9 : set → set → set setsum (setsum (Inj0 (Inj1 ∅ ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMRXMKHK8QfmLhUVFuMCQDnsR5JaRumchM )
∀X0 : ((set → set → set → set → (set → set → set → prop ∀X1 : (set → set → (((set → set → (set → set → set → set → set → set → set → prop ∀X2 : ((set → set → set → set → (set → set → set → prop ∀X3 : (((set → (set → set → set → (set → set → (set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → (set → set → set → (set → set → (set → set → set setsum (setsum (Inj1 (Inj0 ∅ ∅ (Inj1 ∅ ) X6 (λX8 : set ⇒ X7 ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : (set → (set → set → set → (set → set → (set → set → set setsum ∅ ∅ ) (X5 ∅ (λX8 : set ⇒ X5 (setsum ∅ ∅ ) False ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → (set → set → set → set → set → set ∀X7 : (set → set → set → set → set X2 (λX8 : set → set Inj1 (X8 (setsum ∅ (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ setsum (Inj1 (Inj1 ∅ (X5 (Inj1 (Inj0 ∅ ) (setsum (Inj1 ∅ (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : set → set setsum (setsum X7 (X5 (λX9 : set ⇒ λX10 : set → set Inj0 ∅ ) (Inj1 ∅ ) (Inj1 (setsum ∅ (Inj1 ∅ (λX8 : set ⇒ ∅ ) ∅ X1 (λX8 : set ⇒ setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (X5 (λX9 : set ⇒ λX10 : set → set setsum ∅ ∅ ) ) (λX8 : (set → set → (set → set → set λX9 : set ⇒ setsum ∅ (Inj0 X7 ) X7 X4 ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set → set → set ∀X7 : (((set → set → set → set → set → set → set → set → set X2 (λX8 : set → set X7 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X8 ∅ ) ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X6 (X6 ∅ (setsum ∅ ∅ (Inj0 (Inj0 ∅ (λX8 : set ⇒ X6 (Inj1 ∅ (X5 (Inj0 (setsum ∅ ∅ (λX9 : set ⇒ X7 (λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ) (λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ ) (setsum (X7 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ∅ X1 (λX8 : set ⇒ setsum (setsum (Inj0 (Inj0 ∅ (X5 (setsum ∅ ∅ (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ X9 ) (X6 ∅ ∅ (Inj0 ∅ ) (λX8 : (set → set → (set → set → set λX9 : set ⇒ Inj0 (Inj0 ∅ ) ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : ((set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set → set → (set → set → set → set (Inj0 (X5 (λX8 : set → set Inj0 (X5 (λX9 : set → set ∅ ) ) ∈ setsum (Inj0 ∅ ∅ → X1 (λX8 : set ⇒ X7 (Inj0 (X5 (λX9 : set → set setsum ∅ ∅ ) (setsum (Inj1 ∅ (setsum X8 (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set λX9 : set ⇒ Inj0 (Inj1 ∅ ) ∅ (X4 (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj0 ∅ ) X2 (λX8 : set → set Inj1 ∅ ) ∅ (λX8 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : (set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set X5 (λX9 : (set → set → set → set λX10 : set → set Inj0 (setsum (Inj0 ∅ X7 ) ) (setsum ∅ (Inj0 (setsum X6 ∅ (λX8 : set ⇒ Inj0 ∅ ) (setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ X6 ) → (∀X4 : (((set → set → set → set → set → set → set → ((set → set → set → set ∀X5 : set → set ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set → set Inj1 ∅ ) (setsum (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ (λX8 : set ⇒ setsum X8 ∅ ) ∅ (Inj1 (setsum (X5 (setsum ∅ ∅ (Inj0 (Inj0 ∅ ∈ X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (X8 (λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set → set X6 (Inj0 (setsum ∅ ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X6 (setsum ∅ ∅ (λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ ∅ ) (Inj1 ∅ ) (setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFzfVoVVLWyrrDr32ycTQsH9Px1XHuuu4b )
∀X0 : (set → set → set → set → set → (set → set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : (set → set → (set → set → set → prop ∀X3 : (set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 (setsum X7 (setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj1 (Inj0 ∅ X9 ) X3 (λX8 : set ⇒ setsum X6 X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (Inj0 ∅ X10 ) (X6 ∈ setsum (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set → (set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (Inj1 (setsum (Inj1 X6 X7 ∅ (Inj0 X7 (λX8 : set ⇒ ∅ ) (setsum X7 ∅ X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → (set → set → set → set → set → set (Inj1 (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (X6 X4 ∈ Inj1 (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum ∅ (setsum ∅ (setsum ∅ ∅ ) X1 (λX8 : set → set Inj0 (setsum ∅ (X8 (setsum ∅ ∅ ) X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set ∅ ) (Inj1 ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (setsum (Inj0 ∅ (Inj0 (Inj0 ∅ ∈ setsum (Inj0 (Inj0 (Inj1 ∅ (Inj1 (setsum X6 (setsum ∅ ∅ → X1 (λX8 : set → set ∅ ) (Inj0 (setsum (X4 (λX8 : set → set → set Inj1 ∅ ) ∅ X3 (λX8 : set ⇒ setsum (X5 X8 X7 (λX9 : set ⇒ setsum X9 ∅ ) (setsum ∅ (setsum X7 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 X8 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ X8 ) ∅ (setsum (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (setsum (Inj1 ∅ ∅ (Inj0 X4 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ X7 ) (setsum (Inj1 ∅ X7 (setsum ∅ (Inj0 (Inj0 X4 (X6 (λX8 : (set → set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X8 ) ∅ (λX8 : set ⇒ ∅ ) (setsum (setsum ∅ (Inj1 X7 (setsum (X6 (λX8 : (set → set → set λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ∅ (Inj0 (Inj1 (Inj1 (setsum ∅ ∅ ∈ Inj0 (Inj0 (Inj0 X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMGEYKZ38giefsGf9w4LauuoxzUpjCnPhy )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → (set → set → set → (((set → set → set → set → prop ∀X3 : (set → set → set → (set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → (set → set → set ∀X7 : set → (set → set → set → set → set → set X0 (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ X7 (setsum X8 (Inj0 (Inj0 ∅ (λX10 : set ⇒ λX11 : set ⇒ X10 ) ∅ (setsum (Inj0 (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) (X7 (setsum ∅ ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (X7 (Inj1 (X7 ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 X8 X8 ) (X5 (Inj1 (Inj1 ∅ (λX8 : set ⇒ setsum (setsum (Inj1 ∅ (setsum (Inj1 ∅ ∅ (Inj0 X8 ) ) → (∀X4 : ((set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set (Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj1 ∅ X8 (X9 X10 ) → X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum X8 (Inj0 (X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ setsum X6 ∅ ) ∅ (λX8 : set ⇒ Inj1 (Inj0 (setsum ∅ X8 ) X0 (λX8 : set ⇒ Inj1 (Inj1 (setsum (Inj1 ∅ X6 ) X6 ) → (∀X4 : (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (λX8 : (set → set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → ((set → set → set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X8 (λX12 : (set → set → set Inj1 ∅ ) ) (λX8 : (set → set → set ∅ ) (Inj0 ∅ ∈ X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ X5 (X6 (Inj1 (setsum ∅ ∅ ) (setsum (Inj1 (Inj0 ∅ (Inj0 (X5 (setsum ∅ ∅ (Inj0 X4 X1 (λX8 : set ⇒ ∅ ) (X6 ∅ (setsum (Inj0 (X6 X7 ∅ ) → (∀X4 : ((set → set → (set → set → set → set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ setsum X8 ∅ ) (setsum (Inj0 ∅ X5 (Inj1 X7 X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ Inj0 (Inj0 X6 ) X6 (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : set ⇒ Inj0 (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ ) (setsum X5 ∅ (λX8 : set ⇒ ∅ ) X0 (λX8 : set ⇒ Inj0 (setsum (Inj1 (setsum ∅ ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) X6 (X4 ∈ setsum ∅ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTMTLjrxiyhSstbkX3kV47qtEiyZeuiSay )
∀X0 : (set → set → (set → set → set → set → (set → (set → set → set → set → (set → set → prop ∀X1 : ((set → (set → set → (set → set → set → set → set → (((set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → (((set → set → set → set → set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → ((set → set → set → set ∀X6 : ((set → set → (set → set → set → set ∀X7 : set , (setsum ∅ ∅ ∈ Inj0 ∅ → X3 (λX8 : (((set → set → set → set → set → set setsum ∅ ∅ ) X4 X3 (λX8 : (((set → set → set → set → set → set X7 ) ∅ ) → (∀X4 : (set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : set → set X3 (λX8 : (((set → set → set → set → set → set ∅ ) (X7 X5 X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum X8 (X10 ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj1 (X9 (X7 ∅ (Inj1 ∅ ) (λX8 : set ⇒ X5 ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : (set → set → set ∀X7 : set → (set → set → set → set X3 (λX8 : (((set → set → set → set → set → set Inj0 (X6 (λX9 : set ⇒ X7 X9 (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) ) ) (Inj1 (Inj0 ∅ X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → set → set λX10 : set ⇒ ∅ ) ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → set → set λX10 : set ⇒ setsum (X8 (λX11 : (set → set → set → set X8 (λX12 : (set → set → set → set X10 ) ) ∅ ) (X4 (λX8 : set ⇒ Inj1 ∅ ) (X7 ∈ Inj0 (X6 (λX8 : (set → set → set ∅ ) (Inj1 X7 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set X3 (λX8 : (((set → set → set → set → set → set X8 (λX9 : (set → set → set → set X9 (λX10 : set ⇒ Inj1 (X9 (λX11 : set ⇒ ∅ ) ∅ ) (Inj0 (X9 (λX10 : set ⇒ ∅ ) ∅ ) ) (setsum ∅ (Inj1 (Inj0 ∅ X1 (λX8 : set → (set → set → (set → set → set → set setsum (setsum (X7 (λX9 : (set → set → set → set λX10 : set ⇒ X8 ∅ (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (X8 X6 (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ X6 ) (X8 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set setsum X6 (setsum (Inj0 ∅ X5 ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set ∀X7 : (set → set → (set → set → set → (set → set → set → set (Inj1 (X6 (λX8 : set → set setsum (Inj0 ∅ ∅ ) ∈ Inj0 (X7 (λX8 : set ⇒ X5 X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X7 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ ) (Inj0 (Inj0 ∅ → X1 (λX8 : set → (set → set → (set → set → set → set ∅ ) (λX8 : (set → set → set Inj0 (Inj1 (X7 (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX9 : set ⇒ Inj1 ∅ ) ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum X9 ∅ ) (X4 (λX8 : set ⇒ λX9 : set → set X6 (λX10 : set → set setsum (setsum ∅ ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ X7 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum (Inj0 (setsum ∅ ∅ X8 ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X10 ) (λX8 : set ⇒ Inj0 X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → ((set → set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMP2Ab1Y4EgSLtxBNYGivSoyod81yGCMdBM )
∀X0 : ((set → set → (((set → set → set → (set → set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → set → set → set → (set → (set → set → set → set → prop ∀X3 : (set → set → set → set → set → (set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (setsum ∅ ∅ ∈ Inj1 (setsum (setsum (Inj0 ∅ (Inj1 ∅ (Inj1 (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X3 (λX8 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (Inj1 (Inj0 X6 (Inj1 (X4 (X5 ∅ X7 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum X6 (setsum X6 (Inj0 (Inj1 ∅ (λX8 : set ⇒ Inj0 (Inj1 X6 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) ∅ (Inj0 (Inj0 (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj0 X5 (λX8 : set ⇒ Inj1 (setsum (Inj1 ∅ (Inj1 X5 ) (setsum X5 (setsum X5 (setsum ∅ ∅ (Inj1 (setsum ∅ X6 ∈ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ setsum X9 ∅ ) (setsum (X6 ∅ (Inj1 (Inj0 (X6 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum X10 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 (X7 X6 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (Inj0 ∅ ) X3 (λX8 : set ⇒ Inj0 (Inj1 ∅ ) ∅ (Inj0 ∅ (setsum ∅ (Inj1 ∅ (λX8 : set ⇒ Inj1 (setsum (setsum X6 ∅ (X7 (Inj0 ∅ ∅ ) (Inj0 (X5 (setsum X6 ∅ (setsum ∅ (setsum ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : (set → (set → set → set → (set → set → set → set X1 (λX8 : set ⇒ Inj0 (X7 (λX9 : set ⇒ λX10 : set → set ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) ) ∅ X1 (λX8 : set ⇒ Inj0 (X7 (λX9 : set ⇒ λX10 : set → set Inj1 (setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) X5 ) → (∀X4 : (((set → set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (setsum (X5 ∅ (λX8 : set → set ∅ ) (Inj0 ∅ X7 False ) → (∀X4 : ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → ((set → set → set → set → set (Inj1 (X4 (λX8 : set → set → set ∅ ) (λX8 : set ⇒ ∅ ) ∈ X6 → X2 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) X0 (λX8 : set → set λX9 : ((set → set → set → (set → set → set → set λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ X10 (λX13 : set ⇒ X12 ) ) (λX8 : set ⇒ λX9 : set → set Inj1 (setsum (X9 (Inj0 ∅ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 (Inj0 (setsum ∅ ∅ ∈ X4 → X0 (λX8 : set → set λX9 : ((set → set → set → (set → set → set → set λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set X7 ) X3 (λX8 : set ⇒ X7 ) ∅ ∅ (setsum ∅ X7 (λX8 : set ⇒ Inj0 (setsum ∅ (setsum ∅ (Inj1 ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGmJmpB3aX8mfzHtYuFXWgsj8Uq6m4QozG )
∀X0 : ((set → set → set → (((set → set → set → set → set → (set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → set → set → (set → set → set → (set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → set → set → ((set → set → set → set → set → set → set → set → prop (∀X4 : (set → set → set ∀X5 : ((set → set → (set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj1 (X4 (λX8 : set ⇒ Inj1 ∅ ) → X3 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ X10 (λX13 : set ⇒ ∅ ) ∅ ) (Inj1 (setsum X6 ∅ ) → (∀X4 : set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set → set → (set → set → set X3 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ X10 (λX13 : set ⇒ Inj0 X11 ) (Inj0 (X10 (λX13 : set ⇒ ∅ ) (Inj1 ∅ ) (setsum (Inj0 X6 (X4 (setsum (setsum ∅ ∅ (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X4 (Inj1 X6 ∈ Inj0 X6 ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : (set → set → ((set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set → set → set Inj1 (X10 ∅ (Inj1 (X10 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj1 ∅ ) ∅ (λX8 : set ⇒ setsum (setsum ∅ (Inj0 (setsum ∅ ∅ X7 ) (Inj1 ∅ (λX8 : set ⇒ Inj1 (setsum X7 X7 ) (Inj1 (X5 X4 (Inj1 X4 (Inj1 (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : (set → set → (set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ setsum (setsum ∅ X8 (Inj1 X8 ) (Inj1 X7 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ setsum (Inj1 (Inj0 X7 X8 ) (setsum X7 (X5 (setsum ∅ (setsum ∅ ∅ (setsum X7 (Inj0 ∅ ∅ (X6 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ X8 ) (λX10 : set ⇒ X9 ) (Inj1 (X6 (λX10 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ ∅ ) X8 (setsum ∅ ∅ (Inj1 ∅ ) (Inj1 (Inj0 ∅ (λX8 : set ⇒ X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X5 (λX8 : set ⇒ X8 ) X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 X6 ) (setsum (setsum ∅ (setsum (setsum ∅ ∅ ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → (set → set → set (Inj1 ∅ ∈ Inj1 ∅ → X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set → set → set Inj0 (Inj0 (X8 (X10 ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set → set → set setsum (Inj1 (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X6 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : (set → (set → set → set → set X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) X3 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 (setsum (setsum ∅ ∅ X12 ) (X7 (λX8 : set ⇒ λX9 : set → set setsum (X7 (λX10 : set ⇒ λX11 : set → set X8 ) ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFTk2eP1YFAqjvNmGeyNiqqCBfjj2rNzpB )
∀X0 : ((set → set → ((set → set → set → (set → set → set → set → set → (set → set → (set → set → set → set → prop ∀X1 : (set → set → (((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → prop ∀X3 : (set → (((set → set → set → (set → set → set → set → set → (set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set setsum (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (setsum ∅ (Inj0 ∅ (Inj0 (X7 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set → set setsum (X5 (Inj1 (setsum ∅ ∅ (setsum (X5 ∅ (Inj1 (X7 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set setsum (Inj1 (Inj1 ∅ (X7 (λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set ⇒ Inj0 (setsum (Inj0 X6 (Inj0 ∅ ) (Inj1 ∅ (λX8 : set → set Inj0 (X8 (Inj0 X6 ) X1 (λX8 : set ⇒ setsum X8 (Inj1 (X7 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ) (λX8 : (set → set → set → set X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set setsum (Inj0 (X9 (λX10 : set → set ∅ ) (λX10 : set ⇒ Inj0 ∅ ) (X6 ∅ (Inj0 (X7 (Inj1 ∅ ) (λX8 : set ⇒ X5 ) ∅ (λX8 : set → set ∅ ) X2 (λX8 : set → set ∅ ) (setsum (Inj0 (Inj1 (setsum ∅ ∅ (X6 (setsum (setsum ∅ ∅ (Inj1 ∅ X5 ) → (∀X4 : set → set ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set setsum (Inj1 (Inj1 (setsum ∅ ∅ ∅ ) X7 (setsum (Inj1 ∅ (Inj1 (Inj1 ∅ X1 (λX8 : set ⇒ setsum (Inj0 (Inj1 X8 (Inj0 (Inj0 X6 ) (λX8 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set → set (X5 (λX8 : set ⇒ X8 ) ∈ Inj0 (setsum X4 (X5 (λX8 : set ⇒ Inj0 ∅ ) → X3 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ setsum (Inj0 (setsum (X7 ∅ ∅ (setsum ∅ ∅ (Inj1 (setsum (Inj0 ∅ ∅ ) (X7 ∅ X6 (λX8 : set → set ∅ ) X1 (λX8 : set ⇒ setsum (setsum (Inj1 (Inj1 ∅ ∅ (Inj0 ∅ ) (λX8 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : (set → (set → set → set → set → set → set ∀X7 : set → set → set X1 (λX8 : set ⇒ setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) (X7 X8 (X5 (λX9 : set → set → set ∅ ) (Inj0 ∅ ) (λX8 : (set → set → set → set ∅ ) (X5 (λX8 : set → set → set ∅ ) ∈ Inj1 (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (setsum ∅ X7 ∈ Inj0 X6 → X0 (λX8 : set → set λX9 : (set → set → set → (set → set → set → set Inj1 (X9 (λX10 : set ⇒ λX11 : set ⇒ Inj1 X10 ) (λX10 : set ⇒ setsum X7 X10 ) (X9 (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ X8 ∅ ) X6 ) (λX8 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set X0 (λX8 : set → set λX9 : (set → set → set → (set → set → set → set setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKk2rjt9BbCVBVzNQ6pzEKRxbz7NGnQzaJ )
∀X0 : ((set → set → ((set → set → set → set → set → prop ∀X1 : ((set → set → set → set → (set → set → set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : ((set → set → (set → set → set → set → (((set → set → set → set → set → set → (set → (set → set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 ∈ setsum X6 X4 X3 (λX8 : set → set → (set → set → set X7 ) (λX8 : (set → set → set → set → set Inj1 (Inj0 (Inj1 X7 ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set → (set → set → set → set ∀X7 : set , X3 (λX8 : set → set → (set → set → set X6 (Inj1 (Inj0 (setsum ∅ ∅ (λX9 : set ⇒ Inj1 (setsum X7 (X8 ∅ ∅ (λX10 : set ⇒ ∅ ) ) (setsum ∅ ∅ ) (λX8 : (set → set → set → set → set Inj0 (setsum X7 (X8 (λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 (Inj1 (Inj0 ∅ ) ∅ ∅ X0 (λX8 : set → set λX9 : (set → set → set Inj1 (Inj1 ∅ ) (setsum (setsum (X5 ∅ ∅ ∅ (Inj1 X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj0 ∅ → X1 (λX8 : set → set → set X5 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X9 ∅ ) X2 (λX8 : set → set setsum ∅ (setsum ∅ (X5 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X8 ∅ ) (setsum ∅ ∅ ) ∅ ) → (∀X4 : ((set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 (Inj1 (Inj1 (Inj0 ∅ ∈ setsum (Inj1 X5 ∅ → X2 (λX8 : set → set X6 ) X6 X2 (λX8 : set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set (Inj1 (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ∈ Inj0 (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (X8 (λX11 : set ⇒ ∅ ) ) → X1 (λX8 : set → set → set setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : set → ((set → set → set → set → (set → set → set → set ∀X7 : set → ((set → set → set → set → set (X5 ∅ (setsum (setsum (X5 ∅ ∅ ∅ (Inj1 ∅ ∅ (Inj0 (Inj1 (Inj1 ∅ ∈ Inj0 (Inj0 (X5 ∅ ∅ (Inj1 ∅ → X1 (λX8 : set → set → set setsum (setsum ∅ ∅ (X8 (Inj1 (Inj1 ∅ (X8 (X7 ∅ (λX9 : set → set ∅ ) ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (setsum X11 X9 ) X0 (λX8 : set → set λX9 : (set → set → set ∅ ) (Inj1 (Inj0 X4 ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : (set → set → set → set → set X3 (λX8 : set → set → (set → set → set Inj0 (X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : (set → set → set → set → set Inj0 (X5 (λX9 : set ⇒ λX10 : set → set X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ Inj1 ∅ ) ) ) (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (X6 (λX10 : (set → set → set ∅ ) (Inj0 (setsum ∅ ∅ ) ∅ ∅ X0 (λX8 : set → set λX9 : (set → set → set X9 (λX10 : set ⇒ Inj1 (X8 (setsum ∅ ∅ ) ) X4 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : set → set λX9 : (set → set → set X6 (λX10 : set ⇒ X7 ) ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTqX3BV1hYRLb8911NaGcccF3wRo7fbxLD )
∀X0 : ((set → (set → set → set → set → set → set → ((((set → set → set → set → set → set → prop ∀X1 : (set → set → ((((set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → ((set → set → set → (set → set → (set → set → set → prop ∀X3 : (set → set → set → (((set → set → set → set → (set → set → set → set → ((set → set → set → set → ((set → set → set → set → prop (∀X4 : set → ((set → set → set → set ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → ((set → set → set → set (X4 (setsum (Inj1 (Inj1 ∅ ∅ (λX8 : set → set ∅ ) ∈ setsum ∅ ∅ → X1 (λX8 : set ⇒ Inj1 (setsum ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) X3 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set → set X6 ) (setsum (setsum ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ (X4 (Inj1 (setsum ∅ ∅ (λX8 : set → set ∅ ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum X7 ∅ ) (λX8 : (set → set → set → set λX9 : set → set → set X7 ) (λX8 : set → set λX9 : set ⇒ X6 (setsum (Inj1 (X6 ∅ ∅ (Inj0 (X6 ∅ ∅ (Inj0 X7 ) (λX8 : set → set X8 (X5 (λX9 : set → set → set setsum ∅ (setsum ∅ ∅ ) (X5 (λX9 : set → set → set ∅ ) ∅ (Inj1 ∅ ∅ ) (setsum (setsum (setsum (X5 (λX8 : set → set → set ∅ ) ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj0 ∅ (X5 (λX8 : set → set → set X6 X7 ∅ ) (Inj1 (Inj1 ∅ (setsum (Inj1 ∅ (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∈ Inj1 (setsum (X6 (setsum ∅ ∅ (Inj0 ∅ ∅ ) → (∀X4 : set → ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 X5 ∈ Inj1 (Inj1 (setsum (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ → X2 (λX8 : set → set X7 ) ∅ (λX8 : set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (X8 ∅ ) (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (Inj0 (setsum X6 (setsum ∅ ∅ (setsum X5 (Inj0 (Inj1 ∅ X2 (λX8 : set → set Inj0 (setsum (X8 ∅ X7 ) (Inj0 (Inj0 (setsum (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set → set Inj1 X5 ) (λX8 : set ⇒ X7 ) (λX8 : set ⇒ X8 ) X5 ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set → set ∀X6 : (set → set → set ∀X7 : (set → set → set → (set → set → (set → set → set X2 (λX8 : set → set Inj1 ∅ ) ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X8 ) (X5 (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X6 (λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ X7 (λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X1 (λX8 : set ⇒ setsum ∅ (setsum (Inj0 (Inj0 ∅ (Inj1 (X6 (λX9 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum (Inj0 (Inj1 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ setsum ∅ (Inj0 (Inj1 ∅ → X1 (λX8 : set ⇒ Inj0 X8 ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj1 (setsum (Inj1 X5 (Inj0 ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) X0 (λX8 : set → (set → set → set → set → set X5 ) (λX8 : ((set → set → set → set X6 ) ∅ ) → (∀X4 : (set → set → set ∀X5 : set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 (Inj1 (setsum X6 (setsum ∅ ∅ ) (λX8 : set → set Inj0 X7 ) (setsum (setsum ∅ (Inj1 (Inj1 ∅ (setsum (X5 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ (X4 (λX8 : set ⇒ Inj1 ∅ ) X0 (λX8 : set → (set → set → set → set → set ∅ ) (λX8 : ((set → set → set → set setsum (setsum X6 (Inj1 (Inj0 ∅ (Inj1 (X8 (λX9 : set → set Inj0 ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : set → (set → set → set → set → set X7 ) (λX8 : ((set → set → set → set ∅ ) (setsum ∅ (Inj0 X7 X2 (λX8 : set → set ∅ ) (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum (setsum (Inj1 (Inj0 ∅ (Inj1 (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X6 (λX9 : set ⇒ ∅ ) ) X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcfeEh5WVDTJgiu5LC2sZUxgoXaSFAfbyT )
∀X0 : (((((set → set → set → set → set → ((set → set → set → (set → set → set → set → ((set → (set → set → set → (set → set → set → prop ∀X1 : (set → set → (set → set → (set → set → prop ∀X2 : (set → (set → set → ((set → set → set → set → set → (set → set → prop ∀X3 : ((set → set → set → set → (((set → set → set → set → set → set → set → set → set → set → prop (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) X3 (λX8 : set → set → set X7 ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj1 (Inj0 X9 (setsum ∅ X11 ) ) → (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → (set → set → set X3 (λX8 : set → set → set Inj0 (X7 (λX9 : (set → set → set λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX9 : set ⇒ X6 ) ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set → set → set X6 (setsum (X6 ∅ (Inj0 ∅ ∅ ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set X9 X7 ) (λX8 : set ⇒ X6 (setsum ∅ (X6 (Inj1 ∅ (setsum ∅ ∅ (setsum X5 ∅ ) ) → (∀X4 : ((set → set → set → set → set → set → set → set ∀X5 : set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set X8 ) (λX8 : set ⇒ Inj1 (X6 (λX9 : set → set → set ∅ ) ) (Inj1 (setsum (Inj1 (X5 ∅ ∅ ∅ (setsum (Inj1 ∅ ∅ ∈ setsum (Inj1 X7 (X5 X7 (Inj0 (X5 ∅ ∅ ∅ ∅ ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (Inj0 (Inj0 (setsum ∅ ∅ (Inj0 X7 ∈ Inj1 (Inj1 (setsum ∅ ∅ → X1 (λX8 : set ⇒ X7 ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : set → set ∀X7 : set , (Inj1 (setsum (Inj0 (X5 ∅ ∅ (λX8 : set ⇒ ∅ ) (X5 X7 (Inj1 ∅ (λX8 : set ⇒ Inj1 ∅ ) ∈ Inj0 ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ X5 ∅ (Inj0 (setsum ∅ (Inj1 ∅ (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → ((set → set → set → set → set X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X0 (λX8 : (((set → set → set → set → set → ((set → set → set → (set → set → set X5 (setsum X6 (setsum ∅ (setsum ∅ ∅ ) (λX8 : set → (set → set → set λX9 : set → set setsum (Inj1 (X7 (λX10 : set → set → set Inj1 ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) X6 ) ) → (∀X4 : set → set → set ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → ((set → set → set → (set → set → set ∅ ) (λX8 : set → (set → set → set λX9 : set → set X6 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNjkBUt69cVSpS6MfqjST7jF7mqrxi8Qov )
∀X0 : (((((set → set → set → set → set → set → set → set → set → (set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : (set → ((set → set → set → set → set → set → set → set → set → set → prop (∀X4 : (((set → set → set → set → set → set ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 ∅ ∈ X4 (λX8 : (set → set → set → set Inj1 (setsum (X7 ∅ (Inj1 ∅ ) → X2 (λX8 : (((set → set → set → set → set → set X5 (setsum (Inj1 (Inj0 ∅ (setsum (Inj1 ∅ (Inj0 ∅ (Inj0 X6 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ X6 ) (Inj1 ∅ (setsum ∅ ∅ (λX8 : set → set Inj0 (setsum (Inj1 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) X6 X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ Inj1 (X9 (λX11 : set ⇒ X10 ) ∅ (X7 ∅ ) (setsum ∅ (Inj1 ∅ (setsum (Inj0 (Inj1 (setsum ∅ ∅ (X5 (X7 ∅ (Inj1 (Inj1 ∅ (setsum (X4 (λX8 : (set → set → set → set ∅ ) (setsum ∅ ∅ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ ∅ ) ∅ (Inj1 ∅ X6 False ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : (((set → set → set → set → set → set Inj0 (Inj1 (Inj1 (X8 (λX9 : (set → set → set → set ∅ ) ) (Inj1 X6 (Inj1 (X7 (Inj0 ∅ (X5 (Inj1 ∅ ∅ (Inj1 ∅ (λX8 : set → set setsum (X7 X6 X6 (setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ X6 ) ∅ X2 (λX8 : (((set → set → set → set → set → set ∅ ) (setsum ∅ ∅ (setsum X6 ∅ (λX8 : set → set Inj1 (Inj1 ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (Inj0 ∅ ) (setsum (X7 (setsum (setsum ∅ ∅ ∅ (setsum X4 (X7 ∅ ∅ (setsum (setsum (X7 ∅ ∅ (Inj1 ∅ (Inj0 (X5 ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set setsum (Inj0 X7 X5 ) ∅ (Inj0 X5 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum X7 (X6 (λX9 : set ⇒ λX10 : set → set X7 ) ) (Inj1 (Inj1 (setsum (setsum ∅ ∅ X5 False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X1 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set (setsum X6 X4 ∈ Inj1 (setsum (Inj0 (X5 ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum (Inj0 ∅ ∅ → X1 (λX8 : set ⇒ ∅ ) ∅ X2 (λX8 : (((set → set → set → set → set → set X8 (λX9 : (set → set → set → set X9 (λX10 : set ⇒ Inj1 X10 ) (Inj1 (X9 (λX10 : set ⇒ ∅ ) ∅ ) ) ∅ (Inj0 X4 (λX8 : set → set X6 ) (λX8 : set ⇒ X8 ) (X7 (λX8 : set → set → set Inj1 (Inj0 (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ ∅ ∈ setsum (setsum ∅ (setsum (X5 ∅ ∅ (setsum ∅ ∅ (X4 (Inj0 ∅ → X0 (λX8 : (((set → set → set → set → set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set → set → set setsum (setsum X5 X6 (Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj1 (setsum (Inj0 ∅ X10 ∅ ) (setsum ∅ (Inj0 ∅ ∈ X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTNrkJQua8CqtLEV6QrCDF3EHMmoDrskEd )
∀X0 : (set → set → ((set → set → (set → set → set → set → set → (set → set → prop ∀X1 : ((set → set → (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → ((((set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set → set (setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (X5 ∅ ∅ (setsum X4 (Inj0 (X6 ∅ ∈ Inj1 (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 ∅ X8 ) (setsum (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X5 (setsum ∅ ∅ (Inj0 ∅ (setsum ∅ (X5 (setsum ∅ ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (setsum (Inj1 X6 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → (set → set → set ∀X7 : set , (Inj1 (setsum (Inj1 X5 ∅ ∈ setsum (setsum ∅ (Inj1 (setsum ∅ ∅ X5 → X1 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set Inj0 (X10 (λX11 : set ⇒ X8 ∅ ) ∅ ) (λX8 : ((set → set → set → set → set setsum (Inj0 ∅ (setsum (setsum (Inj1 ∅ (X6 (λX9 : set → set → set ∅ ) (λX9 : set ⇒ ∅ ) (setsum (Inj0 ∅ (Inj1 ∅ ) (Inj1 (Inj0 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) X2 (λX8 : set ⇒ Inj0 (X6 (λX9 : set → set → set setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj1 X6 → X2 (λX8 : set ⇒ X5 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ ∅ ) X1 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set setsum (setsum ∅ (setsum (X9 (λX11 : set → set λX12 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ (Inj0 ∅ (setsum X7 ∅ ) (λX8 : ((set → set → set → set → set X6 ) (X5 X7 (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → (set → set → set → (set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set X7 ) (λX8 : ((set → set → set → set → set X7 ) (Inj0 (X5 (Inj0 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X1 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set Inj0 ∅ ) (λX8 : ((set → set → set → set → set setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) ) X6 (λX8 : set → set λX9 : set ⇒ setsum ∅ (X8 ∅ ) X2 (λX8 : set ⇒ Inj0 (setsum (Inj1 (Inj1 ∅ (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (X7 (X8 (X8 ∅ (setsum X9 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , (Inj0 (setsum (Inj1 (Inj1 ∅ X5 ∈ Inj1 (setsum (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) (setsum ∅ ∅ (Inj0 (Inj1 ∅ → X0 (λX8 : set ⇒ Inj1 (Inj0 X7 ) (λX8 : set → set λX9 : set → set → set λX10 : set ⇒ setsum (X8 (Inj1 (Inj0 ∅ (Inj1 ∅ ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set → ((set → set → set → (set → set → set → set (Inj0 (Inj1 (setsum ∅ X4 ∈ Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X0 (λX8 : set ⇒ Inj0 (Inj1 (X6 (λX9 : (set → set → set → set X7 ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ ) ) (λX8 : set → set λX9 : set → set → set λX10 : set ⇒ X9 (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ) (λX8 : set ⇒ setsum (X7 (Inj1 (setsum ∅ ∅ (λX9 : set → set X8 ) (λX9 : set ⇒ ∅ ) (Inj1 (Inj1 ∅ (Inj0 (X5 (Inj0 ∅ (λX9 : set → set setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) X1 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set Inj0 (X8 (X8 ∅ ) (λX8 : ((set → set → set → set → set X5 (setsum (setsum (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (Inj0 (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set → set setsum (setsum (Inj1 ∅ ∅ (setsum (X6 (λX10 : (set → set → set → set ∅ ) ∅ ) (λX9 : set ⇒ ∅ ) ) (X6 (λX8 : (set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMEqtv2H31FUuSFQqkgJjv5eXmZ7yHtU8fL )
∀X0 : (set → ((set → set → set → set → set → set → (set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → (set → set → set → set → ((set → set → set → set → set → ((set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → set → ((set → set → set → set → prop ∀X3 : (set → set → (set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set X2 (λX8 : set ⇒ X7 (λX9 : (set → set → set → set X8 ) ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum (Inj0 (Inj1 (Inj0 ∅ (Inj1 (setsum ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 X9 ) X3 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → set → set ∀X7 : set , (X5 (λX8 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) ∈ setsum (setsum ∅ (setsum (setsum ∅ ∅ ∅ ∅ → X3 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum (setsum ∅ (setsum ∅ ∅ (setsum X7 X7 ) (λX8 : set ⇒ Inj0 (X5 (λX9 : set ⇒ X9 ) ) X1 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : (set → set → set → set → set λX10 : (set → set → set X10 (λX11 : set ⇒ ∅ ) ) (λX8 : set → set → set → set Inj0 (Inj1 ∅ ) (Inj0 (X5 (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : ((set → set → set → set → set (Inj0 ∅ ∈ setsum ∅ ∅ → X2 (λX8 : set ⇒ Inj0 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X9 (λX10 : set ⇒ X10 ) ∅ ) (λX8 : set → set λX9 : set ⇒ X7 (λX10 : set → set → set Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → ((set → set → set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ X6 (λX8 : set ⇒ λX9 : set → set Inj0 (setsum ∅ (X9 ∅ ) → X2 (λX8 : set ⇒ setsum (X6 (λX9 : set ⇒ λX10 : set → set ∅ ) ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X6 (λX10 : set ⇒ λX11 : set → set X11 X10 ) ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 ∅ (setsum X9 (setsum ∅ (Inj1 ∅ ) X1 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : (set → set → set → set → set λX10 : (set → set → set ∅ ) (λX8 : set → set → set → set setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (Inj1 ∅ (setsum ∅ (X6 (λX9 : set ⇒ λX10 : set → set Inj1 ∅ ) ) (X6 (λX8 : set ⇒ λX9 : set → set setsum (X6 (λX10 : set ⇒ λX11 : set → set Inj1 ∅ ) (Inj1 X8 ) ) → (∀X4 : (set → (set → set → set → set → ((set → set → set → set → (set → set → set ∀X5 : (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum (setsum (Inj1 (Inj0 ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj0 ∅ ∈ setsum ∅ (Inj0 (Inj1 ∅ → X1 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : (set → set → set → set → set λX10 : (set → set → set ∅ ) (λX8 : set → set → set → set ∅ ) (setsum (Inj0 ∅ X6 X1 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : (set → set → set → set → set λX10 : (set → set → set Inj0 ∅ ) (λX8 : set → set → set → set ∅ ) (Inj1 (X5 (λX8 : set ⇒ Inj0 ∅ ) (X5 (λX8 : set ⇒ ∅ ) (Inj1 ∅ (X5 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : (set → set → set → set → set λX10 : (set → set → set ∅ ) (λX8 : set → set → set → set X7 ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set → set → set setsum (setsum (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 (X5 (λX9 : set ⇒ X9 ) ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 (setsum (setsum X6 ∅ (setsum ∅ (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 (Inj1 (setsum ∅ (Inj0 ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → set → set → set setsum X8 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (setsum X8 (Inj0 ∅ X8 ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → (set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X9 X7 ) ∈ setsum ∅ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMR2EWxtvTuLZ3d4wEQwQgGP7KwoCqXQoim )
∀X0 : (((set → (set → set → set → set → set → set → (((set → set → set → set → set → set → set → (((set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → set → (((set → set → set → set → prop ∀X3 : (set → (set → set → set → set → set → prop (∀X4 : ((set → set → (set → set → set → (set → set → set ∀X5 : set → set → set → set → set ∀X6 : set → set ∀X7 : set → set → set X1 (λX8 : set ⇒ X8 ) (λX8 : set → set → set → set λX9 : set ⇒ X8 (Inj0 (setsum (Inj0 ∅ (X7 ∅ ∅ (X8 (X6 X9 ∅ (Inj1 (setsum ∅ ∅ (setsum X9 (X6 (X8 ∅ ∅ ∅ ) (setsum (Inj0 (X7 (Inj1 ∅ (Inj1 ∅ (setsum (setsum ∅ (Inj1 ∅ ∅ (λX8 : set → set ∅ ) (setsum ∅ (setsum (X6 (Inj0 ∅ (setsum (X5 ∅ ∅ ∅ ∅ (X6 ∅ (setsum (X6 (X6 (X7 ∅ ∅ (X7 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set → set setsum (setsum (Inj1 (Inj0 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X6 ∅ ) (X4 (λX8 : set → set λX9 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : (set → (set → set → set → set → ((set → set → set → set → set ∀X5 : set → set → set → set → set ∀X6 : set → (set → set → set → (set → set → set ∀X7 : (((set → set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set setsum (X7 (λX10 : (set → set → set λX11 : set ⇒ X10 (λX12 : set ⇒ ∅ ) ) (Inj0 (setsum (Inj1 ∅ ∅ ) (Inj1 (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 X9 ) (X7 (λX8 : (set → set → set λX9 : set ⇒ Inj1 ∅ ) X2 (λX8 : ((set → set → set → set → set → set X5 ∅ (Inj0 ∅ (Inj0 (X5 (Inj1 ∅ (setsum ∅ ∅ (Inj0 ∅ (X5 ∅ ∅ ∅ ∅ (Inj1 (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set setsum (X7 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : ((set → set → set → set → set → set Inj1 (setsum X5 (setsum (Inj1 ∅ (Inj0 ∅ ) (λX8 : (set → set → set setsum ∅ (Inj0 (setsum (Inj1 ∅ (X8 (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → ((set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : ((set → set → set → set → set → set Inj0 (setsum (Inj1 ∅ (Inj0 ∅ ) (λX8 : (set → set → set Inj1 (setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ X7 X5 ) (λX8 : set → set → set → set λX9 : set ⇒ Inj0 ∅ ) ∅ (λX8 : set → set Inj1 (X6 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX9 : set → set ∅ ) ) (Inj1 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set Inj0 ∅ ) X4 ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ ∅ ) ∅ (λX8 : set → set X7 ) ∅ (setsum (X4 (λX8 : (set → set → set ∅ ) X5 (Inj0 (Inj0 (Inj1 (X4 (λX8 : (set → set → set ∅ ) ∈ Inj0 (setsum (setsum (X4 (λX8 : (set → set → set ∅ ) ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 ∅ ∈ setsum ∅ (setsum (X5 (Inj1 ∅ (setsum (Inj0 ∅ (Inj1 ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ X8 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum ∅ (setsum ∅ ∅ X6 ∅ ) (setsum ∅ (Inj0 X7 (λX8 : set → set Inj0 (setsum X7 X7 ) ∅ (setsum (Inj1 (Inj0 X6 (setsum (setsum ∅ (X5 ∅ (Inj0 X4 X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : (set → set → set → set → set → set Inj0 (Inj1 (setsum (Inj1 ∅ ∅ ) (λX8 : (set → set → set → set X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : (set → set → set → set → set → set Inj1 (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set → set Inj0 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHezcCXbcuzEmH4wqxRkGsfqBcVSxPiQru )
∀X0 : (((set → set → set → set → set → set → set → set → set → (set → set → prop ∀X1 : (((set → (set → set → set → set → (set → set → set → set → set → prop ∀X2 : (((set → set → set → (set → set → set → (set → set → set → set → (((set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X3 : (set → set → (set → (set → set → set → set → prop (∀X4 : (set → set → (set → set → set → set ∀X5 : (set → set → set → ((set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , (setsum ∅ (setsum ∅ (setsum ∅ (Inj0 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → (set → set → set (X5 ∈ setsum (setsum (setsum (Inj1 ∅ (Inj0 ∅ (Inj0 ∅ (X7 X4 (λX8 : set → set Inj0 ∅ ) (λX8 : set ⇒ setsum (X6 ∅ (Inj1 ∅ ) → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj0 (setsum (setsum (X7 ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ ∅ ) X3 (λX8 : set ⇒ X6 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj0 (setsum (X7 ∅ (λX10 : set → set setsum ∅ ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj1 (setsum (Inj1 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj1 X7 ) X2 (λX8 : (set → set → set → (set → set → set → (set → set → set → set λX9 : ((set → set → set → set → set λX10 : set → set λX11 : set → set X9 (λX12 : set → set λX13 : set ⇒ setsum (setsum ∅ (setsum ∅ ∅ ∅ ) ) (setsum ∅ ∅ X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → set → (set → set → set → (set → set → set → set λX9 : ((set → set → set → set → set λX10 : set → set λX11 : set → set Inj0 ∅ ) (Inj1 ∅ (setsum X6 (Inj0 (setsum X6 (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set → set ∀X7 : set → set → set (X6 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 X4 ∈ X4 → X1 (λX8 : (set → (set → set → set → set → (set → set → set X5 ) (setsum (Inj1 (Inj0 (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set → ((set → set → set → set ∀X5 : (((set → set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X1 (λX8 : (set → (set → set → set → set → (set → set → set Inj1 (Inj0 (Inj0 ∅ ) (Inj1 (X5 (λX8 : (set → set → set setsum (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X8 (X8 ∅ ) (Inj0 ∅ ∈ Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set (setsum (Inj1 (Inj1 (Inj0 ∅ ∅ ∈ X7 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X0 (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ ∅ ∅ (λX8 : set ⇒ Inj1 (Inj0 (Inj1 X8 ) X0 (λX8 : (set → set → set → set λX9 : set ⇒ setsum (Inj1 (setsum X6 (setsum ∅ ∅ (Inj0 (X7 (X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) ) ∅ (setsum (Inj1 (Inj0 (Inj0 ∅ (setsum (setsum (Inj1 ∅ ∅ (X5 (setsum ∅ ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ λX11 : set ⇒ setsum X11 ∅ ) ) (Inj0 (setsum (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ∅ (λX8 : set ⇒ X8 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPcDxmdY4qAGdWASW3J8FAEvHEcrbTVk9s )
∀X0 : (((set → set → (set → set → set → set → set → set → prop ∀X1 : (((set → (set → set → set → set → (set → set → set → set → set → ((set → set → set → set → set → ((((set → set → set → set → set → set → ((set → set → (set → set → set → set → prop ∀X2 : (((set → set → set → set → set → (set → set → (((set → set → set → set → (set → set → set → set → prop ∀X3 : ((set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → set (setsum (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ (X7 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ Inj1 (X9 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ∈ setsum X6 X6 → X3 (λX8 : set → set setsum (Inj1 (setsum (setsum ∅ ∅ ∅ (setsum (X8 ∅ ∅ ) (setsum (X5 (λX8 : set → set → set λX9 : set ⇒ X8 (X8 ∅ ∅ (Inj0 ∅ ) (X5 (λX8 : set → set → set λX9 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (setsum (setsum (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X7 ∅ X7 ∈ X6 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) → X3 (λX8 : set → set Inj1 X5 ) (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X1 (λX8 : (set → (set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → set → set X5 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj0 (setsum (setsum ∅ (Inj0 ∅ X7 ) ) → (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set → set X3 (λX8 : set → set ∅ ) ∅ X2 (λX8 : (set → set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ Inj1 (setsum X8 X6 ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X9 (X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ ∅ ) (X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ Inj0 ∅ ) (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X2 (λX8 : (set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ X8 ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) X0 (λX8 : (set → set → (set → set → set → set Inj0 ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : (set → set → set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : (set → (set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ setsum (setsum (Inj1 (Inj0 ∅ (Inj0 ∅ (setsum X9 X9 ) (λX8 : ((set → set → set → set → set setsum (setsum ∅ (setsum ∅ (Inj0 ∅ (setsum (setsum X7 (X5 (λX9 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → (set → set → set → set ∀X7 : set → set X1 (λX8 : (set → (set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ setsum (setsum (setsum (Inj1 ∅ (Inj1 ∅ ∅ ∅ ) (λX8 : ((set → set → set → set → set X6 (Inj0 (Inj1 (X7 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (Inj0 ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (Inj1 ∅ ∈ Inj0 (Inj0 (X6 X5 (λX8 : set ⇒ X6 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (Inj1 ∅ ) → (∀X4 : ((set → set → (set → set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → (set → set → set → set setsum (X8 (λX9 : set ⇒ X8 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ X10 ) ) (λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ ) (setsum X6 (X5 ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : (set → set → (set → set → set → set X6 (λX9 : set ⇒ ∅ ) ) (setsum ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdEzW1HqPRXCeqw3mpEE4GkF7C61i1vtf1 )
∀X0 : (set → set → ((set → set → set → set → prop ∀X1 : (set → (set → set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ X5 → X1 (λX8 : set ⇒ λX9 : set → set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X6 ) ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : (((set → set → set → set → ((set → set → set → set ∀X6 : set → set → (set → set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj0 (Inj0 (Inj1 (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ ∅ ) X1 (λX8 : set ⇒ λX9 : set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X7 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X6 ∈ X7 → X2 (λX8 : set ⇒ ∅ ) X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set X2 (λX8 : set ⇒ Inj0 ∅ ) (setsum (setsum (setsum X5 (X7 (λX8 : set ⇒ ∅ ) ∅ (setsum X5 (setsum ∅ (Inj0 ∅ X2 (λX8 : set ⇒ X8 ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set → set → set X9 (Inj0 (setsum (Inj0 ∅ ∅ (setsum (X9 (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ ∅ (setsum (X9 ∅ ∅ ∅ (Inj0 ∅ X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum (Inj1 (Inj0 ∅ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set → set → set setsum X8 (X9 ∅ (Inj1 (X9 ∅ ∅ ∅ (Inj0 X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) (X5 ∈ Inj1 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 ∅ ∈ X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ (Inj0 (Inj1 ∅ ) (setsum (X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X9 ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) X4 (setsum (Inj0 ∅ (setsum ∅ ∅ (λX8 : set ⇒ setsum (setsum ∅ (Inj0 ∅ ∅ ) (setsum (Inj1 (Inj0 ∅ ∅ → X0 (λX8 : set ⇒ setsum (Inj0 (Inj0 (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) X2 (λX8 : set ⇒ ∅ ) (Inj1 X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVfkRiySMqj91x3pzYT1J1qpRHaqWM8iGf )
∀X0 : (((set → (set → set → set → set → set → set → (set → set → set → prop ∀X1 : ((set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : (set → set → (set → (set → set → set → prop ∀X3 : (set → set → (((set → set → set → set → set → ((set → set → set → set → (set → set → set → set → ((set → set → set → ((set → set → set → set → prop (∀X4 : (((set → set → set → set → set → (set → set → set → set ∀X5 : set → set → set → set ∀X6 : (set → set → (set → set → (set → set → set ∀X7 : set , (Inj1 X7 ∈ X5 (Inj1 (Inj1 (setsum ∅ ∅ ∅ (Inj0 (Inj0 (setsum ∅ ∅ → X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ Inj0 (X5 (Inj0 ∅ (setsum ∅ (X5 ∅ ∅ ∅ (Inj1 (setsum ∅ ∅ ) ∅ X3 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : (set → set → set → set → set λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set → set setsum (X8 (X8 ∅ (X8 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set → set X3 (λX8 : set ⇒ X5 ) (λX8 : (set → set → set → set → set λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set → set setsum (Inj0 (X6 (λX9 : (set → set → set X7 ∅ ∅ ) (setsum ∅ ∅ ∅ (setsum X5 (Inj1 ∅ ) (setsum (X7 (Inj1 (Inj1 ∅ (Inj1 X4 (X7 (Inj0 X4 (setsum ∅ (Inj0 ∅ X0 (λX8 : (set → (set → set → set → set → set setsum (X7 (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 (X6 (λX9 : (set → set → set ∅ ) ∅ ∅ (setsum X5 (Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X2 (λX8 : set ⇒ Inj1 (Inj1 X6 ) (λX8 : set ⇒ λX9 : set → set setsum (setsum (setsum (setsum ∅ ∅ (X9 ∅ ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X2 (λX8 : set ⇒ setsum (setsum (Inj0 (setsum ∅ ∅ (Inj1 X5 ∅ ) (λX8 : set ⇒ λX9 : set → set setsum (Inj0 (Inj0 (setsum ∅ ∅ X8 ) X0 (λX8 : (set → (set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (X10 ∅ ) ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → ((set → set → set → set → set X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ X7 (λX9 : set → set λX10 : set → set λX11 : set ⇒ X11 ) (λX9 : set → set λX10 : set ⇒ X8 ) ) ∅ X1 (λX8 : set → set → set → set → set λX9 : (set → set → set → set setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → (set → set → set ∀X7 : set , X1 (λX8 : set → set → set → set → set λX9 : (set → set → set → set setsum (setsum (setsum (X8 ∅ ∅ ∅ ∅ (X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ (X8 (setsum (X6 (λX10 : set → set λX11 : set → set ∅ ) ∅ (λX10 : set ⇒ ∅ ) (X8 ∅ ∅ ∅ ∅ ∅ ∅ (setsum (Inj0 ∅ (Inj0 ∅ ) (X6 (λX8 : set → set λX9 : set → set setsum (setsum ∅ (Inj0 ∅ (Inj0 (Inj1 ∅ ) ∅ (λX8 : set ⇒ X7 ) False ) → (∀X4 : set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : (set → set → set → set → set λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (X8 (λX12 : set ⇒ Inj1 ∅ ) (setsum (Inj0 ∅ ∅ (X8 (λX12 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set → set ∅ ) (λX8 : set → set setsum ∅ (Inj1 ∅ ) (Inj0 (setsum ∅ (setsum (setsum ∅ ∅ (X6 ∅ X0 (λX8 : (set → (set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (Inj0 (Inj1 ∅ ) ) (λX8 : set ⇒ ∅ ) (setsum (X5 (Inj1 (setsum ∅ ∅ (X5 (setsum (Inj0 ∅ (X4 ∅ ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ X8 ) X7 (Inj0 (Inj0 (Inj0 ∅ ∈ Inj0 (Inj0 (Inj0 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdnve4crkX9SxvFY8WENd17KzqUHuUabPf )
∀X0 : (set → (set → set → set → (set → set → (set → set → set → set → prop ∀X1 : (set → (set → set → set → ((set → (set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → set → (set → set → (set → set → set → (set → set → set → prop ∀X3 : (set → set → set → set → set → set → ((((set → set → set → (set → set → set → set → set → prop (∀X4 : (set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ X4 (λX8 : set ⇒ setsum (Inj1 (Inj1 ∅ (X5 (λX9 : set ⇒ Inj0 ∅ ) ) → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX8 : ((set → set → set → (set → set → set → set Inj0 (setsum (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : ((set → set → set → (set → set → set → set Inj1 (setsum X5 (Inj0 ∅ ) (setsum ∅ (setsum (Inj1 ∅ (Inj0 (Inj0 ∅ ∈ Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum ∅ ∅ ∈ Inj0 (setsum (Inj1 (setsum ∅ ∅ (X7 (X7 ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X2 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : (set → set → (set → set → set (setsum (Inj0 (Inj1 (Inj1 ∅ (X7 (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (Inj0 ∅ ) ∈ Inj1 (X4 ∅ (setsum ∅ (X4 ∅ ∅ ∅ ∅ ∅ (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set → set Inj0 X8 ) (λX8 : set → (set → set → set X8 (Inj0 (X7 (λX9 : set ⇒ X6 (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ ) (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set → set X7 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → ((set → set → set → set → (set → set → set → set (Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ ∈ setsum (setsum X4 (Inj0 ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → set Inj1 (setsum (setsum (setsum ∅ ∅ X6 (X9 (Inj0 ∅ ) (λX8 : set → (set → set → set ∅ ) (λX8 : set → set → set setsum (setsum ∅ (Inj0 ∅ (setsum (X7 (λX9 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 X10 ) (λX8 : ((set → set → set → (set → set → set → set Inj0 (setsum (Inj0 (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → set X7 (λX10 : set → set λX11 : set ⇒ setsum (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) ) (λX8 : set ⇒ setsum (setsum ∅ (setsum (Inj0 ∅ ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (Inj0 (X6 ∅ ∅ ) X4 X0 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ Inj0 (setsum ∅ (Inj1 X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum X5 (X7 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) ∅ (setsum X5 X5 ∈ setsum (setsum (X7 (Inj0 ∅ X5 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYiRgkqgm3x3LixaaoWR5MczDy234Ej6XM )
∀X0 : (set → (set → (set → set → set → set → ((set → set → set → set → set → set → prop ∀X1 : (((set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → set → (set → set → set → (((set → set → set → set → set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum X8 ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum X10 (X9 (setsum (Inj1 ∅ (X9 ∅ ∅ (setsum ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X9 ) (λX8 : (set → set → set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X9 X11 (X8 (λX12 : set ⇒ Inj0 ∅ ) ∅ ∅ ) X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : set , (Inj0 (setsum ∅ (setsum X7 (Inj1 ∅ ∈ X7 → X2 (λX8 : set ⇒ setsum (setsum X8 (Inj1 (Inj1 ∅ (Inj0 (X6 (λX9 : (set → set → set Inj1 ∅ ) ) X4 ) → (∀X4 : set → ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set → set → set ∀X7 : (((set → set → set → set → set → (set → set → set → set X2 (λX8 : set ⇒ X7 (λX9 : (set → set → set → set setsum (Inj1 (Inj0 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ ∅ ) (setsum X5 (setsum (X7 (λX8 : (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (Inj0 ∅ False ) → (∀X4 : set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 X6 ∈ Inj0 (X4 (setsum (setsum ∅ ∅ (X4 ∅ ∅ (Inj0 (X4 ∅ ∅ → X1 (λX8 : (set → set → set → set → set → (set → set → set X7 (setsum X6 (setsum (Inj1 ∅ (X7 ∅ ) ∅ X1 (λX8 : (set → set → set → set → set → (set → set → set X7 X6 ) (X4 ∅ (Inj1 (setsum ∅ (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → (set → set → set (setsum (X7 (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (Inj1 (setsum ∅ ∅ ∈ Inj1 ∅ → X1 (λX8 : (set → set → set → set → set → (set → set → set X8 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 (X8 (λX12 : set ⇒ λX13 : set ⇒ λX14 : set ⇒ X12 ) (setsum ∅ ∅ (λX12 : set ⇒ X9 ) ) (Inj1 (X5 (λX9 : set ⇒ λX10 : set → set setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) (setsum (setsum (setsum ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ ∅ X6 X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (X5 (λX8 : set ⇒ λX9 : set → set setsum ∅ (X7 ∅ (λX10 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ X7 ∅ (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ) ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set → set ∀X7 : set → set (Inj1 (Inj1 (Inj0 (Inj1 ∅ ∈ Inj0 (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set X9 (Inj1 (Inj0 X8 (λX11 : set ⇒ Inj1 (setsum (Inj0 ∅ ∅ ) ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZxMcPDqHfemea5pkWsyBegR5aATiZcevr )
∀X0 : (set → (set → set → set → set → set → prop ∀X1 : (((set → (set → set → set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → (set → set → (set → set → set → ((((set → set → set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : (set → (set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : (set → set → set → set (setsum ∅ (setsum ∅ X4 ∈ Inj1 (Inj0 X5 → X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set Inj0 (setsum (Inj0 (setsum ∅ ∅ (setsum (X9 ∅ (X9 ∅ ) (setsum (setsum (Inj0 ∅ X4 (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (setsum (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set setsum X7 (Inj0 (setsum (Inj1 ∅ X8 ) ∅ (X5 ∈ Inj1 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set Inj0 (Inj1 (X11 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set → set ∀X6 : set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set X10 ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set X9 (λX11 : set ⇒ Inj1 ∅ ) ) X2 (λX8 : set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set setsum (Inj0 ∅ (setsum (Inj0 (setsum ∅ ∅ (X10 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (setsum ∅ (setsum (Inj1 (Inj1 ∅ X6 X1 (λX8 : (set → (set → set → set → set → set Inj1 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set → set X1 (λX8 : (set → (set → set → set → set → set setsum (setsum X6 (Inj1 (Inj1 ∅ X5 ) (λX8 : set ⇒ ∅ ) X1 (λX8 : (set → (set → set → set → set → set Inj1 (setsum ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set X0 (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 X5 ∅ X0 (λX8 : set ⇒ λX9 : set → set ∅ ) (X4 (λX8 : set ⇒ X6 X8 ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set ∀X7 : (((set → set → set → set → set → (set → set → set → set X0 (λX8 : set ⇒ λX9 : set → set X9 X8 ) (Inj0 (setsum ∅ X4 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFNLa9ZPKG8pwU9XN51z11WYBtzLMtv1ae )
∀X0 : ((set → set → (set → set → set → set → (set → set → set → set → set → set → (set → set → (set → set → set → set → set → (set → set → (set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → prop ∀X3 : (set → set → set → set → (((set → set → set → (set → set → set → set → (((set → set → set → (set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set ∀X7 : (set → set → set → ((set → set → set → set (setsum X5 X5 ∈ X5 → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : (set → set → set → (set → set → set setsum (setsum (Inj0 (Inj1 ∅ (Inj1 (Inj1 ∅ (Inj1 (setsum (Inj0 ∅ ∅ ) (λX8 : (set → set → set λX9 : set → set Inj0 (Inj1 (setsum (Inj0 ∅ (X8 (λX10 : set ⇒ ∅ ) ) (λX8 : set → set setsum ∅ (X7 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set setsum (X6 (λX10 : set → set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ ) ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : (set → set → set → (set → set → set X7 (λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) (λX11 : set ⇒ ∅ ) ) (λX9 : set → set Inj0 ∅ ) ) (λX8 : (set → set → set λX9 : set → set setsum (Inj1 ∅ (X9 ∅ ) (λX8 : set → set setsum (X7 (λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX9 : set → set X8 (Inj1 ∅ ) (X7 (λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX9 : set → set Inj0 (setsum ∅ ∅ ) ) ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , (Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ∈ setsum X7 (setsum ∅ (setsum (setsum ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) (λX8 : (set → set → set → (set → set → set X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : (set → set → set λX9 : set → set ∅ ) (λX8 : set → set ∅ ) X1 (λX8 : set → set λX9 : ((set → set → set → set → set → set → set Inj1 (Inj1 (Inj1 (X6 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) X7 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , (setsum ∅ (X5 (setsum (Inj1 ∅ (Inj0 ∅ ∈ setsum (X6 (Inj0 (setsum ∅ ∅ X4 → X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 (Inj0 ∅ (Inj1 (Inj1 X11 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) (X6 (X6 X7 (λX8 : set ⇒ X7 ) (λX8 : set ⇒ Inj0 (X6 (Inj1 ∅ ) X2 (λX8 : set ⇒ Inj0 (Inj1 (setsum (setsum ∅ ∅ (X5 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum ∅ (setsum X10 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ X9 X9 ) False ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set (Inj1 (setsum (Inj1 (setsum ∅ ∅ (setsum (X4 (λX8 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set ∅ ) ∈ setsum (Inj0 ∅ ∅ → X1 (λX8 : set → set λX9 : ((set → set → set → set → set → set → set Inj0 (Inj1 (X8 ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : ((set → set → set → set → set → set → set ∅ ) (X6 (Inj1 (setsum (setsum ∅ ∅ X5 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum (Inj0 ∅ (X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (X10 ∅ (Inj1 (Inj1 (Inj1 ∅ ) X6 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ Inj0 (Inj1 (setsum X7 ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 ∅ → X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum (Inj1 (setsum ∅ ∅ X12 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set ⇒ setsum X8 (X6 (setsum ∅ X8 ) (λX8 : set ⇒ setsum ∅ (Inj0 ∅ ) X2 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSHdDeZ1mUqDfAVbvCFifBMZM8w9RPd5hH )
∀X0 : (set → set → (((set → set → (set → set → set → set → ((set → set → set → set → set → prop ∀X1 : ((((set → set → (set → set → set → set → set → (set → set → set → set → set → set → (set → set → (set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → (set → set → prop ∀X3 : (set → set → set → ((((set → set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (λX8 : ((set → set → set → set → set X6 ) (λX8 : set ⇒ setsum ∅ X5 ) X4 X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set X7 ) (λX8 : set ⇒ setsum (Inj1 (setsum ∅ (setsum ∅ ∅ ∅ ) (setsum X6 X4 ) → (∀X4 : (set → set → set → set ∀X5 : (set → (set → set → set → set → (set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : ((set → set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ ∅ ) ) (λX8 : set ⇒ Inj1 ∅ ) (Inj0 (Inj1 (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set (X7 (λX8 : set ⇒ ∅ ) ∈ Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ X9 (setsum (setsum X8 (Inj1 ∅ ∅ (λX11 : set ⇒ X8 ) ) (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → (set → set → set → (set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ Inj0 ∅ ) False ) → (∀X4 : set → (set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 X9 ) (λX8 : ((set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ ∅ ) ∅ X1 (λX8 : ((set → set → (set → set → set → set → set → (set → set → set → set X6 ) ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (setsum (Inj1 (X5 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X1 (λX8 : ((set → set → (set → set → set → set → set → (set → set → set → set setsum (Inj0 ∅ (setsum X5 (Inj1 (Inj1 ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ (Inj1 (Inj1 ∅ ∅ (λX8 : set ⇒ X5 ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ X6 ) False ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → (set → set → set Inj1 (X8 (λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX9 : set ⇒ X6 ) ) (λX8 : set → set λX9 : set ⇒ X7 ) (setsum ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → ((set → set → set → set X0 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 (Inj1 X6 (Inj0 (setsum ∅ (X8 ∅ ) ∅ (Inj0 (X5 (λX8 : (set → set → set λX9 : set ⇒ X6 ) ∈ Inj1 (Inj0 (Inj0 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMShYdHhkG6JJdJxfF1vTqHPHjcgDy7VHUS )
∀X0 : ((set → set → set → set → prop ∀X1 : ((set → ((set → set → set → set → (set → set → set → set → set → prop ∀X2 : (set → set → set → (set → (set → set → set → set → set → ((set → set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set (Inj1 (Inj0 ∅ ∈ Inj0 X6 → X0 (λX8 : set → set Inj1 (X7 (λX9 : set → set Inj0 (X8 ∅ ) ) ∅ X3 (λX8 : (((set → set → set → set → set → set → (set → set → set → set Inj0 (setsum ∅ ∅ ) (setsum X6 X6 (Inj0 (Inj0 (X7 (λX8 : set → set setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → set → (set → set → set → set X8 (λX9 : (set → set → set → set λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) ) (Inj0 ∅ (Inj0 (Inj0 (X5 (Inj0 ∅ X6 False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → set → (set → set → set → set ∅ ) (setsum (Inj1 (Inj1 (setsum ∅ ∅ (X6 ∅ ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set → set → set X9 (setsum (Inj1 ∅ (X6 (setsum ∅ ∅ X7 ) (setsum ∅ X7 (λX8 : set → set ∅ ) X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj1 ∅ ) X4 (λX8 : set → set setsum ∅ (Inj1 ∅ ) (setsum (X5 (setsum (setsum ∅ ∅ ∅ ∅ False ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set , (Inj1 (Inj0 ∅ ∈ setsum (Inj1 (setsum X7 X5 (X6 (Inj1 (X4 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ X8 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set → set X6 X7 (setsum (Inj0 (Inj0 ∅ X7 X7 ) ∅ (λX8 : set → set ∅ ) X7 X1 (λX8 : set → ((set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 X5 ) → (∀X4 : set → (set → set → set → set ∀X5 : (set → set → ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → ((set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (Inj0 (Inj0 (Inj1 (Inj1 ∅ X3 (λX8 : (((set → set → set → set → set → set → (set → set → set → set ∅ ) ∅ (Inj1 (setsum X6 (setsum ∅ (X5 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set X8 (setsum (Inj1 (X8 ∅ ∅ ) X7 ) → (∀X4 : set → ((set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set X7 ) (Inj1 (X5 ∅ X0 (λX8 : set → set X6 ) (Inj1 (setsum (Inj1 (Inj1 ∅ (X5 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGgpPojQXNQZSa6wgxHgxqMAgcaQnADSmA )
∀X0 : (set → set → ((set → set → set → (set → set → set → ((set → set → set → set → set → ((set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → ((set → set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → set → set → (set → set → ((set → set → set → (set → set → set → set → prop ∀X3 : ((set → set → set → (set → set → prop (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 (X7 (setsum (setsum ∅ ∅ (X7 ∅ ∈ Inj0 (setsum (setsum (Inj1 ∅ X5 (setsum ∅ ∅ → X3 (λX8 : set → set setsum (setsum (Inj1 (Inj0 ∅ (Inj1 (Inj0 ∅ (X7 (setsum X5 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X3 (λX8 : set → set Inj0 (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ X6 ) False ) → (∀X4 : (((set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set → set ∅ ) (setsum ∅ (X4 (λX8 : (set → set → set λX9 : set → set Inj0 (X6 (λX10 : set → set λX11 : set ⇒ ∅ ) ) (Inj1 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 X7 → X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ X9 ) (λX8 : set ⇒ X5 ) (λX8 : set → set → set λX9 : set → set Inj1 ∅ ) X4 X1 (λX8 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set Inj1 (setsum ∅ X7 ) ∅ ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set ∅ ) (Inj0 (Inj0 (X4 ∅ X1 (λX8 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set setsum (Inj1 (Inj1 (X6 ∅ (setsum ∅ (setsum ∅ (X6 ∅ ) (setsum (setsum X7 (X5 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) (setsum ∅ ∅ (Inj1 ∅ ∅ ) → (∀X4 : (((set → set → set → set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → (set → set → set ∀X7 : set → (set → set → (set → set → set X1 (λX8 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set X7 (Inj1 (Inj1 (setsum ∅ ∅ (λX9 : set ⇒ Inj1 (X7 (Inj1 ∅ (λX10 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ ∅ ) ) (λX9 : set ⇒ ∅ ) ) (setsum (X7 (X7 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ X8 ) (Inj1 (Inj1 (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → (set → set → set ∀X7 : (set → set → set → set X1 (λX8 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set Inj0 (setsum ∅ ∅ ) (Inj0 ∅ X0 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set X8 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ ∅ ) (λX8 : set → set ∅ ) (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → (set → set → set X0 (λX8 : set ⇒ X6 (Inj0 (X7 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set → set Inj0 (setsum ∅ ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set Inj0 (X10 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (X8 (Inj0 ∅ (X8 (setsum ∅ ∅ ) (λX8 : set → set Inj1 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X8 (setsum ∅ ∅ ) (Inj0 (Inj1 (Inj0 (setsum ∅ ∅ X5 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMc3Dt14sGpZWS7VrwqJFtP4atrNo6ytvNW )
∀X0 : (set → ((set → set → set → set → (set → set → set → (set → set → set → ((((set → set → set → set → set → set → set → (set → set → set → set → set → prop ∀X1 : ((set → set → set → ((set → set → set → (set → set → set → (set → set → set → set → set → set → prop ∀X2 : ((set → set → set → ((set → set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → (set → (set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : (set → (set → set → set → set → set λX9 : set → (set → set → set → set X6 ) (λX8 : set ⇒ X6 ) ) → (∀X4 : ((set → set → set → (set → set → set → (set → set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : ((set → set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set λX9 : set → (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X5 (setsum X7 (setsum X7 X7 ∈ X7 → X2 (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) X2 (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (setsum X9 X10 (setsum X10 (X8 ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : (set → set → (set → set → set → (set → set → set ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 (X4 ∅ (setsum (X4 ∅ ∅ ∅ X7 ∅ → X2 (λX8 : set → set Inj1 (setsum (Inj1 (Inj1 ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X8 ∅ ) X3 (λX8 : (set → (set → set → set → set → set λX9 : set → (set → set → set → set Inj0 (X8 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) ) (λX8 : set ⇒ Inj1 (X6 (λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum (X9 (λX12 : set ⇒ ∅ ) ∅ ) ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set → set → set → set ∀X7 : set , (Inj1 (Inj0 (X6 ∅ (X5 ∅ (Inj1 ∅ ∈ Inj0 (Inj0 ∅ → X1 (λX8 : set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set ∅ ) (setsum ∅ X7 (Inj0 (setsum (X5 (X5 ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → (set → set → set → set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : set → set → set → set X1 (λX8 : set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set setsum ∅ (setsum (X8 ∅ (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ (X7 ∅ (setsum (X4 ∅ (Inj0 ∅ (Inj1 ∅ (X7 (setsum (X6 (λX8 : set → set ∅ ) ∅ (setsum ∅ ∅ (X4 (X4 ∅ (X5 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 ∅ (X6 (λX10 : set → set ∅ ) ∅ ∅ ) (Inj0 (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ X1 (λX8 : set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set X10 (Inj1 (X7 (setsum ∅ ∅ ∅ (X9 (λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) (X9 (λX11 : set ⇒ λX12 : set ⇒ Inj1 (X9 (λX13 : set ⇒ λX14 : set ⇒ ∅ ) (λX13 : set ⇒ ∅ ) ) (λX11 : set ⇒ Inj1 X11 ) ) (Inj0 ∅ (X5 (X4 (setsum (X4 ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (Inj0 (Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set → set λX11 : set → set X10 (setsum (Inj1 (Inj0 ∅ (X10 (Inj1 ∅ (Inj0 ∅ (Inj0 (Inj1 ∅ ) (λX8 : ((set → set → set → set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set → set λX11 : set → set Inj1 (X10 (setsum (X11 ∅ (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set → set → set Inj0 (setsum (Inj0 (Inj1 ∅ (setsum (X5 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) X6 ∅ (Inj0 (Inj1 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → (set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set → set λX11 : set → set setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set → set X6 (setsum (Inj1 (Inj1 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ setsum X5 (X6 (X7 (setsum ∅ ∅ (λX9 : set ⇒ X8 ) ) (Inj0 ∅ ∅ ∅ X2 (λX8 : set → set X5 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 X10 (Inj0 (setsum (X8 ∅ X10 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGRFQ47KK5A1u9crp7HaGrF69Rx1Ty4Czd )
∀X0 : (set → (set → set → set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → ((((set → set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 (setsum (Inj0 (Inj1 ∅ X6 ∈ Inj0 (setsum ∅ (X5 (Inj0 ∅ → X3 (λX8 : (set → (set → set → set → set → set setsum ∅ ∅ ) (Inj1 (Inj1 ∅ X3 (λX8 : (set → (set → set → set → set → set setsum (setsum X7 (X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (Inj0 (X5 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set X3 (λX8 : (set → (set → set → set → set → set Inj1 ∅ ) (setsum (Inj1 (setsum X5 (setsum ∅ ∅ ∅ (X5 ∈ X6 X4 ) → (∀X4 : set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj0 ∅ → X2 (λX8 : ((set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → set → set setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (X6 ∈ Inj0 ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X1 (λX8 : ((set → set → set → set Inj0 (setsum X7 X7 ) (λX8 : ((set → set → set → set X7 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → (set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : (set → (set → set → set → set → set X1 (λX8 : ((set → set → set → set Inj1 (X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set setsum (X5 (λX9 : (set → set → set → set Inj0 (setsum ∅ ∅ ) (setsum (Inj1 ∅ ∅ (λX9 : set ⇒ Inj1 X9 ) (X8 (λX9 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) X2 (λX8 : ((set → set → set → set setsum (setsum (X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 X10 ) ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X8 ) (X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (Inj0 (setsum (Inj0 ∅ X4 ∈ Inj1 ∅ → X0 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ X1 (λX8 : ((set → set → set → set X6 (Inj0 X7 (X8 (λX9 : set → set Inj0 (X8 (λX10 : set → set ∅ ) ) ) (λX8 : ((set → set → set → set X7 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXs7wAYhkAvFLeCyeJoAgZb3mP9vFseyq1 )
∀X0 : (((((set → set → set → set → set → (set → set → set → set → set → set → (set → set → set → set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : ((set → set → set → set → set → prop ∀X3 : (set → set → set → (set → set → prop (∀X4 : set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (X6 ∈ Inj1 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ X6 → X3 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X7 ∅ ∈ X5 → X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (Inj1 X6 ) X2 (λX8 : set → set Inj1 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ X6 ) (setsum X6 (setsum (Inj1 (Inj1 ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj1 ∅ ∈ Inj0 (X5 (setsum X4 X4 → X0 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj0 (setsum (Inj0 (Inj0 ∅ (setsum ∅ (Inj1 ∅ ) (setsum (Inj1 ∅ (X7 (λX8 : (set → set → set → set setsum ∅ (X8 (λX9 : set ⇒ ∅ ) ∅ ) X2 (λX8 : set → set Inj0 (X8 (X5 (X5 ∅ ) (Inj1 (X7 (λX8 : (set → set → set → set X6 ) ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set X8 X6 ) (setsum X4 ∅ ∅ X1 (λX8 : set → set X7 ) X7 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → (set → set → set → set ∀X7 : set , (Inj1 X4 ∈ setsum ∅ (Inj1 X7 → X1 (λX8 : set → set Inj0 (Inj1 ∅ ) (Inj1 (X5 (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X1 (λX8 : set → set X5 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj0 (Inj0 ∅ ) ) ∅ (X7 (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) ∈ Inj0 (setsum X4 X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set X8 ∅ ) ∅ X0 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X9 ) ∅ ) → (∀X4 : (set → set → set → set → set ∀X5 : set → (set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → (set → set → set X0 (λX8 : (((set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 ∅ (Inj1 (X4 (λX8 : set ⇒ ∅ ) ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWvTn8wD3MVEobZgtQiY74aUcqgX76Nfxf )
∀X0 : (set → (((set → set → set → set → set → set → set → (set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → (set → set → set → set → set → prop ∀X3 : ((set → set → set → set → ((((set → set → set → set → set → set → set → set → prop (∀X4 : (set → set → set → set → ((set → set → set → set → set ∀X5 : ((set → set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ (Inj0 X6 ∈ Inj1 (Inj1 (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) → X2 (λX8 : set ⇒ setsum X8 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ setsum (setsum (setsum (Inj0 ∅ ∅ ∅ X8 ) (setsum (setsum (setsum (setsum ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj0 (setsum ∅ ∅ (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ X3 (λX8 : set → set → set Inj0 (setsum (setsum (Inj1 ∅ (Inj1 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set X7 ) (Inj1 (setsum (setsum X7 (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ (setsum (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , (setsum (setsum (setsum X7 (X4 ∅ ∅ (setsum X5 ∅ (Inj0 X7 ∈ Inj1 (setsum ∅ X7 → X3 (λX8 : set → set → set ∅ ) (λX8 : ((set → set → set → set → set Inj1 ∅ ) (setsum ∅ ∅ (Inj1 ∅ X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set → ((set → set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → set → (set → set → set ∀X6 : (set → set → set → set ∀X7 : set → set (setsum (X4 (setsum ∅ (X6 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ (X7 ∅ ∅ ∈ setsum (Inj0 (Inj0 (Inj1 ∅ (X4 (setsum (Inj1 ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (setsum ∅ ∅ → X2 (λX8 : set ⇒ Inj1 (Inj1 (setsum (X5 (λX9 : (set → set → set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) (X5 (λX9 : (set → set → set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ Inj1 (setsum (setsum (Inj1 ∅ (Inj1 ∅ X11 ) (Inj1 (X5 (λX8 : (set → set → set → set ∅ ) (X7 (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ X10 ∅ ) X4 (setsum ∅ X4 ∈ Inj1 (setsum ∅ X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (Inj1 (setsum (setsum ∅ ∅ ∅ ∅ ∅ ) → (∀X4 : (((set → set → set → (set → set → set → set → set → set → set → set ∀X5 : (set → set → set ∀X6 : (set → set → set → ((set → set → set → set ∀X7 : (set → set → ((set → set → set → set → set → set (setsum (Inj0 ∅ (setsum (Inj0 ∅ (Inj0 (Inj1 ∅ ∈ setsum (setsum ∅ (setsum (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ ∅ (X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set → set ∅ ) → X1 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set ⇒ X10 ) (λX10 : set → set setsum (setsum ∅ (setsum ∅ ∅ (Inj0 (X7 (λX11 : set ⇒ ∅ ) (λX11 : set → set ∅ ) ∅ ∅ ) ) (setsum ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (X7 (λX8 : set ⇒ setsum ∅ (X7 (λX9 : set ⇒ ∅ ) (λX9 : set → set Inj0 ∅ ) (setsum ∅ ∅ ∅ ) (λX8 : set → set setsum (X5 (λX9 : set ⇒ setsum ∅ ∅ ) (setsum (X7 (λX9 : set ⇒ ∅ ) (λX9 : set → set ∅ ) ∅ ∅ ∅ ) (X7 (λX8 : set ⇒ X7 (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set Inj1 ∅ ) X8 X8 ) (λX8 : set → set setsum (Inj0 ∅ (Inj0 ∅ ) (Inj1 (X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ ∅ (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) ∅ (Inj1 ∅ (setsum ∅ ∅ (setsum (Inj1 (Inj1 ∅ (setsum (Inj1 ∅ (X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (Inj1 (X7 (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set → set X8 ∅ ) (X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ setsum X9 (setsum (X7 (setsum ∅ ∅ (setsum ∅ X9 ) (Inj1 (setsum X5 ∅ (Inj0 (setsum (Inj0 X6 (Inj0 (X7 ∅ X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ setsum (Inj0 (setsum ∅ (setsum ∅ ∅ X8 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set ∅ ) (λX8 : set ⇒ Inj1 X6 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdd84Bgbw6RJgM3oCnh4iEJNxa122GmeFU )
∀X0 : ((set → (set → set → (set → set → set → set → set → (set → set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → (set → set → prop ∀X2 : ((set → set → (((set → set → set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → prop ∀X3 : (set → set → (set → (set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set → (set → set → set → set X2 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set X9 (λX11 : set → set λX12 : set ⇒ Inj0 (Inj0 (setsum ∅ ∅ ) ) (Inj1 (setsum (Inj0 (Inj0 ∅ (Inj0 (X5 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set ∅ ) X3 (λX8 : set ⇒ setsum ∅ X8 ) (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , (setsum (setsum (setsum ∅ X7 X7 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum (X9 ∅ (X9 ∅ ) (setsum (X6 (λX8 : (set → set → set → set Inj1 X7 ) X5 X2 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set Inj0 (setsum ∅ (Inj1 (Inj0 ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → (set → set → set → (set → set → set ∀X7 : set → (set → set → set → set X0 (λX8 : set → (set → set → (set → set → set Inj0 (X8 (Inj0 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 (X8 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ) ) (Inj0 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 X8 ) X2 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set setsum ∅ (X10 (λX11 : set ⇒ ∅ ) (X7 (Inj0 ∅ (λX11 : set ⇒ λX12 : set ⇒ X11 ) ) (setsum (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set → set Inj0 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set X8 X7 ) (setsum X6 ∅ (λX8 : set ⇒ λX9 : set → set X8 ) False ) → (∀X4 : (((set → set → set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set (setsum ∅ (setsum (Inj0 (Inj0 ∅ ∅ ∈ setsum (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ X6 → X0 (λX8 : set → (set → set → (set → set → set X6 ) X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum X8 ∅ ) X1 (λX8 : set → set λX9 : ((set → set → set → set X6 ) (λX8 : set ⇒ Inj1 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : ((set → set → set → set X6 (λX10 : (set → set → set ∅ ) ∅ ) (λX8 : set ⇒ Inj0 (Inj0 X7 ) (X4 ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X0 (λX8 : set → (set → set → (set → set → set setsum (Inj0 (X8 (Inj1 ∅ (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ (X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → (set → set → (set → set → set Inj0 ∅ ) X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZmMS7rXeity2YBK6Xqs72QPG6bxTb6pqA )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → set → set → set → set → set → set → prop ∀X2 : ((set → set → (set → set → (set → set → set → set → set → set → set → set → ((set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : (set → (set → set → set → set → set ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ (Inj1 ∅ ∈ X6 → X3 (λX8 : set ⇒ ∅ ) (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ X7 ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set λX9 : set → set λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (Inj1 X5 X6 (λX8 : set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set → set λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj0 X5 (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : set → set X5 ) (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) ∈ X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : set → set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 (setsum (X5 (λX8 : set → set → set λX9 : set → set Inj1 ∅ ) (Inj0 ∅ ∅ → X3 (λX8 : set ⇒ ∅ ) (X5 (λX8 : set → set → set λX9 : set → set X7 ) ∅ X1 (λX8 : set ⇒ ∅ ) (Inj1 (X4 ∅ X6 (Inj1 (setsum ∅ ∅ (setsum X6 (setsum (Inj0 (Inj1 ∅ (setsum ∅ ∅ ∅ (setsum (setsum (setsum ∅ X7 (Inj0 (Inj0 ∅ (setsum (X5 (λX8 : set → set → set λX9 : set → set ∅ ) ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : (((set → set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) ∅ ∅ (Inj1 (setsum (Inj1 (Inj1 ∅ (X4 (setsum ∅ ∅ (X5 (λX8 : (set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ X7 (setsum (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ (X4 (Inj0 (Inj0 ∅ ∅ False ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set → set ∀X7 : set → (set → set → set X3 (λX8 : set ⇒ Inj1 ∅ ) (setsum (setsum (Inj0 ∅ (Inj1 (setsum ∅ ∅ X4 X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ (Inj0 ∅ ) ∅ X2 (λX8 : set → set λX9 : set → set λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ X10 (Inj0 (setsum (Inj1 ∅ X11 (Inj1 (Inj0 (Inj0 ∅ ) ∅ (Inj0 (Inj1 (X6 (setsum ∅ ∅ ∅ ∅ (Inj1 ∅ (λX8 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMbuz4s29KXnofSyRHFg6w38ruQv12MxwJu )
∀X0 : (set → set → ((set → set → set → set → set → set → (set → (set → set → set → set → ((set → set → set → set → prop ∀X1 : ((((set → set → (set → set → set → set → ((set → set → set → (set → set → set → set → (set → set → set → set → set → prop ∀X2 : (set → (((set → set → set → set → ((set → set → set → set → (set → set → set → set → ((set → set → set → set → (set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set → ((set → set → set → set → set → set ∀X7 : set , (Inj0 (Inj0 X7 ∈ setsum (setsum X7 (setsum ∅ (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (Inj1 (Inj1 (X4 ∅ → X3 (λX8 : set ⇒ X6 (setsum (setsum (setsum ∅ ∅ X8 (X6 (Inj0 ∅ (λX9 : set → set λX10 : set ⇒ X7 ) (setsum ∅ ∅ (λX9 : set → set λX10 : set ⇒ setsum (Inj0 (X9 ∅ X8 ) (setsum (X6 (setsum ∅ ∅ (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (Inj0 ∅ (setsum ∅ (setsum ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : set → (set → set → set → set → set → set ∀X5 : (set → (set → set → set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : set → set → set (Inj1 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ X6 (X6 (Inj1 ∅ (X7 ∅ (setsum ∅ ∅ (setsum ∅ (X6 ∅ (X7 ∅ ∅ ) (setsum (Inj1 (setsum (X7 ∅ ∅ (X7 ∅ ∅ (Inj0 (X4 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (Inj1 ∅ X2 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ Inj0 ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 (setsum (Inj0 (Inj1 ∅ X9 ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set → set (setsum (Inj0 (X7 (setsum ∅ ∅ (X6 (X6 ∅ (Inj1 ∅ (Inj1 (Inj0 ∅ ∈ X5 X4 → X2 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ X9 (λX13 : set → set setsum (X13 (setsum ∅ ∅ (setsum (X11 ∅ (setsum ∅ ∅ ) ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ setsum ∅ (Inj1 (setsum (X9 (λX13 : set → set ∅ ) (Inj0 ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum X11 (Inj1 (X10 (setsum ∅ ∅ ) (Inj1 (setsum (X5 X4 (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) ∅ (Inj0 ∅ (setsum (setsum ∅ ∅ ∅ False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → (set → set → set → set → ((set → set → set → (set → set → set setsum (setsum (X8 (λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set X7 ) (λX9 : set ⇒ X7 ) (Inj1 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) ) → (∀X4 : (set → set → set ∀X5 : set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → (set → set → set → set → ((set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set ∅ ) (X7 (X6 ∅ (λX8 : set → set λX9 : set ⇒ setsum (Inj1 (setsum ∅ ∅ ∅ ) (setsum X4 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj0 (X9 ∅ ∅ (setsum X10 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 X9 ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set Inj1 X9 ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum (X9 (Inj0 ∅ (Inj0 ∅ (Inj1 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 (setsum ∅ (setsum ∅ ∅ (Inj1 X6 ) (X7 (X4 (λX8 : set ⇒ setsum (X7 ∅ ∅ ) ∈ setsum (setsum ∅ (Inj1 (setsum ∅ ∅ (X7 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZA8arrMrmh27FQU2VUWS9accA789gSZRP )
∀X0 : (set → set → set → (set → (set → set → set → set → prop ∀X1 : (set → (((set → set → set → (set → set → set → set → set → (set → set → set → set → (set → (set → set → set → set → (set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → (set → set → ((set → set → set → (set → set → set → prop (∀X4 : ((set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : ((set → set → set → set → ((set → set → set → set ∀X7 : set , (X6 (λX8 : set → set → set ∅ ) (λX8 : set → set ∅ ) ∈ setsum ∅ (Inj1 (setsum ∅ ∅ → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj0 (X6 (λX9 : set → set → set X7 ) (λX9 : set → set ∅ ) ) (λX8 : set → set X8 ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (setsum ∅ (Inj1 ∅ ∅ ) (X6 (λX8 : set → set → set ∅ ) (λX8 : set → set setsum (Inj0 (setsum ∅ ∅ (Inj1 ∅ ) X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ ∅ ) (X4 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj0 (X6 (λX9 : set → set → set ∅ ) (λX9 : set → set ∅ ) X8 ) (λX8 : set → set Inj0 (X8 (X5 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) ) (λX8 : set ⇒ ∅ ) (X4 (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set , (X5 (setsum X4 (X5 ∅ (Inj0 ∅ (Inj1 ∅ (setsum ∅ (Inj0 (Inj1 ∅ (Inj1 (Inj1 (Inj1 ∅ ∈ X6 ∅ (setsum ∅ (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ setsum (setsum (Inj1 ∅ X7 ∅ ) ∅ → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ X9 ) X4 (λX8 : set ⇒ X5 (setsum ∅ (setsum (Inj0 ∅ ∅ (X6 (X6 (Inj0 ∅ (Inj0 ∅ (λX9 : set ⇒ X8 ) (Inj0 ∅ (Inj1 (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ X7 ) (setsum (setsum ∅ ∅ X7 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) X7 X2 (λX8 : set ⇒ X6 (X6 (Inj1 X8 (Inj1 (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ X8 (λX9 : set ⇒ Inj1 (setsum (Inj1 ∅ (Inj1 ∅ ) (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) ∅ ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set ∀X7 : set , (Inj1 (setsum ∅ (Inj1 ∅ ∈ Inj0 (Inj1 (setsum X5 (Inj0 ∅ → X2 (λX8 : set ⇒ setsum (setsum (X6 (λX9 : (set → set → set → set Inj0 ∅ ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ ) (setsum (Inj1 (setsum (Inj0 ∅ ∅ (X4 (setsum (setsum ∅ ∅ X5 (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : ((set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → set → set ∀X7 : ((set → set → set → set → (set → set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (X4 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) False ) → (∀X4 : (set → set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ Inj1 (X6 (λX10 : (set → set → set λX11 : set ⇒ ∅ ) ) (X4 (λX8 : set ⇒ ∅ ) (setsum (X5 (X6 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (setsum (X5 ∅ (setsum ∅ ∅ (Inj0 ∅ (λX8 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : set → set setsum (Inj0 (X5 X7 (X6 (λX9 : (set → set → set λX10 : set ⇒ Inj0 (X8 ∅ ) ) (λX8 : set ⇒ setsum X7 (setsum (setsum ∅ ∅ ∅ ) (Inj1 (X6 (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj0 ∅ ∅ ) X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set → set Inj0 (Inj0 (Inj0 (Inj0 ∅ ) (X4 (λX8 : set ⇒ X8 ) (setsum (setsum (Inj1 ∅ ∅ (X5 ∅ (Inj1 (X6 (λX8 : (set → set → set λX9 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 ) (λX8 : set ⇒ Inj1 (Inj1 (setsum ∅ (X6 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ) ) → (∀X4 : ((set → set → set → set → ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ X4 (λX8 : set → set → set ∅ ) (λX8 : set → set ∅ ) ∅ (X6 ∅ (X6 ∅ (setsum ∅ ∅ (λX8 : set ⇒ X5 ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (X5 (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set → set Inj0 X8 ) X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ X7 ) X0 (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ X8 ) (X6 X7 ∅ (λX8 : set ⇒ X7 ) (Inj1 (Inj0 (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj0 (Inj0 ∅ (setsum ∅ (Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ X6 ) (Inj1 X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUZSqAFFwisdX5Mwr8PLAw6K8ZAKKfLPAc )
∀X0 : (set → (((set → set → set → set → ((set → set → set → (set → set → set → (set → ((set → set → set → set → (set → set → set → set → set → ((set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → (set → set → set → set → ((set → set → set → set → (set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → set → set → prop ∀X3 : ((set → set → set → set → set → prop (∀X4 : (set → set → set ∀X5 : (set → set → set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X1 (λX8 : ((set → set → set → set → set Inj1 X6 ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (setsum (setsum (X7 ∅ (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum (X8 X6 (setsum ∅ (X7 ∅ (λX10 : set ⇒ ∅ ) (Inj1 ∅ ) (λX8 : set ⇒ Inj0 (setsum X6 X8 ) X3 (λX8 : set → set → set Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set (setsum ∅ X6 ∈ setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ X4 → X3 (λX8 : set → set → set ∅ ) X5 X1 (λX8 : ((set → set → set → set → set setsum (setsum X5 (setsum (setsum ∅ ∅ X5 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (Inj0 X9 ) (Inj1 (Inj1 (X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → (set → set → set → set X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ) X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set λX11 : set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (X8 (setsum ∅ ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) X1 (λX8 : ((set → set → set → set → set Inj1 X7 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set → set ∅ ) ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set ∀X5 : (set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set → set X5 (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ X8 (λX10 : set → set λX11 : set ⇒ Inj1 (setsum ∅ ∅ ) ) ∅ (Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (setsum (setsum ∅ (setsum ∅ ∅ X7 (λX8 : set → set λX9 : set ⇒ Inj1 X6 ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → ((set → set → set → set → set → set ∀X7 : set , (Inj0 (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ∈ setsum (Inj1 (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ∅ X7 → X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set λX11 : set → set X10 (λX12 : set ⇒ Inj0 (Inj1 ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ X8 ) X7 (λX8 : set → set λX9 : set ⇒ setsum X7 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : (set → set → set λX11 : set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj0 ∅ (setsum (Inj1 (X9 (λX12 : set ⇒ ∅ ) ∅ (Inj1 (X9 (λX12 : set ⇒ ∅ ) ∅ ) (setsum (setsum ∅ (setsum X4 (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ X7 (X8 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (Inj1 (setsum (Inj0 ∅ ∅ ∈ Inj1 X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSzaLK9qBeLY1mwoi7SLKAEvKqenmPdLin )
∀X0 : (set → set → set → prop ∀X1 : (((set → (set → set → set → set → set → set → set → set → set → (set → set → prop ∀X2 : (((set → set → (set → set → set → set → set → (set → set → set → set → ((set → (set → set → set → set → set → prop ∀X3 : (set → (set → set → (set → set → set → set → ((set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set (setsum X6 ∅ ∈ Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set setsum ∅ (X7 (λX11 : set → set Inj0 (setsum ∅ ∅ ) ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (Inj0 (setsum ∅ ∅ ∈ Inj1 (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set Inj0 (X9 (Inj0 ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 ∅ ) X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ X7 ) X2 (λX8 : (set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set setsum (X10 ∅ ∅ ∅ ) (λX8 : set → (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set X10 (Inj1 (setsum (setsum ∅ ∅ X9 (Inj1 (X10 (X8 (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set → (set → set → set → set setsum ∅ X7 ) False ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set , (Inj1 ∅ ∈ X5 (λX8 : set ⇒ λX9 : set → set ∅ ) → X1 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ X6 (λX10 : set ⇒ ∅ ) ) (Inj0 (X5 (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) ∅ (λX8 : set ⇒ setsum (setsum (setsum (X5 (λX9 : set ⇒ λX10 : set → set ∅ ) (setsum ∅ ∅ (X6 (λX9 : set ⇒ setsum ∅ ∅ ) ∅ ) X1 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 X7 ∅ (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X1 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) ∅ ∅ (λX8 : set ⇒ setsum X8 (setsum X5 X8 ) (Inj1 (Inj1 ∅ ∈ Inj1 (setsum (Inj1 X5 ∅ ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → (set → set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set (Inj0 (Inj0 (setsum ∅ X5 ∈ X5 → X0 (λX8 : set ⇒ ∅ ) (Inj0 (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : ((set → set → set → ((set → set → set → set → set → set ∀X6 : (set → set → (set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) (setsum (setsum ∅ (X7 (setsum ∅ ∅ (X7 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNTH5V14Jd2ZTqJWfm9EnLr5biViKTjYHa )
∀X0 : (((set → set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (((set → set → set → set → set → set → (((set → set → set → set → prop ∀X3 : (set → set → ((set → set → set → (set → set → set → set → (set → set → set → set → prop (∀X4 : set → set → set → set → set ∀X5 : set → set → (set → set → set → set ∀X6 : (set → set → set → set → ((set → set → set → set → set → set ∀X7 : set → set (X7 ∅ ∈ Inj1 (X7 (Inj1 ∅ → X0 (λX8 : (set → set → set → set ∅ ) (X5 (setsum (setsum (setsum ∅ ∅ ∅ (setsum (X4 ∅ ∅ ∅ ∅ (Inj0 ∅ (setsum (setsum (Inj0 ∅ (Inj1 ∅ (X5 (setsum ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ X5 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (Inj0 (setsum ∅ ∅ ) (Inj1 (X5 (X5 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set ∅ ) (Inj1 (setsum (X4 (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (X4 ∅ ∅ ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ (Inj1 (X4 ∅ ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X8 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → set → set (X7 (λX8 : set ⇒ X8 ) (X5 (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ∅ (setsum ∅ (setsum ∅ (X5 ∅ ∅ ∈ Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set X11 ∅ ) (setsum ∅ (Inj0 (setsum (X7 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (Inj0 (Inj0 (Inj0 ∅ ∅ X0 (λX8 : (set → set → set → set Inj1 (setsum (X8 (λX9 : set ⇒ λX10 : set ⇒ X10 ) (setsum X6 (X5 ∅ ∅ ) (setsum (setsum X4 (setsum (X5 ∅ ∅ (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → set λX9 : set ⇒ setsum ∅ (Inj0 X7 ) X5 (λX8 : (set → set → set setsum (setsum (setsum (Inj1 ∅ X5 (X8 (λX9 : set ⇒ X6 ) (Inj1 ∅ ) X2 (λX8 : (set → set → set λX9 : set ⇒ Inj0 ∅ ) ∅ (λX8 : (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , (Inj0 (setsum ∅ (Inj1 (X5 ∅ ∈ Inj1 ∅ → X2 (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj0 ∅ ∅ ) ∅ (λX8 : (set → set → set setsum (setsum (Inj1 (Inj1 ∅ ∅ (setsum (Inj0 X7 (Inj1 (X6 ∅ (λX9 : set → set ∅ ) ∅ ) X0 (λX8 : (set → set → set → set setsum (X6 ∅ (λX9 : set → set ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set , (X5 ∈ Inj1 (setsum (setsum (Inj0 ∅ ∅ X5 → X1 (λX8 : set ⇒ ∅ ) X5 ) → (∀X4 : set → (set → set → set ∀X5 : set → ((set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X8 ) ∅ (Inj0 X7 ∈ setsum (X6 ∅ (λX8 : set → set X7 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X5 ∈ Inj0 (Inj1 (X6 ∅ → X0 (λX8 : (set → set → set → set ∅ ) X4 X0 (λX8 : (set → set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : (set → set → (set → set → set → (set → set → set ∀X7 : ((set → set → set → set → set → set X0 (λX8 : (set → set → set → set Inj1 (Inj0 (X6 (λX9 : set ⇒ X6 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ) (λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX9 : set ⇒ ∅ ) ) (setsum (X7 (λX8 : set → set → set Inj1 (setsum ∅ ∅ ) (setsum (X6 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set X9 ) (Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum X9 (Inj1 ∅ ) (X6 (λX8 : set ⇒ setsum (X7 (λX9 : set → set → set Inj1 ∅ ) (X5 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (setsum (Inj0 ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (X7 (λX10 : set → set → set ∅ ) ∅ (Inj0 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTgU5qwsc7k8XMsEEPL4rcKakVX8v9FKES )
∀X0 : (set → set → ((set → set → ((set → set → set → set → set → prop ∀X1 : (set → ((set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : ((set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : (set → set → set → set (Inj1 (Inj1 (Inj1 ∅ ∈ setsum (Inj0 (Inj0 ∅ X5 → X2 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : (set → set → set λX11 : set → set Inj0 (Inj1 (Inj0 ∅ ) ∅ ) (Inj0 (Inj0 (setsum (setsum ∅ ∅ (X4 (λX8 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ X3 (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (Inj0 ∅ ) ∅ (X6 (λX8 : (set → set → set λX9 : set → set X6 (λX10 : (set → set → set λX11 : set → set ∅ ) (Inj0 ∅ ) (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set → set (Inj0 (setsum (setsum (setsum ∅ ∅ (X5 ∅ ∅ ∈ Inj1 (X7 (setsum ∅ (X7 ∅ → X3 (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 (Inj1 (X6 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ X7 (setsum (setsum ∅ (Inj1 ∅ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj0 (X7 (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set → set (Inj0 ∅ ∈ X4 (setsum ∅ (X7 (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X6 ) (Inj1 (Inj0 (X4 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 X7 (Inj1 (X5 X7 ∈ setsum (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ X6 ∅ ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 X5 ∈ X7 ∅ → X0 (λX8 : set ⇒ setsum (Inj0 X5 X8 ) (λX8 : set → set λX9 : (set → set → set setsum ∅ (X9 (λX10 : set ⇒ Inj0 ∅ ) ) (Inj1 (setsum X5 (Inj0 ∅ X1 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set Inj0 ∅ ) (X7 (Inj0 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : (((set → set → set → set → set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set ∅ ) (setsum ∅ (Inj0 ∅ False ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 ∈ Inj0 (X4 ∅ X0 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ (Inj1 ∅ X6 ) (λX8 : set → set λX9 : (set → set → set Inj1 (setsum (setsum (Inj0 ∅ ∅ ∅ ) ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set (X7 (λX8 : set → set λX9 : set ⇒ X9 ) ∈ Inj1 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (X4 X6 (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) → X0 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : (set → set → set ∅ ) (X4 (setsum X6 (setsum (setsum ∅ ∅ ∅ ∅ (λX8 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set → set λX11 : set ⇒ ∅ ) ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSNoarGXQfmdmKDnHkG4FkF8WmCGXdc4oj )
∀X0 : ((((set → set → set → set → set → set → ((set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → ((set → set → (set → set → set → set → ((((set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → (set → set → set → set → set → set → prop ∀X3 : (set → set → (set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X6 ∈ Inj1 (Inj1 (Inj1 (X4 ∅ → X2 (λX8 : (((set → set → set → set → (set → set → set → set X5 ) ∅ X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → set → set ∀X7 : set , (X5 (Inj0 (Inj0 ∅ ∅ ∈ X5 ∅ (setsum ∅ (setsum (Inj0 ∅ (X6 ∅ ∅ → X3 (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) X2 (λX8 : (((set → set → set → set → (set → set → set → set setsum (setsum (Inj0 (setsum ∅ ∅ (X6 ∅ (setsum ∅ ∅ (X8 (λX9 : (set → set → set → set λX10 : set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → ((set → set → set → (set → set → set ∀X6 : set , ∀X7 ∈ X4 , X2 (λX8 : (((set → set → set → set → (set → set → set → set Inj1 X7 ) (Inj1 X7 X2 (λX8 : (((set → set → set → set → (set → set → set → set setsum X6 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X6 ) (setsum ∅ X7 ) → (∀X4 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 (Inj0 X5 → X2 (λX8 : (((set → set → set → set → (set → set → set → set ∅ ) (Inj1 X6 X1 (λX8 : set ⇒ λX9 : (set → set → (set → set → set ∅ ) (λX8 : ((set → set → set → set X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → ((set → set → set → set → set → set → set ∀X7 : set → set (setsum ∅ X5 ∈ Inj1 (setsum X4 (Inj1 X5 → X1 (λX8 : set ⇒ λX9 : (set → set → (set → set → set Inj1 (X9 (λX10 : set ⇒ setsum ∅ (Inj1 ∅ ) (λX10 : set ⇒ Inj1 (X9 (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ) ) (λX8 : ((set → set → set → set X5 ) ) → (∀X4 : set , ∀X5 : set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : (set → set → (set → set → set Inj1 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set Inj1 ∅ ) (X7 ∈ setsum X6 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : ((set → set → set → set → set ∅ ) (λX8 : set → set → set → set ∅ ) (λX8 : set → set ∅ ) (setsum (setsum X6 (Inj1 (Inj0 ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set → set X0 (λX8 : ((set → set → set → set → set setsum ∅ (setsum ∅ (Inj1 X5 ) (λX8 : set → set → set → set setsum X5 (Inj0 ∅ ) (λX8 : set → set Inj1 (Inj0 ∅ ) (Inj0 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMarco7iwCC4GdbfZpnzAgzJnaCLX8VZRZw )
∀X0 : ((set → set → set → set → set → ((set → set → set → set → set → (set → (set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → set → (((set → set → set → (set → set → set → set → (set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → set → prop ∀X3 : ((set → set → set → set → (set → ((set → set → set → set → set → prop (∀X4 : (((set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set (Inj1 ∅ ∈ X7 (λX8 : (set → set → set → set Inj0 (Inj0 (Inj1 ∅ ) (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ → X3 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (Inj1 (Inj0 X6 (Inj1 (Inj1 (X9 (λX10 : set ⇒ ∅ ) ) (setsum (X7 (λX8 : (set → set → set → set setsum (X5 ∅ (X8 (λX9 : set ⇒ ∅ ) ∅ ) (X4 (λX8 : (set → set → set ∅ ) ∅ ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 (X4 X6 (λX8 : set → set X8 (Inj1 ∅ ) (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ∈ setsum (setsum X7 X7 ∅ → X3 (λX8 : set → set λX9 : set ⇒ setsum (X8 X7 (Inj0 X7 ) (λX8 : set ⇒ λX9 : (set → set → set X9 (λX10 : set ⇒ Inj0 (X9 (λX11 : set ⇒ setsum ∅ ∅ ) ) ) (setsum (X5 X7 (Inj0 (Inj0 ∅ X3 (λX8 : set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : (set → set → set setsum X6 (setsum ∅ X6 ) (Inj1 (Inj1 (Inj0 ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set ∅ ) (setsum (setsum (Inj0 (Inj1 ∅ ∅ ∅ X2 (λX8 : ((set → set → set → set → set X8 (λX9 : set → set → set setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (setsum ∅ ∅ ) ) (setsum (setsum (setsum (setsum ∅ ∅ ∅ (setsum (Inj1 ∅ (Inj1 ∅ (X6 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set → set X2 (λX8 : ((set → set → set → set → set setsum (X6 (setsum ∅ (Inj0 ∅ (λX9 : set → set λX10 : set ⇒ X8 (λX11 : set → set → set X8 (λX12 : set → set → set ∅ ) ) ) ∅ ) (Inj0 (X4 (setsum (Inj1 ∅ (setsum ∅ ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 (setsum X9 (X8 (λX12 : set ⇒ λX13 : set ⇒ setsum ∅ ∅ ) (λX12 : set ⇒ ∅ ) ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 (X7 (Inj1 (Inj1 ∅ ∈ Inj1 (X4 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X6 (setsum X6 X5 ∈ Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ Inj1 X11 ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 (λX12 : set ⇒ λX13 : set ⇒ Inj0 ∅ ) (λX12 : set ⇒ ∅ ) ) X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : (set → set → (set → set → set ∀X7 : (set → (set → set → set → set → ((set → set → set → set → set (Inj1 (Inj0 (Inj1 (Inj0 ∅ ∈ X5 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 X8 ) → X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj0 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (Inj0 ∅ (setsum ∅ (X8 ∅ (setsum (X8 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum X11 (Inj1 (X10 X11 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPmZxqvTu2Rdy4thQUDnDLwFYd2ScTUwTC )
∀X0 : (set → set → set → prop ∀X1 : (set → ((set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (((set → set → set → set → set → set → (set → set → prop ∀X3 : ((set → set → set → set → set → set → set → ((set → set → ((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : (((set → set → set → set → set → set → set → set (Inj0 X4 ∈ setsum X4 ∅ → X2 (λX8 : (set → set → set → set → set X7 (λX9 : (set → set → set λX10 : set ⇒ Inj1 (X7 (λX11 : (set → set → set λX12 : set ⇒ ∅ ) (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 (Inj1 (setsum ∅ ∅ X5 ) (λX8 : set ⇒ ∅ ) X3 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X9 (Inj0 (X8 ∅ X10 ) (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ Inj0 (X8 (setsum ∅ ∅ ) ) → (∀X4 : set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : (set → set → set → ((set → set → set → (set → set → set → set (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set → set Inj1 ∅ ) (λX10 : set ⇒ X8 ) X9 ) (λX8 : set → set X6 (setsum (Inj1 ∅ ∅ ∅ (λX9 : set ⇒ X6 ∅ ∅ (λX10 : set ⇒ X9 ) (X6 ∅ ∅ (λX10 : set ⇒ ∅ ) ∅ ) (Inj0 (X5 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj1 ∅ → X3 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ setsum (Inj0 (setsum (setsum ∅ ∅ (X8 ∅ (setsum (setsum (Inj0 ∅ (Inj0 ∅ (setsum (X8 ∅ (setsum ∅ ∅ ) X0 (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ X9 ) (λX9 : set → set Inj0 (X6 ∅ ∅ (λX10 : set ⇒ ∅ ) ∅ ) (λX9 : set ⇒ Inj1 (Inj0 ∅ ) (setsum (Inj1 ∅ ∅ (X6 (setsum ∅ (setsum ∅ ∅ (X7 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (λX9 : set ⇒ X6 (setsum ∅ ∅ ∅ (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ ∅ ) (X6 (Inj1 (X6 ∅ (X6 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ (Inj0 (setsum (Inj1 ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → set → set → set Inj0 (setsum (setsum X7 (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : (((set → set → set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj0 (setsum (X5 (λX8 : (set → set → set λX9 : set → set Inj0 ∅ ) (λX8 : set ⇒ X7 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ) (Inj0 ∅ ∈ Inj0 (Inj0 (X7 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) → X2 (λX8 : (set → set → set → set → set setsum (Inj0 (X8 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) (X8 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set ⇒ X6 ) X3 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : (set → set → set Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : (set → set → set X6 (setsum (setsum X7 (Inj0 ∅ (Inj0 X7 (setsum ∅ (Inj0 (setsum ∅ ∅ (λX10 : set ⇒ X8 ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 X7 ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set (Inj1 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) ∈ setsum (X4 (X6 (Inj1 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (Inj0 (Inj1 ∅ → X0 (λX8 : set ⇒ Inj0 ∅ ) (setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → set X0 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ (Inj0 (setsum X4 (Inj1 ∅ X1 (λX8 : set ⇒ λX9 : (set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWKMjQGvLZa6sdRUEQwrhyNWZmRxVnpFpT )
∀X0 : (set → set → (set → set → set → set → (set → set → set → (set → set → set → prop ∀X1 : ((((set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → (((set → set → set → set → set → set → prop ∀X3 : ((set → set → set → ((set → set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set Inj1 ∅ ) (setsum (setsum ∅ (setsum (Inj0 ∅ X4 (setsum (setsum ∅ ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ (λX8 : set → set → set λX9 : set ⇒ X6 (λX10 : set → set λX11 : set → set λX12 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → ((set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set X10 (λX11 : set ⇒ X8 (X10 (λX12 : set ⇒ ∅ ) ) ) ∅ (λX8 : set → set → set λX9 : set ⇒ X8 (setsum ∅ X9 (setsum (Inj1 ∅ (Inj0 (Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : (set → set → set → set setsum ∅ (Inj1 X5 ) (setsum (Inj0 (Inj1 ∅ (setsum (setsum X7 (setsum ∅ ∅ X4 ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum (setsum X6 (setsum (X4 (λX8 : set → set → set ∅ ) X6 (Inj1 ∅ ∈ setsum (setsum (Inj0 (Inj1 ∅ ∅ ∅ → X2 (λX8 : set ⇒ setsum (Inj1 ∅ (Inj0 (Inj0 (Inj1 ∅ ) (λX8 : (set → set → set → set setsum (Inj0 (X8 (λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) (Inj0 (X8 (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) ) (X7 (Inj1 ∅ X1 (λX8 : ((set → set → set → set λX9 : set → set Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → ((set → set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : ((set → set → set → set λX9 : set → set X8 (λX10 : set → set X8 (λX11 : set → set ∅ ) ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set λX9 : set → set setsum ∅ ∅ ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set → set (setsum (Inj1 ∅ X4 ∈ Inj1 X5 → X1 (λX8 : ((set → set → set → set λX9 : set → set X7 ∅ (λX10 : set → set ∅ ) (setsum (X7 (X8 (λX10 : set → set ∅ ) (λX10 : set → set Inj1 ∅ ) ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ X6 ) (Inj1 (setsum (Inj0 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (setsum ∅ (setsum (X7 (setsum ∅ ∅ (λX8 : set → set setsum ∅ ∅ ) (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj0 (Inj1 (X5 ∅ → X0 (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj0 (Inj0 ∅ ∅ ) (λX8 : set ⇒ setsum (Inj1 (setsum X6 ∅ X6 ) (Inj0 (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ X3 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set X8 (Inj1 X7 ) (X5 (Inj1 X7 (λX8 : set → set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKkYY3Na1xatB4nbxQ9gwqTWTFb2ef72bv )
∀X0 : ((set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → set → set → ((set → set → set → set → set → set → prop ∀X3 : ((set → set → set → ((set → set → set → (set → set → prop (∀X4 : (set → (set → set → set → set ∀X5 : (set → set → (set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ Inj1 ∅ ) X3 (λX8 : set → set X5 (λX9 : set ⇒ Inj0 (setsum X7 (setsum ∅ ∅ ) (λX9 : set ⇒ X6 ) (λX9 : set ⇒ X7 ) ∅ ) (λX8 : set → set X7 ) (λX8 : set ⇒ X6 ) ) → (∀X4 : set → ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (Inj0 X5 (X6 (Inj1 X5 ∈ Inj0 (X6 (X6 (Inj0 ∅ → X3 (λX8 : set → set ∅ ) (λX8 : set → set setsum (Inj0 (Inj0 X5 (Inj1 (Inj0 (X8 ∅ ) (λX8 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set → set → set → set λX9 : set ⇒ X7 ) ) → (∀X4 : (set → (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ X5 → X3 (λX8 : set → set X8 (setsum X6 (X8 (Inj0 ∅ ) (λX8 : set → set X6 ) (λX8 : set ⇒ X8 ) X2 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set → set → set → set λX9 : set ⇒ X9 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ setsum X9 (X8 ∅ ∅ ∅ ) (Inj1 X7 ∈ Inj0 X4 ) → (∀X4 : set → set ∀X5 : set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (Inj1 ∅ (Inj1 ∅ ) ∅ ∈ setsum (Inj0 (Inj1 ∅ X7 → X1 (λX8 : ((set → set → set → set → set → set X6 ) (λX8 : set → set setsum ∅ (setsum (Inj0 (setsum ∅ ∅ X7 ) (setsum (Inj1 X6 (setsum ∅ (setsum ∅ ∅ X1 (λX8 : ((set → set → set → set → set → set ∅ ) (λX8 : set → set X6 ) (X5 (X4 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (setsum (Inj1 ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → (set → set → set → set (X5 ∈ Inj0 ∅ → X1 (λX8 : ((set → set → set → set → set → set X6 (Inj1 (Inj1 ∅ (X8 (λX9 : set → set → set λX10 : set ⇒ X10 ) ∅ (setsum (setsum ∅ (X8 (λX9 : set → set → set λX10 : set ⇒ ∅ ) (Inj0 ∅ ) (λX8 : set → set ∅ ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set → set → set → set λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set (setsum (setsum ∅ (setsum (X5 (λX8 : set → set → set ∅ ) (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ∈ X7 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ setsum X9 X11 ) ) ∅ → X0 (λX8 : set → set → set X6 ) (setsum ∅ (Inj1 (X5 (λX8 : set → set → set setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X0 (λX8 : set → set → set setsum (X8 (X5 X6 (Inj0 ∅ (λX9 : set ⇒ X8 ∅ ∅ ) (X5 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (setsum X6 (Inj0 ∅ X6 ) X6 (Inj0 (Inj0 ∅ ∈ setsum ∅ (setsum (Inj0 (Inj1 ∅ (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZ5pYWaUWQ3nGDeT3vu1SqCrDG2RdAduY3 )
∀X0 : (set → (((set → set → set → set → set → set → set → ((set → (set → set → set → set → ((set → set → set → (set → set → set → prop ∀X1 : (set → (((set → set → set → (set → set → set → set → (set → set → set → (set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : ((set → set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (setsum X7 (Inj0 (Inj1 (setsum ∅ ∅ X3 (λX8 : set → set X6 X7 (λX9 : set → set λX10 : set ⇒ Inj0 (X9 (Inj0 ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ X7 ) (setsum X7 (setsum X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set X3 (λX8 : set → set setsum ∅ X6 ) (setsum (setsum ∅ ∅ (setsum (setsum X6 ∅ (Inj0 (setsum ∅ ∅ (Inj0 (Inj1 ∅ ∈ setsum (X7 (λX8 : set ⇒ ∅ ) (setsum X4 (setsum ∅ ∅ (setsum ∅ X5 ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → (set → set → set (setsum (setsum (Inj1 (Inj1 ∅ (X7 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X7 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (Inj1 (X4 (X7 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∈ setsum (X5 (setsum (setsum ∅ ∅ (Inj0 ∅ (setsum ∅ (X5 (Inj1 ∅ → X2 (λX8 : set ⇒ setsum ∅ (Inj1 (X5 (setsum ∅ ∅ ) (Inj1 (Inj0 X6 ) → (∀X4 : (set → (set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ Inj1 X8 ) (setsum (Inj1 (Inj1 X7 (Inj0 (X5 (setsum ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set → set X8 ) X7 (Inj0 (setsum (Inj0 ∅ ∅ ∅ ∈ setsum (Inj1 (setsum (Inj0 ∅ (Inj1 ∅ X7 ) → (∀X4 : set → (set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : set → set X10 (setsum X8 (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X2 (λX8 : set ⇒ ∅ ) X4 ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set ∀X7 : (((set → set → set → set → set → set (X4 (Inj1 (setsum (setsum ∅ ∅ ∅ ∅ (λX8 : set ⇒ X6 (λX9 : set → set ∅ ) (λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) ) (setsum ∅ ∅ ∈ Inj1 ∅ → X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set λX10 : set → set Inj0 (setsum ∅ (X7 (λX11 : (set → set → set → set Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set ⇒ X9 (λX11 : set → set λX12 : set ⇒ ∅ ) ) (λX8 : set → (set → set → set → set λX9 : (set → set → set λX10 : set → set setsum (Inj0 ∅ ∅ ) (Inj0 ∅ ∈ X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMK2pzJCKcGwn2hUTitqC2GkA8i8KT25fZi )
∀X0 : (((set → (set → set → set → set → set → set → set → prop ∀X1 : (set → (set → set → set → (set → (set → set → set → set → set → (set → set → ((set → set → set → set → prop ∀X2 : (((set → set → (set → set → set → set → set → set → (set → (set → set → set → set → set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : (set → set → (set → set → set → set → set → set λX9 : set → (set → set → set → set setsum ∅ ∅ ) (setsum ∅ (setsum (setsum (Inj0 ∅ ∅ (Inj1 (Inj1 ∅ X3 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : (((set → set → set → set → set → set X3 (λX8 : set ⇒ X7 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set → set ∅ ) (X4 ∈ Inj0 (Inj1 (Inj0 ∅ ) → (∀X4 : set → (set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X5 ∈ setsum (setsum (X6 (X4 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (X4 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ → X2 (λX8 : (set → set → (set → set → set → set → set → set λX9 : set → (set → set → set → set Inj0 (X9 X7 (λX10 : set ⇒ Inj0 ∅ ) (X9 (setsum ∅ ∅ (λX10 : set ⇒ X9 ∅ (λX11 : set ⇒ ∅ ) ∅ ) (Inj1 ∅ ) X7 ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set → set → set X2 (λX8 : (set → set → (set → set → set → set → set → set λX9 : set → (set → set → set → set setsum (X9 (setsum (Inj0 ∅ (Inj0 ∅ (λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set ⇒ ∅ ) (X8 (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ ) ∅ ∅ ) ∅ False ) → (∀X4 : set → set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set setsum ∅ (Inj1 (setsum (X9 ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ X9 (setsum (Inj0 X10 (Inj1 (Inj1 ∅ X10 ) (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : set ⇒ setsum (setsum ∅ (Inj0 ∅ (X8 (X7 (λX10 : (set → set → set → set X9 ) ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set setsum X8 X8 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ X10 ) (λX8 : set ⇒ setsum (Inj0 (Inj0 (X7 (λX9 : (set → set → set ∅ ) (setsum X6 (X7 (λX9 : (set → set → set X9 (λX10 : set ⇒ ∅ ) ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj0 (setsum X5 ∅ ∈ Inj1 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ X5 (X4 (Inj1 (setsum ∅ ∅ → X2 (λX8 : (set → set → (set → set → set → set → set → set λX9 : set → (set → set → set → set setsum (X9 X7 (λX10 : set ⇒ Inj0 ∅ ) (Inj0 (X9 ∅ (λX10 : set ⇒ ∅ ) ∅ (setsum (Inj1 (X8 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ∅ ∅ ) (setsum (setsum X7 ∅ ∅ X0 (λX8 : (set → (set → set → set → set → set Inj0 (Inj1 (Inj0 (Inj0 ∅ ) (Inj0 ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set ∀X7 : (((set → set → set → set → set → set → set → set X0 (λX8 : (set → (set → set → set → set → set ∅ ) (X7 (λX8 : (set → set → set ∅ ) ∅ ∅ (Inj0 (setsum ∅ (setsum ∅ ∅ X0 (λX8 : (set → (set → set → set → set → set Inj0 ∅ ) (X4 (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWTdFEym1KJg7Hs88t9p1Pf1cTdCkXSthG )
∀X0 : (((set → set → set → set → (set → set → set → set → set → prop ∀X1 : ((set → set → set → (set → set → prop ∀X2 : ((set → (set → set → set → set → ((set → set → set → set → set → prop ∀X3 : (set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set (Inj1 X4 ∈ setsum (setsum (Inj1 (Inj0 ∅ (setsum ∅ (setsum ∅ ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) (Inj1 (setsum ∅ (setsum (Inj1 ∅ (Inj1 ∅ (λX8 : set ⇒ X7 X6 (Inj0 (Inj0 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set ⇒ X7 ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 (Inj1 (setsum ∅ ∅ ∈ Inj1 ∅ → X2 (λX8 : set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (setsum ∅ (Inj0 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : ((set → set → set → set → set → set → (set → set → set → (set → set → set X2 (λX8 : set → (set → set → set X5 (setsum ∅ (setsum (X8 ∅ (λX9 : set ⇒ ∅ ) (X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set → set setsum (X8 (Inj0 ∅ (λX10 : set ⇒ setsum ∅ ∅ ) (Inj1 (Inj1 ∅ ) (X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX9 : set ⇒ ∅ ) (Inj1 (X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X10 ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) X0 (λX8 : (set → set → set → set → (set → set → set X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ setsum (setsum (X7 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (Inj0 ∅ ∅ ) ) (Inj1 (X7 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set → set → set λX12 : set ⇒ λX13 : set ⇒ X13 ) (λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX11 : set ⇒ Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ X8 ) ) ) → (∀X4 : set → set ∀X5 : ((set → set → (set → set → set → set → ((set → set → set → set → set ∀X6 : set → (set → set → set ∀X7 : (((set → set → set → (set → set → set → set → set (setsum (Inj0 (Inj1 (Inj0 ∅ (Inj0 (setsum ∅ ∅ ∈ setsum ∅ (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ (Inj0 ∅ ) → X2 (λX8 : set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (X8 (setsum ∅ (Inj0 ∅ (Inj0 X9 ) X1 (λX8 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ (Inj0 X8 ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → (set → set → set → (set → set → set ∀X6 : set → (set → set → set → set ∀X7 : ((set → set → set → set → ((set → set → set → set (setsum (X6 (setsum (Inj0 ∅ (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 (λX10 : set → set → set ∅ ) (λX10 : set → set ∅ ) ∅ ) X4 ∈ X7 (λX8 : set → set → set setsum (Inj0 (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set ∅ ) → X1 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) X1 (λX8 : set → set ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX9 : set ⇒ X7 (λX10 : set → set → set Inj0 ∅ ) (λX10 : set → set Inj0 (Inj1 ∅ ) ) ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set X0 (λX8 : (set → set → set → set → (set → set → set setsum (setsum ∅ (setsum ∅ ∅ (setsum (X7 (setsum ∅ ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) ∅ X0 (λX8 : (set → set → set → set → (set → set → set setsum (setsum ∅ (X7 (setsum ∅ ∅ (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) ) (setsum (X6 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set → set X0 (λX8 : (set → set → set → set → (set → set → set ∅ ) (Inj1 ∅ X2 (λX8 : set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 (setsum X10 X10 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWZb8d5Xwf8bjYD3nuxqtNAFzr9V4SEdDZ )
∀X0 : (set → set → ((((set → set → set → (set → set → set → set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : ((set → set → (set → set → set → set → set → set → set → prop ∀X3 : ((set → (set → set → set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : set → set → (set → set → set ∀X7 : set , X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ X8 (setsum (Inj0 (setsum ∅ ∅ (Inj0 X9 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) ) ∅ (Inj1 (setsum (setsum (Inj0 ∅ ∅ ∅ X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ setsum (Inj1 (X8 (setsum ∅ ∅ (λX12 : set ⇒ λX13 : set ⇒ ∅ ) X11 ) (X5 X7 (Inj0 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → set ∀X7 : ((set → set → set → set → set → (set → set → set X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ setsum (Inj1 ∅ (Inj0 (Inj1 (X8 ∅ (λX12 : set ⇒ λX13 : set ⇒ ∅ ) ) ∅ ∅ (Inj0 (Inj1 (Inj1 ∅ ∈ Inj1 (X7 (λX8 : set → set λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum (X5 ∅ (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum (setsum (Inj1 ∅ X6 X6 ∈ Inj1 ∅ → X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) ∅ X2 (λX8 : set → set → (set → set → set → set λX9 : set ⇒ Inj1 (Inj0 (setsum (setsum ∅ ∅ X6 ) (X4 (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → (set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set (setsum X6 (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∈ Inj0 (setsum (setsum ∅ X6 (setsum (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ ∅ → X2 (λX8 : set → set → (set → set → set → set λX9 : set ⇒ Inj1 (setsum (Inj1 X6 (Inj1 (Inj1 ∅ ) ∅ X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ X10 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X10 (Inj0 ∅ (setsum ∅ ∅ ∅ ) ∅ (X4 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 (λX10 : (set → set → set λX11 : set → set Inj1 ∅ ) (X7 (λX10 : (set → set → set λX11 : set → set Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → (set → set → set → set (setsum ∅ X4 ∈ setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (X7 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 X6 ∈ Inj1 (Inj0 ∅ → X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum X10 ∅ (setsum (Inj0 (Inj0 ∅ ∅ ) (setsum (X5 (λX8 : (set → set → set → set λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set → set X7 ) ∅ X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X12 ) ∅ ) → (∀X4 : set → set → set → set → set ∀X5 : (set → set → (set → set → set → set ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : (set → set → set → set → (set → set → set → set (X4 (Inj1 (X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ X8 ) (setsum ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) (X6 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (Inj1 (setsum ∅ (X4 ∅ ∅ ∅ ∅ ∈ setsum (Inj1 (Inj0 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ → X0 (λX8 : set ⇒ setsum ∅ (Inj0 (Inj1 (X6 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → (set → set → set → set X8 (λX9 : set → set Inj0 (setsum (X9 ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 (X6 (Inj1 ∅ (λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ ∅ ) ) ∅ ) ∅ ) → (∀X4 : (set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ X7 ) (λX8 : ((set → set → set → (set → set → set → set X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ setsum X6 (setsum ∅ ∅ ) X7 ) (Inj1 ∅ (X6 ∈ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXPWDSKNj6a912j1K2S8xyY6wRFnjr7x7p )
∀X0 : (set → set → (((set → set → set → set → (set → set → set → prop ∀X1 : (set → set → (((set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (((((set → set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → (set → set → set → set → set ∅ ) X4 ) → (∀X4 : set → ((set → set → set → set → (set → set → set ∀X5 : (set → set → ((set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : (((set → set → set → set → (set → set → set → set → set setsum ∅ ∅ ) (X5 (λX8 : set ⇒ setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum ∅ (setsum ∅ (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ X3 (λX8 : (((set → set → set → set → (set → set → set → set → set ∅ ) (setsum (X4 (setsum (setsum ∅ ∅ (X5 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∅ (λX8 : set → set λX9 : set ⇒ X8 ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → (set → set → set X1 (λX8 : set ⇒ X5 ) (λX8 : (set → set → set → set λX9 : (set → set → set ∅ ) (setsum X5 (Inj1 X5 X2 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set ⇒ setsum ∅ (Inj1 (setsum ∅ ∅ ) (Inj1 ∅ ∈ Inj1 (setsum (Inj1 X6 ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X6 (Inj1 (X6 (X5 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ Inj0 (setsum X8 ∅ ) ) (λX8 : (set → set → set → set λX9 : (set → set → set X6 ∅ (λX10 : set → set λX11 : set ⇒ X11 ) ) (setsum (Inj1 ∅ (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set X1 (λX8 : set ⇒ setsum X8 ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ (X7 (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) ) (setsum X5 (setsum ∅ X5 (Inj0 X5 ∈ Inj0 X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → ((set → set → set → set (Inj0 ∅ ∈ X7 (λX8 : (set → set → set λX9 : set ⇒ setsum (X7 (λX10 : (set → set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX10 : set → set setsum ∅ ∅ ) (setsum (X6 ∅ (Inj0 ∅ ) (λX8 : set → set X5 ) → X0 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set X6 (Inj0 (Inj1 (Inj1 ∅ ) X0 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set X7 (λX10 : (set → set → set λX11 : set ⇒ ∅ ) (λX10 : set → set Inj0 ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : set , (X5 (X5 (setsum (Inj0 ∅ X4 ∈ X6 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum (X8 (λX11 : set ⇒ X11 ) X10 ) → X0 (λX8 : set ⇒ setsum (setsum (setsum ∅ (Inj0 ∅ (Inj1 ∅ (setsum X8 X8 ) (λX8 : (set → set → set → set λX9 : set → set setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ X10 ) ∅ ) X2 (λX8 : set ⇒ X8 ) (setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ (setsum (X5 (Inj0 ∅ (setsum (setsum ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVFsP7tgX8Fci33gR3LhonfJbFFNhs3MeP )
∀X0 : (set → set → set → set → prop ∀X1 : (((set → (set → set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → set → set → set → set → ((set → (set → set → set → set → set → set → ((set → set → set → (set → set → set → (set → set → prop ∀X3 : (((set → set → set → (((set → set → set → set → set → set → set → (set → ((set → set → set → set → (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → set → prop (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ ∈ X7 ∅ → X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ setsum X9 ∅ ) (λX8 : set → set Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ ∅ ) X3 (λX8 : (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (Inj1 X6 ∅ ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum (setsum X10 ∅ (setsum (Inj0 (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum (setsum ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set X7 ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) ∅ (Inj0 X5 X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 ) (λX8 : set → (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ setsum (Inj1 (Inj1 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → ((set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set , (Inj0 X7 ∈ Inj1 (setsum (setsum (X6 ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ ∅ → X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ X8 (setsum (Inj0 X7 (setsum X7 (Inj1 ∅ (λX10 : set ⇒ X7 ) ∅ ) (λX8 : set → set X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 (Inj1 X11 ) (λX9 : set → set ∅ ) (λX9 : set ⇒ setsum (Inj0 ∅ ∅ ) (X8 X7 ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ X6 ) (λX8 : set → set X8 (X8 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) (λX8 : set ⇒ X8 ) (Inj1 X4 ∈ Inj0 X5 ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set → set → set ∀X7 : set , X1 (λX8 : (set → (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : (set → (set → set → set → set X6 (Inj1 ∅ ) (λX8 : set ⇒ X5 ∅ ) X3 (λX8 : (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (X6 (setsum (Inj0 ∅ (Inj0 ∅ (Inj1 (Inj1 X8 ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X6 (Inj0 (X6 (setsum ∅ ∅ ) (X6 (Inj1 (setsum (setsum ∅ ∅ X7 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set (X4 ∈ Inj0 ∅ → X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 X12 ) (λX8 : set → (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum X6 X6 ) (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (setsum ∅ ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ X6 ∅ (λX10 : set → set X9 ) ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMThpaR5E61DrV6qh9NAoeb5ZceD6VLJmXM )
∀X0 : (((((set → set → set → set → (set → set → set → set → set → (set → set → set → set → set → prop ∀X1 : (((set → set → ((set → set → set → set → (set → set → set → set → (set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : ((set → set → set → set → (set → set → set → set → (((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → (set → set → (set → set → set → set ∀X6 : (set → set → set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → (set → set → set → set X7 ) (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ X7 ) ∅ (setsum ∅ (setsum ∅ X7 (setsum ∅ ∅ X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : (set → set → set → set setsum (Inj0 ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (Inj0 (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , (Inj0 (setsum ∅ ∅ ∈ Inj1 (setsum (setsum (X6 ∅ (Inj1 ∅ ∅ → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum ∅ X12 ∅ ) (λX8 : (set → set → set → set Inj1 (setsum (Inj0 X7 ∅ ) (setsum (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) (λX8 : set ⇒ ∅ ) X4 X2 (λX8 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X2 (λX8 : set ⇒ X6 ) X6 ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X5 (X5 (setsum X6 ∅ ∅ (setsum (setsum X7 (Inj0 ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (setsum ∅ (Inj0 (Inj1 X6 (X7 ∈ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set → set (Inj0 (Inj1 ∅ ∈ setsum (setsum (X7 (setsum ∅ ∅ (setsum ∅ ∅ ∅ X4 → X1 (λX8 : (set → set → ((set → set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ setsum X10 (setsum (Inj0 ∅ (Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : set , (X5 ∈ X7 → X1 (λX8 : (set → set → ((set → set → set → set → (set → set → set X5 ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum (Inj0 ∅ X8 ) X0 (λX8 : (((set → set → set → set → (set → set → set → set X8 (λX9 : (set → set → set → set λX10 : set → set ∅ ) ) (λX8 : set ⇒ ∅ ) X4 (Inj0 (Inj1 X7 ∅ ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (setsum (setsum (X4 (λX8 : (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) (Inj1 ∅ (Inj0 ∅ ∅ ∈ X4 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ X9 ) (X6 (setsum ∅ ∅ ) X5 (λX8 : set ⇒ X8 ) → X0 (λX8 : (((set → set → set → set → (set → set → set → set X5 ) (λX8 : set ⇒ ∅ ) ∅ (Inj0 X7 (Inj1 X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → (set → set → set → set X5 ) (λX8 : set ⇒ Inj1 (Inj0 (Inj0 X5 ) (Inj1 X6 X4 ∅ X1 (λX8 : (set → set → ((set → set → set → set → (set → set → set setsum X6 X6 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTWYXBfwREa4QiS4s2Q8nJ946WRdgwdkke )
∀X0 : (set → set → set → set → (set → set → (set → set → set → set → prop ∀X1 : ((set → ((set → set → set → set → set → ((set → set → set → (((set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → (((set → set → set → set → prop ∀X3 : (set → (set → set → set → set → set → prop (∀X4 : (((set → set → set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set (X6 ∅ ∈ X7 ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (setsum (X7 ∅ X8 (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X10 (X7 (setsum (X10 ∅ ∅ ) (setsum ∅ (X4 (λX8 : (set → set → set → set λX9 : set → set Inj1 ∅ ) (X7 (setsum ∅ ∅ ∅ X3 (λX8 : set ⇒ λX9 : set → set → set Inj1 (Inj0 (X9 X8 (X6 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set X7 (Inj1 ∅ (Inj0 (setsum (X9 ∅ ∅ ∅ (X6 (setsum ∅ ∅ ∅ ) (setsum (Inj1 (Inj1 ∅ (setsum (X5 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ X1 (λX8 : set → ((set → set → set → set X6 ∅ ) (λX8 : set → set setsum ∅ ∅ ) (λX8 : (set → set → set Inj0 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum (Inj1 (Inj1 ∅ (Inj0 ∅ ∈ X7 → X2 (λX8 : (((set → set → set → set → set X6 ) (λX8 : (set → set → set X6 ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set → set → set X2 (λX8 : (((set → set → set → set → set Inj0 ∅ ) (λX8 : (set → set → set Inj0 (Inj1 (setsum (X7 (λX9 : set → set → set λX10 : set ⇒ ∅ ) ∅ ∅ X6 ) (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ ∈ Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) (setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ X1 (λX8 : set → ((set → set → set → set Inj0 X6 ) (λX8 : set → set setsum ∅ (Inj1 X5 ) (λX8 : (set → set → set X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 ∅ (setsum (setsum ∅ ∅ X9 ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set Inj0 (setsum ∅ X5 ) (λX8 : set → set ∅ ) (λX8 : (set → set → set ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) X7 ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set → set → (set → set → set ∀X7 : (set → set → (set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (setsum (X10 (Inj1 ∅ (Inj1 (X10 ∅ ∅ ) (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj0 ∅ ∈ setsum (Inj0 (Inj0 ∅ (X7 (λX8 : (set → set → set → set setsum ∅ (Inj1 ∅ ) → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (X7 (λX11 : (set → set → set → set X8 ) ∅ ) (Inj1 ∅ X1 (λX8 : set → ((set → set → set → set Inj1 (Inj0 (setsum (Inj1 ∅ (Inj0 ∅ ) (λX8 : set → set setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ X5 ) (λX8 : (set → set → set setsum ∅ (Inj0 (X8 (λX9 : set ⇒ X7 (λX10 : (set → set → set → set ∅ ) ) ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMaQoRGDpkekfGRr9XRjuGS5HFVu8NcS67L )
∀X0 : ((set → set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : ((set → set → set → (set → set → (((set → set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : ((set → set → set → set → ((set → set → set → set → set → set → set → (set → set → set → prop (∀X4 : set → ((set → set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set → (set → set → set (Inj0 (setsum (setsum ∅ ∅ (Inj0 (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∈ Inj0 ∅ → X2 (λX8 : set → set X6 ) (λX8 : set ⇒ setsum (setsum ∅ X8 (X5 (λX9 : set ⇒ X9 ) ) (λX8 : (set → set → set setsum (X8 (λX9 : set ⇒ X9 ) (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set Inj1 (Inj0 (Inj1 ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ setsum X9 (setsum (Inj1 ∅ X6 ) ) (setsum (X4 (Inj0 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ Inj1 (Inj1 ∅ ) (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ X3 (λX8 : set → set X7 (setsum ∅ (X5 (λX9 : set ⇒ ∅ ) (setsum (Inj1 ∅ ∅ (λX9 : set ⇒ X8 (Inj1 (X7 ∅ ∅ (λX10 : set ⇒ ∅ ) ) ) (setsum (X5 (λX8 : set ⇒ X5 (λX9 : set ⇒ setsum ∅ ∅ ) ) ∅ (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 (X5 (λX8 : set ⇒ ∅ ) X6 ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X7 : set → set → set X3 (λX8 : set → set Inj1 (X7 (setsum (X6 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ∅ ) (Inj0 (Inj1 ∅ (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (X7 (Inj1 ∅ (Inj1 (setsum (setsum ∅ ∅ (X7 ∅ ∅ (λX8 : set ⇒ Inj1 (X5 (X5 ∅ (setsum ∅ ∅ ∅ ) (Inj1 ∅ (X7 ∅ (X6 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ Inj1 X8 ) (setsum (Inj1 ∅ ∅ ∈ Inj1 (X5 (X7 ∅ ∅ ∅ ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj0 X5 ∈ Inj1 (setsum X5 (setsum (X6 ∅ (Inj0 ∅ → X2 (λX8 : set → set setsum (Inj1 (X6 (Inj0 ∅ (setsum ∅ (X8 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set Inj0 X7 ) (λX8 : set → set setsum ∅ (setsum (Inj0 (X8 ∅ (Inj1 ∅ ) (λX8 : set ⇒ X8 ) ∅ ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set → set ∀X7 : set → set (Inj0 ∅ ∈ setsum (setsum ∅ (X7 (Inj0 ∅ (setsum (Inj0 (Inj0 ∅ (Inj0 (Inj1 ∅ → X2 (λX8 : set → set X5 ) (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) (λX8 : (set → set → set setsum ∅ (setsum ∅ (Inj0 X5 ) (λX8 : set → set Inj1 (Inj1 ∅ ) (λX8 : set ⇒ Inj0 (Inj0 X8 ) (X6 (λX8 : set ⇒ λX9 : set ⇒ setsum X9 ∅ ) X5 (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X0 (λX8 : set → set λX9 : set ⇒ Inj1 X9 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 ∅ ) (Inj1 ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (X7 (λX10 : (set → set → set Inj0 ∅ ) X8 ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : set → ((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (Inj1 (setsum ∅ ∅ (Inj0 (Inj1 X9 ) (Inj0 (Inj1 (Inj0 (setsum ∅ ∅ X2 (λX8 : set → set X5 ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set Inj1 (X7 ∅ (λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) (λX8 : set → set ∅ ) (λX8 : set ⇒ X7 (Inj1 ∅ (λX9 : set → set λX10 : set ⇒ X9 X10 ) ) (Inj0 ∅ ) → (∀X4 : set → (set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set ∅ ) (λX8 : set ⇒ X7 ) (λX8 : (set → set → set X6 ) (λX8 : set → set X5 ) (λX8 : set ⇒ setsum X8 ∅ ) ∅ X0 (λX8 : set → set λX9 : set ⇒ Inj1 (X8 ∅ ) (Inj0 (Inj0 X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj0 (setsum ∅ (setsum (Inj1 ∅ ∅ → X0 (λX8 : set → set λX9 : set ⇒ setsum (setsum (Inj0 X7 ∅ (setsum X6 (Inj0 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X7 ) X1 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum X7 ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMb8jKqZ3usutQm2vntJkhu2UKTWNc4vvRt )
∀X0 : (set → set → (((set → set → set → (set → set → set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → ((set → set → set → set → set → (set → set → set → (set → set → set → (((set → set → set → set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : ((set → set → set → ((((set → set → set → (set → set → set → set → set → set → prop ∀X3 : (((set → set → set → set → ((set → (set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set → set (X6 ∈ Inj1 (Inj0 ∅ → X0 (λX8 : set ⇒ X7 ∅ (λX9 : set → set ∅ ) ∅ (setsum (setsum (X7 ∅ (λX9 : set → set ∅ ) ∅ ∅ (Inj0 ∅ (Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (Inj1 ∅ ∅ ) X3 (λX8 : (set → set → set ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj1 (X7 (X8 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set → set X9 ) ∅ X9 ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : (set → set → (set → set → set → set ∀X5 : set → set → set → set ∀X6 : ((set → set → set → set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → set setsum (X5 (setsum (X6 (λX9 : set → set → set λX10 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (Inj0 (Inj1 ∅ (Inj1 (X5 ∅ ∅ ∅ X7 ) (λX8 : set → (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum X9 ∅ ) False ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set → set (setsum (setsum (Inj1 (setsum ∅ ∅ ∅ (setsum (X7 (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ∅ ∈ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ → X2 (λX8 : set → set X8 (X6 (λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (Inj0 ∅ ∅ ) ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ Inj1 (X7 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set X8 (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ Inj0 (setsum (Inj0 (Inj0 ∅ (setsum ∅ X7 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → set ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ Inj1 (Inj1 (setsum ∅ ∅ ) X1 (λX8 : (((set → set → set → set → set → ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set setsum (X11 (Inj0 ∅ ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj1 X8 ) (setsum X5 (Inj0 ∅ X5 X4 ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → set → set → set (setsum (setsum X6 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) (setsum ∅ ∅ (setsum (X5 (Inj0 ∅ (setsum X6 ∅ ∈ Inj0 (setsum (setsum (setsum ∅ ∅ ∅ ∅ → X1 (λX8 : (((set → set → set → set → set → ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ setsum (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ X6 ) (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ setsum (Inj1 ∅ (X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (X4 (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X6 ) (Inj1 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) (Inj1 (setsum ∅ ∅ X0 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (Inj0 (setsum ∅ ∅ (Inj1 X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (((set → set → set → set → set → ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set X9 ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X5 (setsum (setsum (setsum (Inj0 ∅ X6 (setsum X4 X5 (setsum (Inj1 (Inj1 ∅ X7 ∅ X0 (λX8 : set ⇒ X6 ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ ∅ ) ) → (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → (set → set → set → set X0 (λX8 : set ⇒ X7 (setsum X8 (setsum ∅ (setsum ∅ ∅ ∅ (λX9 : set ⇒ setsum X9 (X7 (Inj0 ∅ X8 (λX10 : set ⇒ X9 ) (Inj0 ∅ ) (setsum (X7 X8 (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) X5 (setsum (setsum ∅ ∅ (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ λX12 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) (λX11 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum (setsum ∅ (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) X0 (λX8 : set ⇒ setsum (X7 (setsum (setsum ∅ ∅ (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (X7 (Inj1 ∅ (X6 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ ∅ (X6 (Inj1 X8 ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVPWy5vi3Kh3RPtVjwaocs9nUBQYAegnaU )
∀X0 : ((set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → prop ∀X3 : (set → set → (set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum X6 ∅ ∈ X6 → X3 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum X11 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → (set → set → set → (set → set → set → set (setsum (X4 (X4 (setsum ∅ ∅ ∅ ∈ X6 → X3 (λX8 : set ⇒ setsum (Inj1 (Inj1 (Inj1 ∅ (setsum ∅ (X7 (λX9 : (set → set → set → set λX10 : set → set ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) ∅ X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum ∅ X5 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : set , (X5 (Inj1 (setsum X7 X6 (λX8 : set → set Inj1 ∅ ) ∈ Inj0 ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (X4 ∈ Inj0 ∅ → X2 (λX8 : set ⇒ setsum ∅ (Inj1 X6 ) (λX8 : set → set ∅ ) X2 (λX8 : set ⇒ Inj0 (X5 X7 (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set → set X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set → set → set (Inj0 (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ∈ Inj1 (setsum ∅ (X6 X4 (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X3 (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) (Inj1 (setsum ∅ ∅ X1 (λX8 : set ⇒ X6 ∅ ∅ ) (Inj0 (X7 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) X4 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ setsum ∅ (X7 (setsum (setsum ∅ ∅ X6 ) ∅ ∅ False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ setsum X5 (X7 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ∅ X0 (λX8 : set → set Inj1 ∅ ) (Inj1 ∅ X6 ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set → set → (set → set → set ∀X7 : set → set (setsum (setsum (X7 ∅ (Inj1 ∅ X5 ∈ X5 → X0 (λX8 : set → set ∅ ) (Inj1 (setsum ∅ ∅ (setsum (Inj0 (X4 ∅ (λX8 : set ⇒ X8 ) (Inj1 (setsum (X7 ∅ (setsum ∅ ∅ X1 (λX8 : set ⇒ Inj0 (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ ) (X4 (setsum ∅ (setsum X5 (setsum ∅ ∅ (λX8 : set ⇒ X6 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (setsum ∅ (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVTnUJSUWJmeAm7A3zzfsnCBJHrmLSAHSX )
∀X0 : (set → (((set → set → set → set → (set → set → set → set → set → set → prop ∀X1 : ((set → (set → set → set → (set → set → set → set → set → (set → set → set → prop ∀X2 : (((set → set → set → (set → set → set → set → set → ((((set → set → set → set → set → set → (set → set → set → set → (((set → set → set → set → (set → set → set → (set → set → set → set → prop ∀X3 : (((set → set → ((set → set → set → set → (set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → ((set → set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : (set → set → ((set → set → set → set λX9 : set → set Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : (set → set → set → set → (set → set → set → set → set → set ∀X6 : set → set ∀X7 : set → set X3 (λX8 : (set → set → ((set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ setsum ∅ (X7 (X7 ∅ ) (λX10 : set → set ∅ ) ) (λX8 : set ⇒ X7 (setsum (Inj1 (Inj1 ∅ ∅ ) (Inj1 (setsum (setsum (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∈ setsum (X7 ∅ (Inj1 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → (set → set → set → set → (set → set → set ∀X5 : (((set → set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set (setsum (Inj0 ∅ (X6 (X7 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ∈ Inj0 ∅ → X2 (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ Inj0 (X7 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (X6 (Inj1 (Inj0 ∅ (setsum (X7 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) (X7 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (setsum (X5 (λX8 : (set → set → set λX9 : set ⇒ setsum (X8 (λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) ∅ X2 (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ Inj0 (setsum (setsum (X6 ∅ ∅ (X8 (λX10 : set ⇒ setsum ∅ ∅ ) (X7 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (X9 (X9 ∅ (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (setsum (setsum (Inj0 (X6 ∅ (Inj0 (X6 ∅ (Inj0 (Inj0 (setsum ∅ ∅ ) → (∀X4 : (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set (setsum ∅ (Inj1 (X5 (λX8 : (set → set → set setsum ∅ ∅ ) ∅ (Inj0 ∅ (X5 (λX8 : (set → set → set ∅ ) ∅ ∅ ∅ ∈ Inj0 (Inj0 ∅ → X2 (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ Inj1 (Inj1 (setsum X6 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set Inj0 (setsum (Inj1 ∅ (X8 (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (setsum (Inj1 (X7 (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) (setsum (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ X3 (λX8 : (set → set → ((set → set → set → set λX9 : set → set X9 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , (setsum (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ∅ ∈ X7 → X1 (λX8 : set → (set → set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : set → (set → set → set → (set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → (set → set → set (Inj1 (Inj1 (setsum X5 ∅ ∈ Inj0 X5 → X3 (λX8 : (set → set → ((set → set → set → set λX9 : set → set ∅ ) (λX8 : set ⇒ X5 ) X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set λX10 : set ⇒ ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set λX10 : set ⇒ Inj1 (X9 (λX11 : set → set λX12 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX11 : set ⇒ X8 ) ) (setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKhE8UeiXYrzMe7p2hcDebs1ck25DHh7WG )
∀X0 : ((set → ((set → set → set → set → (set → set → set → set → set → (set → set → (set → set → set → set → ((((set → set → set → set → set → set → set → set → (set → set → set → prop ∀X1 : ((set → set → (set → set → ((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → (set → (set → set → set → (set → set → set → set → (set → set → set → prop ∀X3 : (((set → set → set → set → set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set → set → set setsum (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X9 (setsum (setsum ∅ ∅ X8 (λX11 : set ⇒ Inj1 X8 ) ) (λX8 : set ⇒ Inj1 (X5 (λX9 : set ⇒ X6 (Inj0 ∅ ) ) X7 X3 (λX8 : (set → set → set → set → set → set Inj1 (Inj1 ∅ ) (Inj0 ∅ (setsum (Inj1 ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ (λX8 : set ⇒ X5 (λX9 : set ⇒ ∅ ) ) (setsum (Inj0 (Inj1 X4 (setsum (X5 (λX8 : set ⇒ X6 ∅ ) (Inj0 (Inj1 ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → set → set → set → set X5 ) (setsum (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 X5 (Inj1 (setsum X5 (setsum ∅ (Inj0 ∅ (λX8 : set ⇒ setsum ∅ X6 ) (setsum X6 (setsum ∅ (Inj1 (setsum ∅ ∅ False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : set , X0 (λX8 : set → ((set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : ((set → set → set → set → set Inj0 ∅ ) (Inj0 ∅ (Inj0 ∅ (λX8 : set ⇒ X7 ) X7 X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set → set → set X7 ) (λX8 : set ⇒ setsum X5 (setsum (setsum ∅ X8 (setsum ∅ (setsum ∅ ∅ ) (setsum (setsum (X4 (X4 ∅ ∅ ∅ (setsum (setsum ∅ ∅ (X6 (λX8 : (set → set → set ∅ ) (setsum (Inj0 ∅ (setsum (Inj1 ∅ X7 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set → set → set X9 (setsum ∅ X7 (λX11 : set ⇒ X8 ) ) (λX8 : set ⇒ X5 (Inj1 (setsum (setsum ∅ ∅ ∅ ) (Inj1 (setsum ∅ (setsum (setsum ∅ ∅ X7 X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set → set → set X9 X7 (λX11 : set ⇒ setsum (setsum (setsum ∅ ∅ ∅ X11 ) ) (λX8 : set ⇒ X6 ) ∅ ) → (∀X4 : set → set ∀X5 : (set → set → set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : set → set λX9 : set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set → set → set Inj0 ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj1 (Inj0 (Inj1 (setsum ∅ ∅ ∈ Inj1 X7 → X1 (λX8 : set → set λX9 : set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ X11 X12 ) (λX8 : set → set → set Inj0 ∅ ) (Inj0 (Inj0 (X4 (λX8 : set → set → set X6 (λX9 : set ⇒ λX10 : set → set ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) X3 (λX8 : (set → set → set → set → set → set ∅ ) ∅ (Inj1 ∅ (λX8 : set ⇒ setsum ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ X5 ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 (Inj0 (X6 (λX8 : (set → set → set X7 ) → X0 (λX8 : set → ((set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set λX12 : set ⇒ Inj1 (X11 ∅ ) (λX8 : ((set → set → set → set → set ∅ ) (Inj1 (setsum X4 ∅ (Inj0 ∅ (λX8 : set ⇒ Inj0 (Inj0 (X6 (λX9 : (set → set → set setsum ∅ ∅ ) ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ ∅ (setsum (setsum ∅ (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X4 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) ∈ X7 (setsum X5 X6 → X0 (λX8 : set → ((set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set X5 ) ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ X3 (λX8 : (set → set → set → set → set → set ∅ ) (setsum (Inj1 (Inj0 (setsum ∅ ∅ X5 X6 (λX8 : set ⇒ ∅ ) (setsum (setsum (setsum (Inj0 ∅ ∅ (setsum ∅ (setsum ∅ ∅ (Inj1 (Inj1 (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTtas4hGz4j1W9yRYWCajvWDc41r9BKTuE )
∀X0 : ((set → set → set → set → (set → set → (set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → set → set → set → set → set → ((set → set → ((set → set → set → (set → set → set → set → prop ∀X3 : ((set → set → set → set → set → set → set → (set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : (((set → set → set → set → set → set → set X3 (λX8 : set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj0 ∅ (Inj1 X10 ) (setsum (setsum (Inj1 (Inj0 ∅ (Inj1 ∅ ∅ ∅ ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set → (set → set → set → set → set → set X3 (λX8 : set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X11 X12 ) (Inj1 (setsum (X4 (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X5 (Inj0 ∅ (Inj0 (setsum ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ∈ Inj1 (Inj0 (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set (Inj1 (Inj0 X4 ∈ setsum (Inj1 ∅ X4 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X8 (Inj1 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 X10 ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ ∅ ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → (set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum X11 (X9 (λX12 : set ⇒ ∅ ) ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum X12 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ X10 ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ Inj0 (setsum X7 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 X9 ) X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ setsum ∅ (Inj1 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 (Inj0 X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set → set → (set → set → set → set X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 ∅ (Inj0 X9 ) X3 (λX8 : set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X9 ) (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ (setsum (Inj1 (setsum X4 (Inj1 ∅ (setsum ∅ (X7 ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set X0 (λX8 : set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X8 ) ) → (∀X4 : ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → set → set ∀X7 : set , (setsum ∅ (setsum X5 (Inj1 (Inj0 ∅ ∈ X6 (λX8 : (set → set → set Inj1 (setsum X7 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (X4 (λX8 : set → set X5 ) ∅ (λX8 : set ⇒ setsum ∅ ∅ ) ∅ → X0 (λX8 : set → set λX9 : set ⇒ setsum (setsum (Inj0 (Inj1 ∅ X7 (setsum (Inj0 ∅ (X6 (λX10 : (set → set → set setsum ∅ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) X3 (λX8 : set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X10 ) X7 (Inj1 (X4 (λX8 : set → set ∅ ) (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ X5 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRdPSQZo95uGrS7RgJqxi63A5StieC6hvB )
∀X0 : ((set → (set → set → set → set → set → (set → set → set → set → set → set → prop ∀X1 : ((((set → set → (set → set → set → (set → set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → set (setsum ∅ (Inj1 ∅ ∈ Inj1 (X7 (λX8 : set ⇒ setsum X6 (Inj0 ∅ ) X6 → X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (Inj1 (X5 ∅ (Inj1 ∅ X3 (λX8 : set ⇒ setsum (Inj1 ∅ X6 ) (Inj0 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X3 (λX8 : set ⇒ ∅ ) (X5 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (Inj0 ∅ ) (setsum (setsum ∅ (Inj1 (X7 (λX8 : set → set → set ∅ ) (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ X6 ∈ X5 (λX8 : (set → set → set → set Inj1 (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set → set (Inj0 ∅ ∈ Inj1 (Inj0 (X6 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) → X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ Inj0 (setsum ∅ X9 ) (Inj0 (setsum (setsum (X7 ∅ X5 (setsum ∅ (X4 (λX8 : (set → set → set → set ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum X7 ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (setsum (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj0 X6 (Inj0 ∅ ) (Inj1 X7 X1 (λX8 : ((set → set → (set → set → set → (set → set → set → set → set ∅ ) (setsum (Inj0 (X5 (Inj1 ∅ (setsum (setsum (Inj1 ∅ X4 (setsum (setsum ∅ ∅ X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : (set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X1 (λX8 : ((set → set → (set → set → set → (set → set → set → set → set Inj1 (X5 (λX9 : set ⇒ setsum X9 (X8 (λX10 : set → set λX11 : set → set ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum X7 ∅ ) (Inj1 X7 ∈ X7 ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → (set → set → set → set (Inj1 (setsum ∅ (Inj1 (X4 (λX8 : set ⇒ ∅ ) ∈ Inj1 (X7 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ Inj0 ∅ ) (setsum (setsum (setsum (Inj0 ∅ ∅ ∅ (X5 (Inj0 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → ((set → set → set → set (Inj1 (Inj0 (X5 ∅ ∈ Inj1 X6 → X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ X9 ) ∅ X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ X8 ∅ (λX12 : set ⇒ X9 ) (X10 ∅ (setsum (X10 ∅ ∅ (Inj0 ∅ ) (X7 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ Inj1 ∅ ) ∅ ) (λX8 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMH9f68A2C5vt4LGvkxBprUQGsBJ4nmuCRa )
∀X0 : (set → ((set → set → set → set → set → set → set → prop ∀X1 : (((set → set → set → set → set → set → (set → set → set → set → prop ∀X2 : ((set → set → (set → set → set → set → set → set → set → set → set → (set → (set → set → set → set → prop ∀X3 : (((((set → set → set → (set → set → set → set → set → (set → set → (set → set → set → (set → ((set → set → set → set → set → ((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : (((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → (set → set → set → set → ((set → set → set → set → set → set (setsum ∅ ∅ ∈ Inj0 (Inj1 (setsum (X6 ∅ (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X3 (λX8 : (((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set X9 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj1 (X9 (λX11 : set ⇒ ∅ ) ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ λX10 : set → set X7 (λX11 : (set → set → set λX12 : set → set λX13 : set ⇒ setsum (X12 ∅ (X11 (λX14 : set ⇒ ∅ ) ) (λX11 : set → set λX12 : set ⇒ Inj0 (Inj1 (X10 ∅ ) (Inj1 (setsum (setsum ∅ ∅ ∅ ) (Inj0 (X4 (Inj0 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 X8 ) ) → (∀X4 : set , ∀X5 : (set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → set → set ∅ ) (setsum X4 (setsum ∅ X6 (setsum (Inj1 ∅ ∅ X2 (λX8 : set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum X9 (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj1 (setsum ∅ ∅ ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : (set → set → ((set → set → set → set → set X2 (λX8 : set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : set → set → set X7 (λX10 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ X9 (setsum (Inj1 ∅ (Inj1 ∅ ∅ ) ) (Inj0 (setsum (X4 (λX8 : (set → set → set Inj0 ∅ ) ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ λX10 : set → set Inj0 ∅ ) (X7 (λX8 : set ⇒ ∅ ) X5 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set → set X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ λX10 : set → set setsum (setsum X9 (Inj0 (Inj1 ∅ (setsum (setsum (X10 ∅ (Inj1 ∅ (setsum (X10 ∅ (Inj1 ∅ ) (X7 ∅ (Inj1 (setsum ∅ (Inj0 ∅ ∅ X2 (λX8 : set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X11 ) (λX8 : set ⇒ λX9 : set → set → set setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set , (setsum (Inj0 (setsum ∅ ∅ ∅ ∈ setsum ∅ ∅ → X3 (λX8 : (((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set Inj0 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum X7 ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → set → set X7 ) X7 (setsum (X5 (λX8 : set ⇒ λX9 : set → set X6 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → set → set X8 ) X4 (setsum X4 (setsum (setsum X6 (setsum ∅ ∅ (Inj1 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMa7uDwCg9VqGyxLGMmEEDXnoK9rdrgDS2o )
∀X0 : (set → ((set → set → set → set → ((set → set → set → set → set → set → prop ∀X1 : (set → (set → (set → set → set → set → set → set → (set → set → ((set → set → (set → set → set → prop ∀X2 : ((set → (set → set → set → (((set → set → set → set → set → set → set → set → (set → set → prop ∀X3 : ((((set → set → set → set → set → set → set → set → ((set → set → set → prop (∀X4 : (set → set → set → set → (set → set → (set → set → set ∀X5 : ((set → set → set → ((set → set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) (setsum (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ X6 ∅ (λX9 : set → set λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ X8 ) ) X3 (λX8 : ((set → set → set → set → set → set → set Inj1 ∅ ) (λX8 : set → set Inj0 (Inj1 (X8 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → set → set setsum (Inj1 ∅ (setsum (setsum X6 (X5 ∅ (setsum X6 (X8 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set → set setsum ∅ (Inj1 (Inj1 ∅ ) X1 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ X10 X7 X10 ) (λX8 : set ⇒ setsum (setsum ∅ (Inj0 (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : set → set setsum (X8 X6 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 ∈ Inj1 (Inj1 (Inj0 (setsum ∅ ∅ X2 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ ∅ ) X5 (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : (((set → set → set → set → (set → set → set → set → set ∀X7 : set , (setsum (setsum (Inj1 (setsum ∅ ∅ (setsum (X6 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (X5 ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (setsum (Inj1 (Inj1 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj0 X7 → X2 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ X8 X10 (λX11 : set ⇒ setsum ∅ (Inj0 (setsum ∅ ∅ ) ) ∅ (λX8 : set ⇒ ∅ ) X1 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj1 ∅ ∈ X7 → X1 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj1 (setsum (setsum (X9 ∅ (λX11 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ X10 ) (λX8 : set ⇒ setsum X8 (Inj0 (X6 X5 ) (λX8 : set → set λX9 : set → set X8 (X8 (setsum (setsum ∅ ∅ (X9 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ setsum X6 X6 ) (λX8 : set → set λX9 : set → set ∅ ) False ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 (X5 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∈ Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set → set X9 (Inj0 ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : (set → set → set → set setsum (setsum (setsum ∅ ∅ (setsum (X10 (λX11 : set ⇒ ∅ ) ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ ∅ ) (X7 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : (set → set → set → set Inj0 ∅ ) (X4 X6 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKZMHw5mr3nxkzvFSsBaoQQoQ19U2UgPra )
∀X0 : (set → set → set → set → ((set → set → (set → set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → ((set → set → set → (set → set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : (set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set Inj0 (Inj1 (Inj0 ∅ ) (Inj1 ∅ X3 (λX8 : set ⇒ λX9 : set → set → set Inj1 (setsum ∅ (setsum ∅ X7 ) (setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set ∅ ) (setsum (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ ∅ ) ) (X4 X6 X5 (setsum ∅ (Inj1 (Inj1 ∅ (X4 (Inj1 X5 X5 ∈ setsum (setsum (Inj1 (setsum ∅ ∅ (Inj0 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X4 ∅ (X4 (Inj0 ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (setsum X4 (Inj1 (Inj0 (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∈ Inj0 (Inj1 (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) X4 → X3 (λX8 : set ⇒ λX9 : set → set → set Inj1 (Inj1 ∅ ) (setsum ∅ X4 X2 (λX8 : set → set setsum (Inj1 (X7 (setsum ∅ ∅ (setsum (Inj0 (setsum ∅ ∅ ∅ ) X6 ) → (∀X4 : (((set → set → set → set → ((set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set X2 (λX8 : set → set setsum (Inj1 ∅ (Inj0 (Inj0 (Inj0 ∅ ) (Inj0 (setsum X6 (X5 ∅ X2 (λX8 : set → set ∅ ) (Inj0 (setsum (setsum (Inj1 ∅ ∅ (setsum ∅ (Inj0 ∅ ) → (∀X4 : (set → (set → set → set → set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set (Inj1 (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 X8 ) (λX8 : set → set X5 ) ∈ Inj1 ∅ → X1 (λX8 : set ⇒ X6 ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → (set → set → set → set → set ∀X6 : set → (set → set → set ∀X7 : set → set → set (Inj1 (Inj0 (X7 (Inj1 ∅ (setsum ∅ ∅ ∈ X7 ∅ (X6 ∅ (λX8 : set ⇒ setsum X8 X8 ) → X1 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj0 (X10 (X8 ∅ (X10 (Inj1 (setsum ∅ ∅ ) X1 (λX8 : set ⇒ Inj1 (setsum (Inj0 ∅ (X7 (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X8 (setsum (setsum (setsum ∅ ∅ (X8 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , (Inj1 (X6 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) ∈ Inj1 (Inj1 (setsum X4 X7 → X1 (λX8 : set ⇒ setsum (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X10 (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum (setsum (setsum ∅ ∅ X5 X5 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) X7 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMF79gCe6WhvreoKQayVkRUxXrgSKoAtikh )
∀X0 : (set → ((set → set → set → set → (set → set → (set → set → set → ((((set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → (((set → set → set → set → set → (set → set → set → set → prop ∀X2 : ((set → (set → set → (set → set → set → set → set → (((set → set → set → set → set → set → set → (set → set → prop ∀X3 : ((set → set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum (setsum (X4 ∅ (setsum ∅ ∅ X6 ∈ Inj1 (setsum (setsum (setsum ∅ ∅ X7 (setsum ∅ (Inj1 ∅ → X3 (λX8 : set → set → set X6 ) (λX8 : set ⇒ Inj0 (Inj0 X7 ) (Inj1 (Inj1 X7 ∅ ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X7 ∅ ∈ Inj1 (Inj0 (setsum X6 (setsum ∅ ∅ → X3 (λX8 : set → set → set ∅ ) (λX8 : set ⇒ ∅ ) X6 ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set → set setsum (setsum (setsum (X9 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) (Inj1 ∅ (setsum ∅ (Inj0 ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : set → (set → set → (set → set → set → set X8 (Inj0 (X6 (λX9 : set ⇒ λX10 : set → set X8 ∅ (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (λX9 : set ⇒ X7 ) (λX9 : set ⇒ ∅ ) (Inj1 (X8 (X6 (λX9 : set ⇒ λX10 : set → set ∅ ) (λX9 : set ⇒ X7 ) (λX9 : set ⇒ ∅ ) (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ Inj0 (Inj1 ∅ ) (Inj1 (setsum (X6 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → set → set ∀X7 : set , (X6 (λX8 : set → set λX9 : set → set Inj0 (Inj1 ∅ ) (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ (X6 (λX8 : set → set λX9 : set → set ∅ ) (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 (Inj1 ∅ ∈ setsum X5 ∅ → X2 (λX8 : set → (set → set → (set → set → set → set setsum (X8 (setsum (setsum ∅ ∅ X7 (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ X9 ) X5 (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ Inj0 (X8 (λX10 : set ⇒ X7 ) ∅ ) (Inj1 ∅ (λX8 : set ⇒ setsum X8 ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set → set X9 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set Inj0 (setsum (Inj1 (Inj1 ∅ (X6 (λX10 : set → set λX11 : set → set ∅ ) (X6 (λX10 : set → set λX11 : set → set ∅ ) ∅ ∅ (Inj1 ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → ((set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : set → set → set Inj1 (Inj1 (X8 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (X6 (λX9 : set → set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set X7 ) (λX9 : set ⇒ ∅ ) ) (X6 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set setsum (Inj0 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 (setsum (setsum ∅ (setsum ∅ ∅ ∅ X1 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 (λX12 : set ⇒ Inj0 (Inj1 (Inj1 ∅ ) (Inj0 (X10 X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set → set X1 (λX8 : set ⇒ setsum ∅ X8 ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ (X6 ∅ ∅ ∈ X5 ) → (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set → (set → set → set → set (Inj0 (X7 (setsum (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (Inj1 ∅ (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (Inj1 ∅ ) ∅ ∈ Inj0 ∅ → X2 (λX8 : set → (set → set → (set → set → set → set ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum X6 X6 ) ∅ (λX8 : set ⇒ X8 ) X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set → set setsum (Inj1 (X10 (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , (Inj1 (X5 (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj1 (Inj0 ∅ (λX8 : set ⇒ Inj1 ∅ ) ∅ ∈ X7 → X0 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set → set ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set Inj1 ∅ ) X3 (λX8 : set → set → set X5 (Inj1 (setsum ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) (λX9 : set ⇒ Inj1 ∅ ) ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ (setsum (setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ (X5 (setsum ∅ ∅ (Inj1 ∅ (λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) ) (Inj0 ∅ ) (setsum (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ∅ (X5 ∅ (setsum X7 (setsum (setsum ∅ ∅ ∅ (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (setsum (setsum ∅ ∅ (Inj1 X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFBwTtvgUpj6yUa7LycLh78mmBuHHNT6er )
∀X0 : ((set → ((set → set → set → set → set → (set → set → ((set → set → set → (set → set → set → set → prop ∀X1 : (((set → set → (set → set → set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → (set → set → set → set → set → (((set → set → set → set → set → prop ∀X3 : ((set → set → (set → set → set → set → ((set → set → set → set → set → set → (set → set → set → prop (∀X4 : (set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X3 (λX8 : set → set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ setsum (X7 ∅ (Inj1 (Inj1 ∅ (λX11 : set ⇒ X8 (Inj1 ∅ (X9 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) (λX12 : set ⇒ X9 (λX13 : set ⇒ λX14 : set ⇒ ∅ ) ) (setsum ∅ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , (X5 (setsum (X6 ∅ (Inj0 (setsum ∅ ∅ ∈ setsum ∅ (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X3 (λX8 : set → set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X0 (λX8 : set → ((set → set → set → set ∅ ) (λX8 : set ⇒ setsum X7 (X5 (X6 (setsum ∅ ∅ ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X9 (X8 (Inj1 (Inj1 ∅ X10 ) ) → (∀X4 : set → (set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → (set → set → set X8 (λX9 : set ⇒ setsum X7 ∅ ) (λX9 : set ⇒ X9 ) ) (λX8 : set ⇒ Inj0 ∅ ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (X5 ∅ (Inj1 (Inj1 (Inj0 ∅ (λX8 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj1 (setsum X7 (Inj0 ∅ ∈ X5 → X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X11 X10 ) X4 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ ∅ ) (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) X0 (λX8 : set → ((set → set → set → set Inj1 (setsum (Inj0 (Inj0 ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ setsum (X8 ∅ ∅ (X9 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set (Inj0 (setsum (X7 (X6 ∅ ∅ ∅ ∈ X4 → X1 (λX8 : (set → set → (set → set → set setsum (X7 (Inj0 (setsum ∅ ∅ (X6 ∅ (X8 (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ X5 ) ) → (∀X4 : (set → set → set → (set → set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → (set → set → set ∅ ) (λX8 : set ⇒ setsum (X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) X1 (λX8 : (set → set → (set → set → set X8 (λX9 : set ⇒ Inj1 (Inj0 ∅ ) (λX9 : set ⇒ X8 (λX10 : set ⇒ Inj0 (Inj0 ∅ ) (λX10 : set ⇒ ∅ ) ) ) (λX8 : set ⇒ setsum X5 X7 ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set → ((set → set → set → set ∅ ) (λX8 : set ⇒ X6 ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → ((set → set → set → set ∅ ) (λX8 : set ⇒ Inj0 X6 ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJbQj6LBnPpv6Z5wFBSMre6N2bP9mStuas )
∀X0 : ((set → set → (set → (set → set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → (((set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → (set → set → prop ∀X3 : (set → set → (set → set → set → set → set → set → ((((set → set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set → set (setsum (setsum (X7 (Inj1 ∅ (setsum (setsum ∅ ∅ ∅ (X5 ∅ ∅ ∈ setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ ) (λX8 : ((set → set → set → (set → set → set X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ) ) ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → set → (set → set → set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : ((set → set → set → (set → set → set ∅ ) X0 (λX8 : set → set λX9 : set → (set → set → set → set λX10 : set → set ∅ ) (Inj1 (setsum ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → (set → set → set ∀X7 : (set → set → set → set → set → set (setsum X4 ∅ ∈ X7 (λX8 : set ⇒ Inj0 (Inj1 (setsum ∅ ∅ ) (Inj0 (setsum (Inj1 ∅ ∅ X4 (setsum ∅ (Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ X9 ) (λX8 : ((set → set → set → (set → set → set Inj1 (setsum (setsum ∅ (Inj0 ∅ ∅ ) X2 (λX8 : set ⇒ setsum ∅ (setsum (setsum X8 X8 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ Inj1 (Inj0 (Inj1 X5 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (Inj0 ∅ ) (Inj1 ∅ (λX8 : (set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) X7 ) X7 ) → (∀X4 : ((set → set → set → (set → set → set → ((set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → (set → set → set ∀X7 : set → ((set → set → set → set → set → set → set X1 (λX8 : set ⇒ Inj0 ∅ ) ∅ (λX8 : (set → set → set → set λX9 : set → set X9 (Inj1 (Inj1 (X8 (λX10 : set ⇒ ∅ ) ∅ ) (setsum (setsum (setsum ∅ ∅ ∅ (setsum (X7 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ ∅ (X7 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ (Inj1 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : set → set λX9 : set → (set → set → set → set λX10 : set → set setsum (setsum (Inj1 (X10 ∅ (Inj0 (Inj0 ∅ X7 ) ∅ ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set λX9 : set → (set → set → set → set λX10 : set → set Inj0 (X8 (Inj0 ∅ ) ∅ X1 (λX8 : set ⇒ X5 (λX9 : set ⇒ X8 ) (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ X10 ) ) (Inj0 (Inj0 X6 (λX8 : (set → set → set → set λX9 : set → set X9 ∅ ) X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMH6d6FpiCs6CFbwfXuaM98M6KrNAtAawCK )
∀X0 : (set → set → ((((set → set → set → set → set → ((set → set → set → set → set → set → set → set → set → prop ∀X1 : (set → (set → set → set → ((((set → set → set → set → (set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → ((set → set → set → set → set → set → set → (set → set → set → (set → set → (set → set → prop ∀X3 : ((((set → set → set → set → (set → set → set → set → set → (((set → set → set → set → set → set → set → set → set → set → prop (∀X4 : ((set → set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set → set → set → set λX9 : set → set Inj0 (X6 ∅ ) (λX8 : set ⇒ X6 (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj1 (Inj0 (Inj0 (Inj1 ∅ ) X3 (λX8 : ((set → set → set → set → (set → set → set X8 (λX9 : set → set → set setsum (Inj1 (Inj0 ∅ (X9 (setsum ∅ ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ X8 (λX10 : set → set → set X10 (Inj1 ∅ ∅ ) (λX10 : set ⇒ X9 ) ) ) (X6 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (setsum (Inj1 ∅ (Inj0 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ ∅ (setsum ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → (set → set → set setsum ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) (setsum (setsum (setsum ∅ ∅ X7 (Inj1 (X8 (λX11 : set ⇒ ∅ ) ∅ ) (setsum ∅ ∅ ∅ X6 (Inj0 X4 ∈ Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → (set → set → set setsum ∅ ∅ ) (setsum X4 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) ∅ (setsum X4 ∅ X4 X2 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set → set → set → set λX9 : set → set X6 ) (λX8 : set ⇒ setsum (X5 (λX9 : set → set → set setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X8 ) X7 ) (λX8 : set ⇒ setsum (setsum ∅ (Inj1 X6 (Inj0 (Inj1 X8 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set → set → set → set λX9 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (X5 (λX9 : (set → set → set ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ (Inj0 X7 ) (Inj1 X6 ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set → set ∀X7 : set , (Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ∈ X4 → X1 (λX8 : set ⇒ λX9 : set → set Inj1 (setsum ∅ (setsum X7 ∅ ) (λX8 : ((set → set → set → set λX9 : set → set → set Inj1 X7 ) X1 (λX8 : set ⇒ λX9 : set → set X9 (X9 ∅ ) (λX8 : ((set → set → set → set λX9 : set → set → set Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : ((set → set → set → set λX9 : set → set → set setsum (X9 ∅ ∅ ∅ ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set → set X6 (λX10 : set → set Inj0 ∅ ) ) (X7 (Inj0 (Inj0 (setsum ∅ ∅ (Inj0 (setsum ∅ (Inj1 (setsum ∅ ∅ (Inj0 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set → set setsum (X8 (λX10 : set → set λX11 : set ⇒ X9 (λX12 : set ⇒ ∅ ) (setsum ∅ ∅ ) (Inj1 (X7 (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 ∅ (X7 (X7 (setsum (setsum ∅ ∅ (Inj0 ∅ (X5 (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ ∅ ∅ (Inj0 ∅ (X5 (Inj1 (setsum (Inj1 ∅ (X5 ∅ ∅ ∅ ∅ X6 (X7 (Inj1 (setsum ∅ ∅ (Inj0 (Inj1 ∅ ∅ (Inj0 (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKroo539dUAksoySwXR2nd5An9BYHwvnZv )
∀X0 : (set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → ((((set → set → set → set → set → set → set → prop ∀X2 : ((set → (set → set → set → set → set → set → (((set → set → set → set → (set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → (set → set → set → set → (((set → set → set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set → ((set → set → set → set → set (X4 ∈ X5 → X3 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set → set setsum (X9 (X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum ∅ (X9 ∅ ∅ (X8 (λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 ∅ ) ) X3 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum X10 X12 (setsum X10 (Inj1 X12 ) (λX8 : (set → set → set → set λX9 : set → set → set setsum (setsum (Inj1 (Inj1 ∅ (X9 (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (Inj1 (Inj1 ∅ ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : ((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum X10 (Inj1 ∅ ) (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) False ) → (∀X4 : set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → set X2 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ Inj1 (setsum X12 ∅ ) ) (λX8 : (set → set → set → set λX9 : set → set → set Inj0 (X8 (λX10 : set ⇒ λX11 : set ⇒ Inj0 (X9 ∅ ∅ ) ) ) → (∀X4 : (((set → set → set → (set → set → set → set → set → set → set ∀X5 : (set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum X7 X6 ∈ Inj0 (setsum (setsum (Inj1 ∅ (Inj0 ∅ (setsum X7 (Inj1 ∅ → X2 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set → set X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) X2 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : (set → set → set → set λX9 : set → set → set setsum X7 (setsum ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set → set ∀X7 : (set → set → set → set (X5 X4 ∈ X4 → X2 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj0 X10 ) (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set setsum (X7 (λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) ) ∅ ) (Inj0 ∅ ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj0 (Inj1 ∅ ) (λX8 : ((set → set → set → set → set setsum ∅ X5 ) (Inj1 (Inj0 (Inj0 (Inj0 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X9 ∅ (setsum (X8 (setsum ∅ ∅ (λX11 : set ⇒ setsum ∅ ∅ ) (setsum X7 X10 ) (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) X0 (λX8 : set ⇒ X5 ) (setsum (setsum ∅ (setsum X4 ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set → set X0 (λX8 : set ⇒ Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMd8n7gVeqFDzqA8fJi2v5yZzXqksninZfc )
∀X0 : (set → set → ((set → set → ((set → set → set → set → set → (set → set → prop ∀X1 : ((set → ((set → set → set → set → set → ((set → set → set → (set → set → set → (set → set → set → set → (set → set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → (set → set → set → set → (set → set → set → set → (((set → set → set → set → set → ((set → set → set → prop ∀X3 : ((set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → set → set → set → set X3 (λX8 : set → set setsum ∅ (Inj1 (Inj0 (Inj1 ∅ ) ∅ (λX8 : set → set setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : (set → set → set (Inj0 ∅ ∈ Inj1 (Inj1 ∅ → X3 (λX8 : set → set Inj1 ∅ ) (Inj0 ∅ (λX8 : set → set X8 (Inj1 (setsum (setsum ∅ ∅ (X8 ∅ ) X2 (λX8 : (((set → set → set → set → set λX9 : set → set → set → set λX10 : set → set X9 (Inj1 (X10 ∅ ∅ (Inj1 (Inj0 (setsum ∅ ∅ ) (Inj0 X5 (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj1 (X8 (λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) ) (X6 (X8 (λX10 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set → set ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set → set X2 (λX8 : (((set → set → set → set → set λX9 : set → set → set → set λX10 : set → set Inj0 ∅ ) (Inj1 (setsum (setsum (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ (setsum (X4 ∅ (setsum ∅ ∅ (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj1 X6 (Inj1 (X8 (λX10 : set ⇒ ∅ ) ) (λX8 : set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set → set ∀X7 : set → set → set (X4 ∈ setsum ∅ (X6 (λX8 : (set → set → set setsum ∅ (Inj1 ∅ ) X4 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) (setsum (Inj1 ∅ ∅ → X2 (λX8 : (((set → set → set → set → set λX9 : set → set → set → set λX10 : set → set setsum ∅ (X10 (Inj0 (Inj0 ∅ ) (X5 (setsum (Inj1 (setsum ∅ ∅ (X5 (X7 ∅ ∅ (setsum ∅ ∅ ∅ (λX8 : (set → set → set λX9 : set ⇒ setsum (X6 (λX10 : (set → set → set Inj1 (setsum ∅ ∅ ) ∅ (λX10 : set ⇒ ∅ ) (Inj1 ∅ (Inj1 (setsum (Inj1 ∅ ∅ ) (λX8 : set → set X6 (λX9 : (set → set → set setsum (Inj0 (setsum ∅ ∅ ∅ ) (X7 (X6 (λX9 : (set → set → set setsum ∅ ∅ ) (X8 ∅ (λX9 : set ⇒ ∅ ) ∅ (Inj1 (setsum ∅ ∅ (λX9 : set ⇒ Inj0 (Inj1 (Inj0 ∅ ) (setsum (X5 ∅ (X7 ∅ ∅ (Inj0 ∅ ) X1 (λX8 : set → ((set → set → set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set setsum (X8 (setsum (setsum ∅ ∅ (Inj1 ∅ (λX11 : set → set λX12 : set ⇒ setsum (X11 ∅ (X9 (λX13 : set ⇒ λX14 : set ⇒ ∅ ) (λX13 : set ⇒ ∅ ) ) (setsum (Inj1 (X9 (λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ Inj0 (Inj0 (X7 (Inj0 ∅ ∅ ) (setsum X4 (Inj0 (Inj1 (X7 ∅ ∅ (setsum (Inj0 ∅ ∅ (setsum (Inj1 (X7 (setsum ∅ ∅ (X6 (λX8 : (set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ (setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ Inj1 (setsum (setsum (Inj1 ∅ (X5 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ (Inj1 ∅ ) (Inj1 ∅ (setsum (Inj0 (setsum ∅ ∅ ∅ (setsum ∅ ∅ X7 X1 (λX8 : set → ((set → set → set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ ∅ ) X4 (Inj0 ∅ (X6 (λX8 : set → set → set ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : set → ((set → set → set → set → set (Inj0 X4 ∈ X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ X8 ) → X1 (λX8 : set → ((set → set → set → set → set λX9 : (set → set → set → (set → set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ ∅ ∅ (X7 (setsum (X7 ∅ (λX8 : set → set Inj0 ∅ ) (Inj1 ∅ X4 (λX8 : set → set setsum ∅ ∅ ) (X7 ∅ (λX8 : set → set setsum ∅ (setsum ∅ ∅ ) (Inj1 (Inj0 ∅ X0 (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : (set → set → set → set X9 (λX10 : set ⇒ Inj1 ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → (set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , (setsum (X5 (λX8 : (set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ ∅ ) ∅ (X5 (λX8 : (set → set → set λX9 : set ⇒ X6 (λX10 : set → set → set X9 ) ) (λX8 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum (Inj1 ∅ ∅ ∈ Inj0 X7 → X0 (λX8 : set ⇒ Inj1 (Inj0 X7 ) (λX8 : set → set λX9 : (set → set → set → set Inj0 (Inj0 (setsum (X6 (λX10 : set → set → set ∅ ) (setsum ∅ ∅ ) (λX8 : set ⇒ setsum (setsum X7 (setsum ∅ ∅ (X6 (λX9 : set → set → set setsum X8 (X9 ∅ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : ((set → set → set → set X0 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set → set λX9 : (set → set → set → set X8 (X8 ∅ ) (λX8 : set ⇒ X5 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYUvVjE9dP9J3rr2NrpgEVZFssQMJbRJXh )
∀X0 : (((((set → set → set → set → set → set → set → set → ((set → set → ((set → set → set → set → set → prop ∀X1 : (((set → set → set → set → set → set → prop ∀X2 : (set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : (set → set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X5 (X4 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ X7 ) ∅ (λX8 : set ⇒ setsum ∅ (Inj0 ∅ ) (Inj0 (setsum (X4 (X4 ∅ (Inj1 X5 ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ Inj0 X7 ) (X4 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum X5 X5 ) X7 False ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , (Inj0 (setsum (setsum ∅ ∅ (Inj1 (Inj1 ∅ ∈ setsum ∅ (Inj0 (X6 (setsum ∅ ∅ (λX8 : set → set ∅ ) → X2 (λX8 : set ⇒ Inj0 (setsum (X6 (setsum ∅ ∅ (λX9 : set → set ∅ ) X7 ) X7 (λX8 : set → set → set λX9 : set → set setsum (X8 (X9 (Inj1 ∅ (X9 (X9 ∅ (X8 (X9 (X9 ∅ (setsum (X6 ∅ (λX10 : set → set ∅ ) (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) X7 (λX8 : set → set → set λX9 : set → set setsum (Inj0 ∅ X7 ) False ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set → set (Inj0 ∅ ∈ Inj1 (setsum (Inj1 (setsum ∅ ∅ (setsum X5 X5 → X0 (λX8 : (((set → set → set → set → set → set → set X6 (X7 ∅ (λX9 : set → set λX10 : set ⇒ Inj0 (X7 (setsum ∅ ∅ ) ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) X1 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (X7 (X6 (Inj1 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) ) → (∀X4 : ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj0 ∅ (setsum (setsum (Inj1 ∅ ∅ ∅ ) (setsum (Inj0 (setsum (X6 ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ X5 (Inj1 (Inj0 ∅ X0 (λX8 : (((set → set → set → set → set → set → set setsum (Inj0 (setsum (X6 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (X6 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ setsum (X8 X7 (setsum (setsum ∅ ∅ (Inj0 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : (((set → set → set → set → set → set → set setsum ∅ (Inj0 (Inj0 (Inj1 ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ setsum (Inj0 (setsum (X9 (λX11 : set ⇒ ∅ ) (X9 (λX11 : set ⇒ ∅ ) (X9 (λX11 : set ⇒ Inj1 (Inj1 ∅ ) ) X0 (λX8 : (((set → set → set → set → set → set → set setsum (Inj0 (X5 (setsum ∅ ∅ (X8 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ X7 (Inj0 (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set → set setsum (setsum (Inj0 (Inj1 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ (X8 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) X3 (λX8 : set ⇒ ∅ ) (X4 (Inj1 ∅ (λX8 : set ⇒ setsum (Inj0 ∅ ∅ ) (Inj1 X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVrBmfokdfnGERAeABKGxqPL1iEKTYTeBi )
∀X0 : (set → (set → (set → set → set → set → set → set → ((((set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X3 : ((set → set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : ((set → set → set → set → set (Inj1 (Inj0 (setsum (setsum ∅ ∅ ∅ ∈ X4 (λX8 : set ⇒ λX9 : set ⇒ X9 ) → X3 (λX8 : set → set Inj1 (X7 (λX9 : set → set → set setsum (setsum ∅ ∅ (Inj1 ∅ ) ) (Inj1 (setsum ∅ (setsum (X7 (λX8 : set → set → set ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : ((set → set → set → (set → set → set → set → set X3 (λX8 : set → set setsum ∅ (setsum ∅ (setsum ∅ (setsum ∅ ∅ ) ∅ X1 (λX8 : set ⇒ X5 X6 (setsum ∅ ∅ ) (Inj0 (X7 (λX8 : set → set → set λX9 : set → set X6 ) (setsum (setsum ∅ ∅ (Inj0 ∅ (setsum (setsum X4 ∅ (setsum (setsum X6 ∅ (setsum (setsum ∅ ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → set X2 (λX8 : (set → (set → set → set → set → set λX9 : set → set λX10 : set → set → set ∅ ) (setsum (setsum ∅ (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set λX9 : set → set λX10 : set → set → set Inj0 (X10 (Inj1 ∅ (X8 (λX11 : set ⇒ λX12 : set → set λX13 : set ⇒ ∅ ) ) X7 (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (X6 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj1 X7 ) ∈ X4 ) → (∀X4 : (set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (Inj1 ∅ ∈ Inj1 (setsum (setsum X6 (setsum ∅ ∅ (setsum ∅ (X4 (λX8 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ setsum X7 (Inj0 ∅ ) X7 (setsum ∅ ∅ ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → (set → set → set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ setsum ∅ (Inj1 ∅ ) (Inj1 (X7 (Inj0 ∅ ∅ X1 (λX8 : set ⇒ setsum (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ X5 ) (X4 (λX8 : set → set → set X5 ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) (X7 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (X7 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set λX9 : set → set λX10 : set → set → set ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj0 X10 ) (λX8 : ((set → set → set → set → set X6 ) ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj0 (X7 X8 (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 ∅ (X9 (setsum ∅ ∅ (λX11 : set ⇒ X8 ) (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set setsum (Inj1 ∅ (setsum (setsum (X7 ∅ ∅ ∅ ∅ ∅ ∅ ) X3 (λX8 : set → set X8 (Inj1 ∅ ) X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZgWmBxdpCkusb3TJhayt3r7NrnYFbcM3J )
∀X0 : (((set → (set → set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → set → prop ∀X1 : ((set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → ((set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ (Inj0 (X5 (λX8 : set ⇒ Inj0 ∅ ) ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ ∅ ) X6 ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (X5 (X5 X7 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (Inj0 ∅ ∈ Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : ((set → set → (set → set → set → ((set → set → set → set → set ∀X7 : set , (X5 ∈ setsum (setsum ∅ X7 ∅ → X3 (λX8 : set ⇒ Inj1 (X6 (λX9 : set → set λX10 : set → set Inj0 (Inj1 ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (X9 ∅ (Inj1 ∅ ) ) ∅ X2 (λX8 : set ⇒ setsum (Inj0 X5 ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → ((set → set → set → set → set X2 (λX8 : set ⇒ setsum ∅ (X7 (λX9 : set → set → set λX10 : set ⇒ ∅ ) (λX9 : set → set setsum (setsum ∅ ∅ X8 ) ∅ ) (λX8 : set ⇒ setsum ∅ (setsum X8 X6 ) (λX8 : set → set setsum (Inj0 (setsum (X8 ∅ (setsum ∅ ∅ (setsum (X7 (λX9 : set → set → set λX10 : set ⇒ X8 ∅ ) (λX9 : set → set X7 (λX10 : set → set → set λX11 : set ⇒ ∅ ) (λX10 : set → set ∅ ) ∅ ) (X5 ∅ (Inj0 (setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj0 (Inj0 (setsum ∅ ∅ ) (setsum (Inj0 (Inj1 (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ X1 (λX8 : set → set → set → set setsum (setsum (X5 (λX9 : set ⇒ X9 ) ∅ (setsum (Inj1 (setsum ∅ ∅ (setsum (X6 ∅ (setsum ∅ ∅ ) (Inj1 (setsum (Inj0 (setsum ∅ ∅ ∅ ) → (∀X4 : (set → (set → set → set → set → ((set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set X1 (λX8 : set → set → set → set Inj0 ∅ ) ∅ False ) → (∀X4 : ((set → set → (set → set → set → set → set ∀X5 : set → set → set ∀X6 : ((set → set → set → set ∀X7 : set → set → set X1 (λX8 : set → set → set → set Inj0 ∅ ) (setsum (setsum (Inj1 (Inj1 ∅ (Inj0 (Inj0 ∅ ∅ X0 (λX8 : (set → (set → set → set → set → ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set → set setsum (setsum (Inj1 (X9 ∅ ∅ (Inj0 (setsum ∅ ∅ X8 ) ) → (∀X4 : set → set → set ∀X5 : (set → set → set → set → set ∀X6 : set → set ∀X7 : (set → set → set → set → set X0 (λX8 : (set → (set → set → set → set → ((set → set → set → set → set X6 ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj0 (X9 (X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X10 ) (Inj1 (Inj1 ∅ ) X0 (λX8 : (set → (set → set → set → set → ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set → set Inj0 (Inj0 (Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcPhJdigfeyQbMWFssEmtH3rttAmBzmYhj )
∀X0 : (set → set → ((((set → set → set → set → set → set → (set → set → set → prop ∀X1 : (set → (set → set → set → (set → set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → set → ((set → set → set → set → set → set → set → (set → set → set → set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → ((set → set → set → set → set → set → set λX9 : set → set → set → set setsum ∅ ∅ ) X6 (Inj0 (Inj0 X4 (λX8 : set → set X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set → set → set X3 (λX8 : ((set → set → set → set → set → ((set → set → set → set → set → set → set λX9 : set → set → set → set Inj1 (Inj1 (setsum (Inj0 ∅ (Inj1 ∅ ) (Inj0 ∅ (setsum X4 (setsum (setsum (setsum ∅ ∅ ∅ (X6 ∅ (λX8 : set → set ∅ ) False ) → (∀X4 : set → ((set → set → set → (set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set , (Inj1 (X6 (λX8 : set ⇒ X7 ) ∈ X7 → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum (setsum X8 X7 (Inj0 (setsum (setsum ∅ ∅ (X6 (λX10 : set ⇒ ∅ ) ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum X5 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 X8 ) X0 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set X9 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set → set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set Inj0 (Inj0 (X9 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (setsum ∅ (X5 X4 (λX8 : set → set λX9 : set ⇒ Inj0 (Inj0 ∅ ) ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set setsum (Inj0 ∅ (setsum ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ X7 ) (Inj1 (Inj0 ∅ X0 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set setsum X9 (setsum (setsum (Inj1 ∅ ∅ X9 ) ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ setsum ∅ (setsum ∅ X8 ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set X0 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) (Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ∈ setsum (Inj0 (setsum ∅ ∅ (Inj0 (Inj1 (X7 (λX8 : (set → set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKuvQKTQNbUGTBTCmueUf1MfDFybz8Fwr1 )
∀X0 : ((set → ((set → set → set → set → set → (set → set → prop ∀X1 : (((((set → set → set → set → set → set → set → (((set → set → set → (set → set → set → prop ∀X2 : (set → set → (set → set → prop ∀X3 : (set → (((set → set → set → set → (set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , (X4 ∈ Inj1 (Inj1 X4 → X0 (λX8 : set → ((set → set → set → set setsum (Inj1 (setsum ∅ (Inj0 ∅ ∅ ) (λX8 : set ⇒ setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum (Inj0 ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ X9 (λX11 : set → set λX12 : set ⇒ setsum X12 (Inj0 (setsum ∅ ∅ ) (λX11 : set ⇒ Inj0 X11 ) (setsum ∅ (Inj0 ∅ ) (λX8 : set → set → set setsum (Inj1 ∅ (setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : (set → (set → set → set → set → set (Inj1 (Inj1 (setsum (X4 (λX8 : (set → set → set → set λX9 : set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∈ setsum (Inj0 X5 (Inj0 (setsum X5 (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set → set → set setsum (X8 X5 (Inj1 (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 X9 ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) ) X2 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set → set ∀X7 : (set → (set → set → set → ((set → set → set → set → set X2 (λX8 : set ⇒ Inj1 (X7 (λX9 : set ⇒ λX10 : set → set setsum (setsum ∅ ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (Inj1 ∅ X8 ) ) (λX8 : set ⇒ ∅ ) (Inj0 (setsum (setsum ∅ X4 (X7 (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ∈ Inj1 (setsum (setsum ∅ X4 (X7 (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set (Inj1 (setsum ∅ (Inj1 ∅ ∈ X6 → X1 (λX8 : (((set → set → set → set → set → set ∅ ) (λX8 : (set → set → set λX9 : set → set setsum (setsum X6 ∅ (X9 (Inj1 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → ((set → set → set → (set → set → set X1 (λX8 : (((set → set → set → set → set → set setsum X5 ∅ ) (λX8 : (set → set → set λX9 : set → set X6 ) (Inj0 (setsum ∅ ∅ ∈ Inj0 ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (Inj0 ∅ X5 ∈ X6 (Inj1 X5 → X2 (λX8 : set ⇒ setsum (Inj1 (Inj0 ∅ (Inj0 (Inj0 (Inj1 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) X0 (λX8 : set → ((set → set → set → set X8 (Inj1 (setsum (Inj1 ∅ ∅ (λX9 : set → set Inj0 (setsum (Inj0 ∅ ∅ ) ) (λX8 : set ⇒ setsum (setsum ∅ X5 (setsum ∅ (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 X7 (setsum (setsum ∅ ∅ (X4 X6 (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) ∈ Inj1 (setsum (Inj1 ∅ X7 → X0 (λX8 : set → ((set → set → set → set X8 X6 (λX9 : set → set ∅ ) ) (λX8 : set ⇒ X8 ) X0 (λX8 : set → ((set → set → set → set ∅ ) (λX8 : set ⇒ X7 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPD5vEvEp8tPmMsGFq42YjHsTT19UA9tke )
∀X0 : (((set → (set → set → set → set → set → (set → set → set → set → set → (set → set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → (set → ((set → set → set → set → prop ∀X2 : ((set → set → set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : (set → (set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → set X3 (λX8 : set ⇒ ∅ ) (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ setsum (setsum (X7 ∅ (Inj0 (setsum ∅ ∅ ∅ ) ∅ (Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ∈ Inj0 (X5 (λX8 : set → set → set λX9 : set → set Inj1 (X7 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 X4 ∈ X4 → X0 (λX8 : (set → (set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ (setsum ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) ∅ (Inj0 (setsum (Inj0 (X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ X9 ) X2 (λX8 : set → set → set → set → set setsum (setsum (Inj1 (Inj0 ∅ (X8 ∅ X6 (Inj0 ∅ (setsum ∅ ∅ ∅ ) X6 ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ∈ Inj1 (X5 (setsum (X5 ∅ ∅ (Inj0 ∅ (setsum X7 (X5 ∅ ∅ → X2 (λX8 : set → set → set → set → set Inj0 (Inj1 (Inj1 X6 ) ∅ X2 (λX8 : set → set → set → set → set X7 ) (setsum X7 ∅ ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (X7 (setsum (Inj1 (X7 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) X5 (λX8 : set → set λX9 : set ⇒ Inj0 (Inj1 X9 ) ∈ setsum (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) X5 (X4 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 ∅ ) (Inj1 (Inj1 ∅ → X1 (λX8 : set ⇒ Inj1 X6 ) (λX8 : set ⇒ λX9 : (set → set → set setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set → set → set ∀X6 : set → set ∀X7 ∈ Inj0 (X6 ∅ X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set Inj1 ∅ ) X3 (λX8 : set ⇒ setsum (setsum ∅ (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) (Inj1 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : (set → (set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ ∅ ) ∅ (X4 (X4 (X7 ∅ (λX8 : set → set λX9 : set ⇒ setsum (Inj1 X6 (setsum ∅ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set , X0 (λX8 : (set → (set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum X12 (setsum (X11 (Inj0 ∅ (setsum ∅ ∅ ) (Inj1 ∅ (Inj0 (Inj0 (Inj1 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ setsum (setsum (X8 (Inj1 ∅ (setsum X9 (setsum ∅ ∅ (Inj0 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJjfsWhaGrxYK8GnRvxtbHmE5oi1FsaA7M )
∀X0 : (set → set → (set → ((set → set → set → (set → set → set → set → prop ∀X1 : (((set → set → set → set → set → (set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → (set → set → (((set → set → set → set → set → prop ∀X3 : (set → set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) (setsum (Inj0 (setsum (setsum ∅ ∅ (X5 (λX8 : (set → set → set → set ∅ ) ∅ ∅ ∅ (setsum (Inj0 (X5 (λX8 : (set → set → set → set ∅ ) ∅ ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : (((set → set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) ∅ X0 (λX8 : set ⇒ setsum (setsum (X6 (λX9 : (set → set → set → set setsum ∅ ∅ ) ∅ (setsum X8 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ Inj0 (X9 (λX12 : set ⇒ ∅ ) ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X2 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (X6 ∅ ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) (λX8 : (set → set → set → set X8 (λX9 : set ⇒ Inj1 ∅ ) ∅ ) ) → (∀X4 : (set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set X7 ) (λX8 : set ⇒ setsum (setsum (setsum ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ X8 (setsum X7 (setsum X7 (setsum ∅ ∅ ) (λX8 : (set → set → set → set Inj1 X7 ) False ) → (∀X4 : (set → set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set setsum (setsum ∅ ∅ (setsum X6 (setsum (Inj1 ∅ (X5 ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ (Inj1 (setsum X7 ∅ ) (λX8 : (set → set → set → set setsum ∅ ∅ ) X1 (λX8 : (set → set → set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ setsum (Inj0 (Inj0 (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set → ((set → set → set → set X1 (λX8 : (set → set → set → set → set → (set → set → set setsum (X8 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) (X7 ∅ (λX9 : set → set X9 ∅ ) (λX9 : set ⇒ ∅ ) (Inj1 ∅ ) (λX8 : set ⇒ X7 X8 (λX9 : set → set Inj0 (Inj1 ∅ ) ) X2 (λX8 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set setsum ∅ (Inj0 (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set setsum X7 ∅ ) X0 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X10 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → set X0 (λX8 : set ⇒ setsum ∅ (Inj1 (Inj0 X8 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (setsum (Inj1 ∅ X4 ∈ setsum (setsum (Inj0 (setsum ∅ ∅ X5 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMT4bZc3W93G4icys7e6vWQTnrYQ5hRe5ix )
∀X0 : ((set → (set → set → set → set → set → ((set → set → set → set → prop ∀X1 : ((set → ((set → set → set → set → set → set → set → set → ((set → set → ((set → set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → set → (set → set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → (set → set → set → set X3 (λX8 : set ⇒ setsum ∅ (setsum (Inj1 (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set λX9 : set ⇒ X6 ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 ∈ Inj1 X6 X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set λX9 : set ⇒ X6 ) X0 (λX8 : set → (set → set → set setsum X7 X7 ) (setsum ∅ (setsum X6 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set ∀X7 : set , (setsum ∅ X4 ∈ Inj1 X5 → X2 (λX8 : (set → (set → set → set → set → set setsum (setsum X7 (setsum (X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set X2 (λX8 : (set → (set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ Inj0 (X6 ∅ ) (Inj0 (Inj1 (Inj0 ∅ (X7 (λX8 : (set → set → set → set X5 ) ∈ setsum (Inj1 (setsum (X7 (λX8 : (set → set → set → set ∅ ) (Inj0 ∅ (Inj1 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 X10 ) (λX8 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj1 (X4 (setsum ∅ ∅ X7 ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → set → set λX9 : set ⇒ X8 ∅ (λX10 : set → set λX11 : set ⇒ X11 ) (X6 (λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X6 (λX9 : set ⇒ setsum X7 (Inj0 (Inj1 ∅ ) (setsum (Inj0 X8 (setsum (X6 (λX9 : set ⇒ ∅ ) ∅ (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (setsum (Inj0 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (setsum X7 (Inj1 (Inj0 (setsum ∅ ∅ X1 (λX8 : set → ((set → set → set → set → set → set λX9 : set ⇒ Inj0 (X8 (Inj1 (setsum ∅ ∅ (λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (X6 (λX10 : set ⇒ ∅ ) ∅ (X8 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum X10 ∅ (X8 ∅ ) (λX8 : set ⇒ setsum (Inj1 (setsum X8 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (X6 (λX8 : set ⇒ Inj1 ∅ ) (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 ∅ ) ∅ (setsum (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (setsum (Inj1 ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (Inj0 (setsum ∅ ∅ ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set → set (Inj1 ∅ ∈ Inj0 ∅ → X0 (λX8 : set → (set → set → set setsum (X6 (Inj0 (X6 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ Inj0 ∅ ) (Inj0 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) X0 (λX8 : set → (set → set → set X6 (Inj0 (Inj1 (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) ) (Inj0 (setsum X5 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → set → (set → set → set → set ∀X6 : set → set → (set → set → set ∀X7 : (set → (set → set → set → set → set → set → set X0 (λX8 : set → (set → set → set X5 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ setsum (X7 (λX10 : set ⇒ λX11 : set → set X10 ) (Inj0 ∅ ∅ (setsum ∅ ∅ (X6 (setsum ∅ ∅ ∅ (λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set → set ∅ ) ∅ ∅ ∅ ) ) (setsum (X5 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ (X8 (setsum ∅ ∅ (λX9 : set ⇒ X9 ) ) (X6 (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj1 ∅ (X4 (Inj1 ∅ ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ (λX8 : set ⇒ X7 (λX9 : set ⇒ λX10 : set → set X8 ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 (Inj0 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUym7dZBSkroLJsEwWxgKdHucvhFW9Jiak )
∀X0 : (set → set → set → set → prop ∀X1 : (set → (set → set → set → (set → set → set → set → prop ∀X2 : ((set → ((set → set → set → set → set → set → set → set → set → set → (set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → ((set → set → set → set → set → set X8 (Inj1 ∅ (λX9 : set → set ∅ ) ∅ (X7 (X8 (Inj1 ∅ (λX9 : set → set X8 ∅ (λX10 : set → set ∅ ) ∅ ∅ ) (Inj0 ∅ (setsum ∅ ∅ (setsum ∅ X6 ) ∅ (setsum (X7 (setsum (setsum ∅ ∅ ∅ (Inj0 X4 (X7 (Inj0 X6 (setsum ∅ (setsum ∅ ∅ (setsum X4 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (Inj1 (X5 (λX8 : set ⇒ X5 (λX9 : set ⇒ setsum ∅ ∅ ) ) X3 (λX8 : set ⇒ setsum (setsum ∅ (Inj0 (Inj1 ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set → set → set → set → set X3 (λX8 : set ⇒ X7 ∅ ∅ X8 (X7 (setsum (Inj0 ∅ (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ) ∅ (X7 (setsum (setsum X4 X4 (setsum ∅ (X7 ∅ ∅ ∅ ∅ (Inj1 (X5 (Inj1 ∅ (λX8 : set → set X8 ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (Inj1 ∅ ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ ∅ ∈ X5 → X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set → set setsum ∅ (Inj1 X8 ) ∅ X2 (λX8 : set → ((set → set → set → set → set → set ∅ ) X6 ∅ X5 (λX8 : set ⇒ ∅ ) (setsum X7 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X2 (λX8 : set → ((set → set → set → set → set → set setsum (setsum (X8 X6 (λX9 : set → set X7 ∅ ∅ (λX10 : set ⇒ ∅ ) ) (Inj0 ∅ (setsum ∅ ∅ (setsum (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) (Inj1 ∅ ∅ ) (setsum (setsum X6 (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ ∅ X5 (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (Inj1 (Inj1 X6 (Inj1 (Inj1 (setsum ∅ ∅ ) (X7 ∅ (Inj1 (setsum ∅ (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ∈ Inj0 (setsum (setsum ∅ ∅ (X7 (Inj0 ∅ (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → ((set → set → set → set → set → set setsum ∅ (Inj1 (Inj0 (Inj0 ∅ ) ∅ ∅ (Inj1 (X5 ∅ X4 (λX8 : set ⇒ X8 ) (setsum (setsum ∅ ∅ X7 (λX8 : set ⇒ X7 ) ∅ X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set → set ∅ ) (Inj0 ∅ ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X7 ∈ X6 → X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set → set ∅ ) ∅ X3 (λX8 : set ⇒ X7 ) (setsum (Inj0 (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ Inj1 ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ ∅ (X6 X4 (setsum (X6 X5 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X6 X7 ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ X5 ∅ ) (Inj0 (Inj1 (Inj1 (Inj1 ∅ (setsum ∅ ∅ X2 (λX8 : set → ((set → set → set → set → set → set Inj0 (Inj0 X6 ) ∅ ∅ (setsum (setsum (setsum (Inj0 ∅ ∅ X6 (setsum (X4 X7 (setsum (Inj1 ∅ (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMaLuaVkor1A1q5XPjE2JCKpC2tTZpHjQhk )
∀X0 : (set → set → (set → set → set → prop ∀X1 : ((((set → set → set → (set → set → set → set → set → ((((set → set → set → (set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : (set → set → (set → set → (set → set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set Inj1 (X7 X5 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ X5 → X3 (λX8 : set ⇒ X6 (setsum X7 (Inj1 X5 (λX9 : set → set ∅ ) (λX9 : set ⇒ X7 ) (setsum (setsum (Inj1 ∅ X7 (setsum (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set ∅ ) ∅ X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set setsum ∅ (Inj1 X5 ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (X4 ∈ Inj1 (X5 (λX8 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X3 (λX8 : set ⇒ X5 (λX9 : (set → set → set setsum (X9 (λX10 : set ⇒ Inj0 ∅ ) (Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj0 ∅ (Inj1 ∅ X9 ) ) (λX8 : ((set → set → set → set setsum (Inj1 (Inj1 ∅ (setsum (setsum (setsum ∅ ∅ X7 ∅ ) ∅ X2 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (Inj1 (setsum (X10 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ X5 (λX9 : set → set → set λX10 : set ⇒ X7 (X7 (Inj0 ∅ ) (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (setsum (Inj0 (Inj1 ∅ (X7 X8 ) (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ ∅ ∈ setsum (X5 (λX8 : set → set → set λX9 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ (X5 (λX8 : set → set → set λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : ((set → set → set → ((set → set → set → set → set → set ∀X6 : (set → set → set → set → (set → set → set ∀X7 : set → set X1 (λX8 : ((set → set → set → (set → set → set → set ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (setsum X11 ∅ (setsum (Inj0 (Inj1 ∅ (X8 (λX12 : set → set ∅ ) (λX12 : set ⇒ X11 ) ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (Inj0 ∅ (X4 (λX8 : set → set → set Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 ∅ (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (X5 (λX9 : set → set ∅ ) (λX9 : set → set ∅ ) ∅ ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → (set → set → set → set X5 ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) X7 X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set setsum ∅ (setsum X7 (Inj1 ∅ ) ∅ ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 ∅ ∈ setsum ∅ (Inj0 (Inj0 ∅ → X0 (λX8 : set ⇒ setsum ∅ (setsum (setsum (Inj1 ∅ X5 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ X5 ) (setsum (Inj0 X7 X5 ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ X6 (λX9 : set → set Inj1 (X9 (Inj0 ∅ ) (X5 (setsum (Inj1 ∅ ∅ ) (λX8 : set ⇒ ∅ ) (X6 (λX8 : set → set ∅ ) (Inj0 (Inj0 ∅ (Inj1 (Inj1 ∅ ∈ Inj1 (setsum (X4 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ (X5 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcTCjKrNe4y6nk4ukHHrdKTN6x3kj3TuRy )
∀X0 : (set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → prop ∀X2 : ((set → set → set → (((set → set → set → set → prop ∀X3 : ((((set → set → set → set → set → ((set → set → set → set → set → set → ((set → set → set → (set → set → set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → (set → set → set → set → set ∀X7 : set → set → (set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj1 (setsum (setsum ∅ (setsum ∅ ∅ (Inj1 ∅ ) ∅ X3 (λX8 : ((set → set → set → set → set λX9 : (set → set → set → set → set → set λX10 : (set → set → set λX11 : set → set ∅ ) (X7 X4 X5 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 (X7 (setsum (setsum ∅ ∅ ∅ (X7 ∅ (Inj1 ∅ (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ Inj0 ∅ ) ∅ (λX11 : set ⇒ X9 ) ) ∅ ) → (∀X4 : ((set → set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : ((set → set → set → set → set λX9 : (set → set → set → set → set → set λX10 : (set → set → set λX11 : set → set ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 ∅ X2 (λX8 : set → set ∅ ) (λX8 : (set → set → set ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set → set X6 ) (λX8 : (set → set → set X7 (X7 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set Inj1 (setsum ∅ (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set Inj1 (Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , (setsum (setsum (Inj1 ∅ ∅ X7 ∈ setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj1 (setsum (X10 (λX11 : set ⇒ ∅ ) X7 ) (setsum ∅ (setsum (Inj0 ∅ (Inj0 X5 X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj1 ∅ ) X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj0 (setsum (Inj1 (setsum ∅ ∅ (setsum X9 ∅ ) X4 (Inj1 ∅ ∈ Inj1 (Inj1 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set → set ∅ ) (λX8 : (set → set → set X6 ) X0 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum (Inj0 X5 (setsum ∅ ∅ ) (setsum ∅ (setsum ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMS2fUh8fxD2BCW9vecKXFhxCb83NofNVE6 )
∀X0 : (set → (set → (set → set → set → ((set → set → set → set → set → set → set → (set → set → ((set → set → set → (set → set → set → prop ∀X1 : (set → set → set → ((set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → set → set → prop ∀X3 : (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set (Inj0 ∅ ∈ Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (X7 (λX11 : set → set Inj1 ∅ ) (X7 (λX11 : set → set Inj1 ∅ ) (Inj1 ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) (Inj0 (Inj1 X5 (Inj0 (setsum (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X2 (λX8 : (set → (set → set → set → set → set Inj1 X5 ) (setsum (Inj0 (Inj0 X5 (setsum (setsum ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ X6 ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set X6 (X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ) (setsum (setsum ∅ X7 (Inj0 (setsum (Inj1 ∅ ∅ False ) → (∀X4 : set → set ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj0 (X4 (X4 (setsum ∅ ∅ ∈ X6 → X1 (λX8 : set ⇒ X7 (λX9 : (set → set → set → set X9 (λX10 : set ⇒ setsum X10 X8 ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) (X7 (λX8 : (set → set → set → set setsum (Inj0 (Inj1 ∅ (Inj0 X6 ) (λX8 : set → set → set X8 ∅ (X7 (λX9 : (set → set → set → set setsum (X7 (λX10 : (set → set → set → set ∅ ) X6 ) ) (λX8 : set ⇒ setsum (Inj0 ∅ (setsum X8 (X7 (λX9 : (set → set → set → set setsum ∅ ∅ ) ) (λX8 : set ⇒ setsum ∅ (Inj0 X8 ) (setsum (Inj0 ∅ (Inj0 (Inj0 (setsum ∅ ∅ ) → (∀X4 : set → (set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set X1 (λX8 : set ⇒ Inj0 (setsum ∅ (setsum (setsum ∅ ∅ X6 ) ∅ (λX8 : set → set → set X5 (λX9 : set ⇒ λX10 : set ⇒ X10 ) ) (λX8 : set ⇒ setsum (Inj0 (setsum (Inj1 ∅ ∅ (X7 (λX9 : set → set λX10 : set → set setsum ∅ (X7 (λX11 : set → set λX12 : set → set ∅ ) ) ) (λX8 : set ⇒ setsum X8 ∅ ) (Inj1 (setsum X6 X6 (X6 ∈ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → (set → set → set → (set → set → set ∀X7 : set → (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set λX11 : set ⇒ Inj1 (Inj1 X8 ) ∅ (λX8 : set ⇒ setsum X8 (setsum (setsum X8 ∅ X8 ) (λX8 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (setsum ∅ (setsum X5 X5 ) → (∀X4 : (set → (set → set → set → (set → set → set ∀X5 : ((set → set → (set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj0 X8 ) (λX8 : set → set Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ X8 ) (Inj1 (X4 (λX8 : set ⇒ λX9 : set → set setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set λX11 : set ⇒ X9 (Inj1 ∅ (λX12 : set ⇒ X11 ) ) (Inj1 ∅ (λX8 : set ⇒ setsum (Inj1 (setsum ∅ ∅ ∅ ) (λX8 : set → set X5 (λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (X8 ∅ ) (λX8 : set ⇒ X5 (λX9 : set → set λX10 : set → set λX11 : set ⇒ X8 ) (setsum (setsum ∅ ∅ (setsum X7 ∅ ) (setsum (setsum (X6 (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (X6 ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set → set X8 ) (λX8 : set ⇒ X7 ) (setsum (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFRdpo2jcoSvZCqTZJ3dyD1rspogRbYLch )
∀X0 : ((set → set → (((set → set → set → set → set → set → set → set → (((set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X1 : (((set → set → set → ((set → set → (set → set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → set → set → ((set → (set → set → set → set → prop ∀X3 : (set → set → set → ((set → (set → set → set → set → set → (((set → set → set → set → set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → (set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj1 (setsum X6 (Inj1 (X7 ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ) (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (Inj1 (Inj1 (X4 (setsum ∅ ∅ (λX8 : set ⇒ X8 ) (setsum (Inj0 (Inj0 X6 (setsum (Inj1 ∅ ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (Inj0 ∅ (Inj1 ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set λX9 : set ⇒ Inj0 (Inj1 ∅ ) (setsum (X4 (λX8 : (set → set → set ∅ ) X5 (λX8 : set ⇒ ∅ ) (setsum (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ (X4 (λX8 : (set → set → set ∅ ) (X5 ∈ X7 (λX8 : set → set λX9 : set → set X8 (X9 (X8 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → (set → set → set Inj0 (Inj0 (X7 (λX9 : (set → set → set → set X8 ∅ (λX10 : set ⇒ ∅ ) ) ) X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (λX8 : set → (set → set → set Inj0 ∅ ) ) → (∀X4 : (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set → (set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ X7 (setsum X8 ∅ (λX10 : set ⇒ Inj0 ∅ ) ) (λX8 : set → (set → set → set X5 ) (X5 ∈ X5 ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , (X6 (λX8 : set → set → set Inj1 ∅ ) ∈ Inj1 (Inj1 (Inj1 X5 → X0 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ X9 ∅ ) X7 X1 (λX8 : (set → set → set λX9 : (set → set → (set → set → set → set Inj0 (Inj0 (setsum ∅ (Inj0 ∅ ) (λX8 : set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : ((set → set → (set → set → set → set → set X1 (λX8 : (set → set → set λX9 : (set → set → (set → set → set → set ∅ ) (λX8 : set → set → set setsum ∅ (Inj1 X5 ) X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj1 X9 ) (λX8 : (set → set → set λX9 : set ⇒ X6 ∅ (λX10 : set ⇒ ∅ ) ) ∅ (λX8 : set ⇒ Inj1 ∅ ) (setsum (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set λX9 : (set → set → (set → set → set → set setsum (Inj1 (setsum (setsum ∅ ∅ ∅ ∅ ) (λX8 : set → set → set X8 (setsum (X6 (λX9 : set → set → set λX10 : set → set Inj0 ∅ ) ∅ (setsum ∅ (Inj1 (Inj1 ∅ ) X0 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (X8 (X9 (λX12 : set → set X10 ) (setsum ∅ ∅ (X9 (λX12 : set → set X12 X11 ) (Inj0 (Inj0 ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ Inj1 (setsum (setsum (X10 ∅ X11 ∅ ) (Inj0 (Inj0 (Inj1 (setsum ∅ ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 (Inj0 (X8 ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum (setsum (X9 (setsum ∅ ∅ (Inj1 (X9 ∅ X11 ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum X7 (setsum X7 ∅ ) (λX8 : set → (set → set → set Inj0 (Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTrKPHTFk3ukEWtX6C1xzsRButkxhXwQa9 )
∀X0 : ((((set → set → (set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → set → ((set → set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : ((set → set → (set → (set → set → set → set → set → (set → set → set → set → set → (((set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X7 ∈ X7 → X3 (λX8 : set → set λX9 : set → (set → set → set → set setsum (X9 ∅ (λX10 : set ⇒ ∅ ) ∅ (X9 (Inj1 X6 (λX10 : set ⇒ Inj1 (X8 ∅ ) X7 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 X8 ) (λX8 : (set → set → set ∅ ) X4 (λX8 : set ⇒ Inj0 (Inj0 (Inj1 (Inj0 ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set λX9 : set → (set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X8 ) (λX8 : (set → set → set Inj1 X6 ) X5 (λX8 : set ⇒ ∅ ) (setsum ∅ X5 False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum X6 X5 ∈ setsum ∅ (setsum ∅ (Inj1 (Inj1 ∅ → X2 (λX8 : set → set Inj1 (setsum (setsum ∅ ∅ (setsum (Inj1 ∅ X6 ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → ((set → set → set → set → set ∀X7 : set → set → set (setsum X4 (Inj1 (Inj0 (setsum ∅ ∅ ∈ X6 (λX8 : set → set → set setsum (X6 (λX9 : set → set → set Inj0 ∅ ) (λX9 : set → set setsum ∅ ∅ ) ∅ ∅ ) (λX8 : set → set X8 ∅ ) (Inj1 ∅ → X2 (λX8 : set → set setsum (X8 (Inj1 ∅ (X7 (setsum ∅ ∅ X5 ) ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∅ X4 (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) (Inj1 X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → (set → set → set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ X6 X6 ) (setsum X6 (setsum ∅ (Inj0 (Inj0 ∅ X4 (λX8 : set → set λX9 : set ⇒ Inj0 (setsum (setsum ∅ (Inj0 ∅ (X7 (λX10 : (set → set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ X11 ) (λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ) X0 (λX8 : ((set → set → (set → set → set → set → set setsum (Inj0 (setsum (X8 (λX9 : set → set λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (setsum (setsum (setsum ∅ ∅ ∅ (setsum X6 (X7 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (setsum (setsum (Inj1 (Inj0 ∅ (setsum ∅ (Inj1 ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set → (set → set → set → (set → set → set X0 (λX8 : ((set → set → (set → set → set → set → set Inj0 (setsum ∅ X5 ) (setsum (Inj1 (Inj1 (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (setsum (X6 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ (setsum X5 ∅ ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set → set X0 (λX8 : ((set → set → (set → set → set → set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj1 ∅ (setsum ∅ (Inj0 (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∈ Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNTJM6aQD69XVSMu5hQzq7hgLGZ8YRFoWi )
∀X0 : (((((set → set → set → set → (set → set → set → set → set → set → set → (set → set → prop ∀X1 : (set → set → (set → set → prop ∀X2 : ((set → set → set → set → set → (set → (set → set → set → prop ∀X3 : ((set → set → set → set → (((set → set → set → set → set → (set → set → (set → set → set → prop (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set (Inj0 ∅ ∈ X6 (Inj0 ∅ (X6 (setsum (setsum ∅ ∅ (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 ∅ → X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (X7 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) X3 (λX8 : set → set → set setsum (X6 ∅ (Inj1 (Inj0 ∅ (X7 (Inj1 (X6 ∅ ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set Inj1 (Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set → set setsum (setsum ∅ ∅ X7 ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set ∅ ) X3 (λX8 : set → set → set X8 (X8 X7 (X6 (setsum ∅ ∅ ∅ ) (λX8 : (set → set → set → set → set λX9 : set → set λX10 : set → set X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set → set (Inj1 (setsum (X7 ∅ (λX8 : set → set X8 ∅ ) ∅ (Inj0 ∅ ∅ ∈ Inj0 (setsum (Inj0 (X7 ∅ (λX8 : set → set ∅ ) ∅ ∅ ∅ → X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (setsum (Inj1 ∅ (X8 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set X7 ) (Inj0 (setsum ∅ (Inj1 ∅ ∈ Inj1 (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj1 (setsum ∅ (X7 (λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set Inj0 (Inj1 ∅ ) X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set → (set → set → (set → set → set → set ∀X7 : set → set → set → set → set X1 (λX8 : set ⇒ Inj1 (setsum (X6 (X6 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ X9 ) (Inj1 ∅ (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ Inj1 (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → (set → set → set ∀X7 : set , (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ ∈ X4 → X0 (λX8 : (((set → set → set → set → (set → set → set → set → set → set X6 (λX9 : set → set → set Inj0 (Inj0 (setsum ∅ ∅ ) (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ (λX9 : set ⇒ setsum (X6 (λX10 : set → set → set ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ ) ) (λX8 : set ⇒ X7 ) ) → (∀X4 : ((set → set → (set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → (set → set → set ∀X7 : set , (Inj0 (setsum ∅ (Inj0 ∅ ∈ X5 → X0 (λX8 : (((set → set → set → set → (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMX1G8anTGyawtBeYmjFbMn1RUNWZcdqS2J )
∀X0 : (set → set → (((set → set → set → (set → set → set → ((set → set → set → set → set → prop ∀X1 : ((set → set → (set → set → set → set → (set → set → set → (set → set → set → set → prop ∀X2 : (((((set → set → set → (set → set → set → set → set → set → ((set → (set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : (set → (set → set → set → set → (set → (set → set → set → prop (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set setsum (Inj0 ∅ X7 ) ∅ (λX8 : set ⇒ λX9 : set → set X9 X8 ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set Inj1 (Inj1 ∅ ) X6 (λX8 : set ⇒ λX9 : set → set X6 ) (Inj1 (X4 (λX8 : (set → set → set X5 ) ∈ X6 ) → (∀X4 : set → set ∀X5 : (((set → set → set → (set → set → set → ((set → set → set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set → set → set X2 (λX8 : (((set → set → set → (set → set → set → set → set X6 (λX9 : set → set → set Inj0 (setsum (setsum ∅ ∅ ∅ ) ) (λX8 : set → (set → set → set λX9 : (set → set → set λX10 : set → set ∅ ) X2 (λX8 : (((set → set → set → (set → set → set → set → set Inj1 (X5 (λX9 : (set → set → set λX10 : set → set ∅ ) (λX9 : set → set λX10 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) ∅ ) (λX8 : set → (set → set → set λX9 : (set → set → set λX10 : set → set X9 (λX11 : set ⇒ X8 (Inj1 ∅ (λX12 : set ⇒ Inj1 (X9 (λX13 : set ⇒ ∅ ) ) ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X2 (λX8 : (((set → set → set → (set → set → set → set → set setsum ∅ (setsum (Inj1 (Inj0 ∅ (Inj0 X6 ) (λX8 : set → (set → set → set λX9 : (set → set → set λX10 : set → set Inj0 (X10 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 (Inj1 (X5 (setsum ∅ ∅ ∈ setsum (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum (setsum X4 (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set (setsum (setsum ∅ ∅ (Inj1 (setsum ∅ (X7 ∅ (λX8 : set ⇒ ∅ ) ∈ X5 (λX8 : set → set ∅ ) → X2 (λX8 : (((set → set → set → (set → set → set → set → set setsum (setsum (X7 (X8 (λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ X8 (λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) ) (Inj1 (setsum ∅ ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → (set → set → set λX9 : (set → set → set λX10 : set → set Inj1 (setsum (setsum (setsum ∅ ∅ ∅ (setsum (Inj1 ∅ ∅ ) X1 (λX8 : set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set → set Inj0 (setsum (Inj1 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (X5 (λX8 : set → set ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : (((set → set → set → set → set → set → set (X6 (λX8 : set ⇒ X5 ) X5 ∈ setsum ∅ (setsum X5 (Inj0 (X6 (λX8 : set ⇒ ∅ ) ∅ → X1 (λX8 : set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set → set Inj1 (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X0 (λX8 : set ⇒ Inj0 (setsum (X6 (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj1 X5 ) (λX8 : (set → set → set → (set → set → set λX9 : (set → set → set → set ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set ∅ ) X0 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : (set → set → set → set ∅ ) ) → (∀X4 : ((set → set → (set → set → set → set → (set → set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 (setsum (Inj1 (setsum ∅ ∅ (Inj1 (X5 (λX8 : set → set → set ∅ ) ∈ Inj1 ∅ → X0 (λX8 : set ⇒ X5 (λX9 : set → set → set X6 ) ) (λX8 : (set → set → set → (set → set → set λX9 : (set → set → set → set ∅ ) X0 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : (set → set → set → set X8 (λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 (X8 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) (λX12 : set ⇒ ∅ ) (setsum (X8 (λX12 : set ⇒ λX13 : set ⇒ ∅ ) (λX12 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX10 : set ⇒ Inj0 (X7 (X9 (λX11 : set ⇒ ∅ ) ∅ ) ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGv7RwX6w485pAPDK3EuqgkXTKKnHdQUkN )
∀X0 : (set → set → set → set → prop ∀X1 : (((set → set → set → set → (set → set → set → set → set → (set → ((set → set → set → (set → set → set → set → set → set → set → prop ∀X2 : ((set → set → set → set → ((set → set → set → set → set → set → prop ∀X3 : (set → ((set → set → set → (set → set → set → (set → set → set → ((set → set → ((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set → set → set → set → set (Inj1 ∅ ∈ setsum (Inj1 (setsum ∅ (setsum ∅ ∅ X4 → X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set → set Inj0 (Inj1 (setsum (X7 ∅ ∅ ∅ ∅ (Inj1 ∅ ) (λX8 : set → set λX9 : (set → set → set → set Inj0 (X6 ∅ ) X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set → set ∅ ) (λX8 : set → set λX9 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set → set ∀X7 : set , (setsum (setsum (setsum ∅ (Inj0 ∅ (setsum X4 X7 (setsum ∅ ∅ ∈ X7 → X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set → set Inj1 X7 ) (λX8 : set → set λX9 : (set → set → set → set X7 ) X1 (λX8 : (set → set → set → set → (set → set → set λX9 : set ⇒ setsum ∅ (setsum (setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) ∅ (setsum ∅ ∅ (setsum X4 (Inj1 (X6 ∅ (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → set → (set → set → set (X4 (X4 ∅ ∈ setsum ∅ ∅ → X2 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum X10 (X7 (X8 (setsum ∅ ∅ (λX11 : set → set λX12 : set ⇒ ∅ ) (λX11 : set ⇒ setsum ∅ ∅ ) ) (setsum (Inj1 (setsum (X4 ∅ (setsum ∅ ∅ (Inj0 (Inj0 (Inj0 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set ⇒ X8 ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set ⇒ X9 ) ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X5 ∈ X5 → X0 (λX8 : set ⇒ X5 ) X4 (Inj1 (Inj0 (setsum ∅ X6 X1 (λX8 : (set → set → set → set → (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj0 (setsum X8 (setsum ∅ ∅ X8 ) X5 ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set → set → (set → set → set λX9 : set ⇒ Inj0 X9 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X8 ) (setsum ∅ (X4 (Inj1 (Inj1 ∅ (setsum (Inj1 (Inj1 (Inj0 ∅ ∅ ∅ (X6 (λX8 : set ⇒ X5 ) (X4 ∅ ∈ Inj1 (setsum (setsum (X6 (λX8 : set ⇒ ∅ ) ∅ ∅ (X6 (λX8 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → (set → set → set ∀X7 : set , (Inj0 (setsum (X6 (λX8 : (set → set → set → set setsum ∅ ∅ ) ∅ (λX8 : set ⇒ ∅ ) X7 ∈ Inj1 (Inj0 (Inj0 (Inj1 ∅ → X1 (λX8 : (set → set → set → set → (set → set → set λX9 : set ⇒ setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X9 (λX12 : set ⇒ Inj1 ∅ ) ) (X6 (λX8 : (set → set → set → set setsum (Inj1 (Inj0 ∅ (X6 (λX9 : (set → set → set → set Inj1 ∅ ) ∅ (λX9 : set ⇒ Inj1 ∅ ) ) (setsum (setsum (setsum ∅ ∅ (X5 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set ⇒ X6 (λX9 : (set → set → set → set setsum X8 ∅ ) ∅ (λX9 : set ⇒ setsum (setsum ∅ ∅ X7 ) ) (Inj0 (X5 ∅ ∅ X0 (λX8 : set ⇒ Inj1 ∅ ) (X5 (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) ∅ X4 X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set → set X10 ∅ ) (λX8 : set → set λX9 : (set → set → set → set X7 (Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMHn2asdHV7iyBr9wmRvVWzUYvCfCxmc7B )
∀X0 : (set → set → set → prop ∀X1 : (set → (set → set → set → set → set → prop ∀X2 : (((set → set → ((set → set → set → set → (set → set → set → set → (((set → set → set → set → (set → set → set → set → set → prop ∀X3 : ((set → (set → set → set → set → set → set → set → (((set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set X3 (λX8 : set → (set → set → set → set → set ∅ ) (setsum (Inj1 ∅ ∅ (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum (Inj0 ∅ (Inj0 (Inj0 (Inj0 ∅ ) X3 (λX8 : set → (set → set → set → set → set Inj1 ∅ ) (X4 X6 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ X10 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → (set → set → set → set → set setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (Inj0 (X8 ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) (Inj1 X6 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum X10 (Inj0 (setsum (Inj1 ∅ ∅ ) (Inj1 X6 ∈ X7 ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∈ Inj0 (setsum X6 X6 → X2 (λX8 : (set → set → ((set → set → set → set → (set → set → set → set λX9 : ((set → set → set → set λX10 : set → set → set ∅ ) (Inj0 ∅ X2 (λX8 : (set → set → ((set → set → set → set → (set → set → set → set λX9 : ((set → set → set → set λX10 : set → set → set ∅ ) (Inj0 X6 ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → (set → set → set → (set → set → set X2 (λX8 : (set → set → ((set → set → set → set → (set → set → set → set λX9 : ((set → set → set → set λX10 : set → set → set Inj0 (Inj1 (X9 (λX11 : set → set X11 ∅ ) ) X6 False ) → (∀X4 : (set → set → set → set → (set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set → (set → set → set → set → set → set ∀X7 : (set → set → set → set → ((set → set → set → set → set (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∈ X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ λX9 : set → set X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 X12 ∅ ) (λX10 : set → set λX11 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (Inj0 ∅ ) ) (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set Inj0 (Inj0 ∅ ) (Inj1 (Inj0 (Inj0 X7 (setsum (Inj0 X7 (setsum (setsum (Inj0 ∅ ∅ X4 (X5 ∈ setsum (Inj0 (setsum ∅ X6 (Inj1 X7 ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum (X6 ∅ (λX9 : set ⇒ Inj1 (Inj0 ∅ ) ∅ ) ∅ ) → (∀X4 : ((set → set → (set → set → set → set → set ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ Inj0 ∅ ) (Inj0 (setsum (setsum (Inj1 ∅ (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (X4 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X9 ∅ ) X0 (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHRonva6nRZ4mT3xkajcKUQpeNGMNTviVK )
∀X0 : (set → (((set → set → set → set → (set → set → set → set → set → set → set → set → (set → set → (set → set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → set → ((((set → set → set → set → set → set → (set → set → set → set → (set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : ((set → set → set → set → (set → (set → set → set → set → ((set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set X3 (λX8 : set ⇒ setsum (setsum X5 (setsum (Inj0 ∅ ∅ (X7 (X7 (setsum ∅ ∅ (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ X8 ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj0 X7 → X3 (λX8 : set ⇒ ∅ ) ∅ X3 (λX8 : set ⇒ Inj0 X5 ) (setsum (setsum ∅ X7 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set X2 (λX8 : set → set → set → set λX9 : set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X2 (λX8 : set → set → set → set λX9 : set → (set → set → set Inj1 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 X9 ) ) → (∀X4 : set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set → set → set λX9 : set → (set → set → set X8 ∅ (X9 ∅ (λX10 : set ⇒ Inj1 X10 ) X7 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ X10 ) X2 (λX8 : set → set → set → set λX9 : set → (set → set → set X8 (setsum X7 X7 ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 X4 ∈ X5 → X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ setsum (setsum (Inj0 (setsum ∅ ∅ (X8 X7 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 X9 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X6 ) ∅ X6 ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : (((set → set → set → set → set → set → (set → set → set → (set → set → set X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj0 X11 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set λX9 : set ⇒ X8 (setsum (setsum ∅ X9 (Inj1 (X7 (λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ) (setsum ∅ ∅ (X7 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (X8 (λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ (Inj0 ∅ ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 (X7 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (Inj0 ∅ ) ∈ X4 (setsum (Inj0 (setsum ∅ ∅ (Inj0 (Inj1 ∅ (setsum (Inj1 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj0 (setsum (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (Inj0 ∅ ∈ Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (setsum X10 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 X9 ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ X10 (Inj1 (setsum (Inj0 ∅ X10 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (setsum X8 X9 ∅ ) X1 (λX8 : set → set λX9 : ((set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum ∅ (Inj1 X10 ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (setsum ∅ ∅ ) ∅ (setsum (Inj0 ∅ (Inj0 (X4 (λX8 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRNRmzvvE7eE88LuhMBSD4hVZS8My5ivuS )
∀X0 : ((set → set → set → set → (((set → set → set → set → ((set → set → set → set → (set → set → set → set → set → prop ∀X1 : (set → ((set → set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : ((set → (set → set → set → set → set → (set → set → prop ∀X3 : ((set → set → set → set → (((set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set (X5 ∈ setsum (Inj1 (setsum X5 (setsum ∅ ∅ (Inj1 (X6 (Inj0 ∅ → X2 (λX8 : set → (set → set → set λX9 : set ⇒ setsum (setsum (X6 ∅ (setsum ∅ (setsum ∅ ∅ (X7 (λX10 : set → set → set X9 ) ) (λX8 : set ⇒ ∅ ) X3 (λX8 : set → set ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set ⇒ Inj0 (X8 (λX10 : set ⇒ setsum (Inj1 ∅ (setsum ∅ ∅ ) (setsum (Inj0 ∅ X9 ) (λX8 : set → set λX9 : set ⇒ X7 (λX10 : set → set → set ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set Inj0 ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X6 X9 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set → set X0 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (X6 (setsum (X6 X5 (setsum (setsum ∅ ∅ X5 X2 (λX8 : set → (set → set → set λX9 : set ⇒ setsum (Inj0 (X6 (setsum ∅ ∅ (X7 (Inj1 (setsum ∅ ∅ (λX10 : set → set λX11 : set ⇒ X10 (setsum ∅ ∅ ) (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → (set → set → set λX9 : set ⇒ setsum (Inj1 (Inj1 ∅ ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set (X6 (X4 (X6 (setsum ∅ ∅ ∈ X6 (Inj1 (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (X7 (λX11 : set → set → set setsum ∅ ∅ ) (setsum ∅ (Inj1 ∅ (setsum X10 (X7 (λX11 : set → set → set X10 ) ) (Inj0 (setsum ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) (setsum (Inj0 (setsum ∅ (X6 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (setsum ∅ (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → set (setsum (setsum (X5 ∅ (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (X5 ∅ (λX8 : set ⇒ ∅ ) (Inj1 ∅ ∈ Inj0 (Inj0 ∅ → X2 (λX8 : set → (set → set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ setsum (setsum (setsum ∅ (X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ∅ ) X0 (λX8 : set → set λX9 : set ⇒ setsum ∅ X6 ) (λX8 : (set → set → set → set λX9 : (set → set → set X8 (λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set → set λX9 : set ⇒ X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ X10 ) ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (Inj0 (Inj1 (setsum ∅ (Inj0 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVQVDskbTttUvar9BAdNLdaBbiB599Cp52 )
∀X0 : (((((set → set → set → (set → set → set → set → set → (((set → set → set → set → (set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → set → (((set → set → set → set → (set → set → set → set → set → set → prop ∀X3 : (set → (set → (set → set → set → set → set → set → set → ((set → set → set → set → prop (∀X4 : ((set → set → set → set → set → set ∀X5 : (set → set → set → set → ((set → set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set ∅ ) ∅ X7 (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set ∅ ) ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj0 (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ setsum (X8 ∅ ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X5 ) ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : (set → set → set → set → (set → set → set → set (X6 (setsum (setsum (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) ∅ (λX10 : set ⇒ Inj1 ∅ ) ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ X11 ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum (Inj1 (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ X8 ) (X6 (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ Inj0 (Inj0 X8 ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 (setsum X9 (Inj1 (Inj1 ∅ ) X6 (Inj1 ∅ (setsum ∅ X6 ∈ Inj1 (Inj1 (Inj0 (X4 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → (set → set → set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → (set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set setsum (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ (setsum (X8 (λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X10 (λX13 : set ⇒ ∅ ) ) ∅ ) ∅ ∅ X1 (λX8 : set ⇒ Inj0 ∅ ) ∅ (Inj0 X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : (set → set → set → set → set → set X1 (λX8 : set ⇒ Inj0 (X7 (λX9 : set ⇒ Inj0 (Inj1 ∅ ) ∅ (Inj1 X5 (Inj1 ∅ ) (setsum ∅ (Inj1 ∅ (X6 ∅ ∅ (λX8 : set ⇒ setsum (setsum X5 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set X8 ) (Inj1 (Inj1 (X7 (λX8 : set ⇒ X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ) (Inj0 ∅ (Inj0 ∅ ∅ (X7 (λX8 : set ⇒ X8 ) (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ (X7 (λX8 : set ⇒ Inj1 ∅ ) (X7 (λX8 : set ⇒ setsum ∅ ∅ ) X5 (Inj0 ∅ ∅ ∅ X4 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → ((set → set → set → set X0 (λX8 : (((set → set → set → (set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set X9 (λX10 : set → set λX11 : set ⇒ X10 (setsum (X8 (λX12 : (set → set → set λX13 : set → set λX14 : set ⇒ ∅ ) (X8 (λX12 : (set → set → set λX13 : set → set λX14 : set ⇒ ∅ ) ) (λX10 : set ⇒ X10 ) (Inj1 (setsum (Inj0 ∅ (Inj0 ∅ ) (setsum (setsum ∅ X6 (setsum (setsum (Inj1 ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : (((set → set → set → (set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set X9 (λX10 : set → set λX11 : set ⇒ setsum ∅ X11 ) (λX10 : set ⇒ setsum ∅ (X9 (λX11 : set → set λX12 : set ⇒ X12 ) (λX11 : set ⇒ ∅ ) (Inj1 ∅ ) (setsum (setsum (Inj0 ∅ ∅ (X8 (λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X10 (λX13 : set ⇒ ∅ ) ) ) X6 (setsum (Inj0 (Inj1 (Inj0 ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMLgZsKULanzEh8BMqgqjPkt6xaFkqXn7Px )
∀X0 : (set → ((set → set → set → set → set → set → set → (set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → ((set → set → set → set → set → (set → set → set → set → (((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ X10 ) (setsum ∅ (Inj0 ∅ (Inj0 X7 (λX8 : set ⇒ setsum X7 ∅ ) ∅ ∅ X3 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X10 ) (λX8 : (set → set → set → set → set ∅ ) ) → (∀X4 : set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum ∅ ∅ (X9 (λX13 : set ⇒ setsum X13 X13 ) ∅ ) (λX8 : (set → set → set → set → set Inj0 (X7 (λX9 : set ⇒ λX10 : set → set Inj0 (Inj0 ∅ ) ) (Inj1 (Inj1 (Inj1 (X5 ∅ ∈ X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : ((set → set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → (set → set → set → set → set (X7 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∅ ∈ setsum (X6 (Inj0 (setsum ∅ ∅ (λX8 : set → set X6 (setsum ∅ ∅ (λX9 : set → set setsum ∅ ∅ ) ) (Inj1 (Inj1 ∅ → X2 (λX8 : set ⇒ Inj1 (X6 (X6 (setsum ∅ ∅ (λX9 : set → set Inj0 ∅ ) (λX9 : set → set ∅ ) ) (setsum ∅ (X7 (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum (setsum (X9 (λX11 : set ⇒ ∅ ) ∅ (Inj1 (setsum ∅ ∅ ) ∅ (Inj1 ∅ (λX8 : set ⇒ ∅ ) (Inj0 (Inj0 (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X6 ∅ ∈ X6 X4 → X1 (λX8 : set ⇒ Inj1 (Inj1 X8 ) (λX8 : set → set → set ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (Inj1 ∅ ) (λX8 : set → set → set X6 ) X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj1 ∅ ) (Inj1 ∅ (Inj1 X7 (λX8 : set ⇒ ∅ ) (Inj0 (Inj0 (X4 ∅ X5 (setsum (Inj1 X7 (setsum X6 (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ X7 (λX11 : set ⇒ setsum (Inj0 ∅ ∅ ) ) X6 (setsum X4 (Inj1 (X5 (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (Inj1 (X5 (Inj0 ∅ ) ∅ (X7 (λX8 : set ⇒ setsum ∅ (X5 (X7 (λX9 : set ⇒ ∅ ) ) X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ X10 ) (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ (Inj0 (X7 (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ setsum X6 (setsum ∅ (Inj0 (X5 ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ (Inj0 X6 (setsum (Inj0 ∅ (Inj1 (X7 (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj0 (setsum ∅ X8 ) ∅ X7 (λX8 : set ⇒ Inj1 (Inj0 X7 ) ∅ ∅ (Inj0 ∅ ∈ Inj1 X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHf4hDjK7fmfktjM5e735qvvcjdeQERjRj )
∀X0 : (set → ((set → set → set → (set → set → set → set → set → (set → (set → set → set → (set → (set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → set → set → set → prop ∀X2 : (set → (set → (set → set → set → set → (set → set → set → (set → set → set → (((set → set → set → set → set → set → set → set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → (set → set → set → set → set → set → set → set → set → (set → (set → set → set → set → prop (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : ((set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (setsum (Inj1 (Inj1 (Inj0 ∅ X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj1 (setsum (Inj0 ∅ ∅ X10 ) ) → (∀X4 : (((set → set → set → set → set → ((set → set → set → set ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set , (X7 ∈ X5 (Inj1 (X5 (setsum ∅ ∅ (setsum ∅ ∅ ∅ (Inj0 ∅ X7 ∅ (Inj1 (X4 (λX8 : (set → set → set → set ∅ ) (λX8 : set → set X6 ) → X3 (λX8 : ((set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X12 ) X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ (X9 (X9 ∅ ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set → set → set λX11 : set → set X10 (X11 (Inj1 (Inj1 ∅ (setsum ∅ X8 ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ Inj0 X9 ) (X5 (Inj0 ∅ X7 ∅ (setsum (Inj0 (X5 ∅ ∅ ∅ ∅ ∅ (Inj1 (Inj1 (Inj1 (Inj1 ∅ ∅ (setsum (setsum (setsum X7 (X5 ∅ ∅ ∅ ∅ (Inj0 ∅ (X4 (λX8 : (set → set → set → set Inj1 (Inj0 ∅ ) (λX8 : set → set Inj0 (X5 ∅ ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (Inj0 X7 ∈ Inj0 (Inj0 (X5 (Inj0 ∅ (λX8 : set ⇒ X7 ) (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set → set → set λX11 : set → set setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (X11 (X9 ∅ (λX12 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ Inj1 (setsum (setsum ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) (Inj1 ∅ (Inj0 (X5 X4 (λX8 : set ⇒ setsum (Inj0 ∅ (X5 ∅ (λX9 : set ⇒ ∅ ) ∅ ) (X5 X6 (λX8 : set ⇒ ∅ ) X4 (setsum (setsum ∅ (Inj0 ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set → set → set λX11 : set → set X11 (setsum (setsum ∅ (X10 ∅ ∅ (X10 (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ setsum X7 (Inj1 (Inj0 (setsum ∅ ∅ ) (setsum (Inj1 (Inj1 ∅ (Inj1 (X5 (setsum ∅ ∅ (Inj0 ∅ X7 (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (setsum (X6 (setsum (Inj0 ∅ ∅ (setsum (Inj0 ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ (setsum (X6 ∅ ∅ (Inj0 ∅ False ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X7 ∅ ∈ setsum (Inj1 X6 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ X9 ) (setsum ∅ (setsum X6 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj1 (Inj0 (Inj1 (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (setsum (setsum X9 (Inj0 ∅ (Inj1 (Inj1 ∅ (Inj1 ∅ ) (setsum (setsum ∅ ∅ ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set ⇒ Inj0 (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ X10 ) (λX8 : set ⇒ λX9 : set → set X7 ) (λX8 : set ⇒ λX9 : set → set Inj1 X8 ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set → ((set → set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set ⇒ setsum (X7 (Inj0 (setsum ∅ ∅ (λX11 : set → set X10 ) (Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (setsum (setsum X7 (setsum (Inj1 ∅ ∅ (setsum (Inj0 ∅ (Inj0 (Inj0 ∅ ∈ X4 → X0 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set X9 (setsum X6 X8 ) (λX8 : set ⇒ λX9 : set → set Inj0 (Inj1 (Inj0 X8 ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcDNngqDHbMeaZu4nWGbHYRp7xV5SH6wkL )
∀X0 : (set → (set → set → set → set → prop ∀X1 : (((((set → set → set → set → (set → set → set → set → set → set → set → (((set → set → set → set → set → set → (set → set → prop ∀X2 : (((set → set → set → set → set → ((set → (set → set → set → set → set → set → prop ∀X3 : (set → set → set → (((set → set → set → set → set → set → prop (∀X4 : (set → (set → set → set → (set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ setsum (Inj0 (X5 (setsum ∅ ∅ ∅ ) (X5 (X5 (Inj1 X7 (λX8 : (set → set → set → set λX9 : set ⇒ Inj1 X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → (set → set → set ∀X7 : set → set X3 (λX8 : set ⇒ X5 ) (Inj0 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) X2 (λX8 : (set → set → set → set X8 (λX9 : set ⇒ setsum ∅ (X8 (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) ∅ ) (λX8 : set → (set → set → set → set X5 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (setsum X7 (Inj0 (Inj1 ∅ ∅ ∈ Inj0 X6 → X2 (λX8 : (set → set → set → set ∅ ) (λX8 : set → (set → set → set → set X5 ) (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → set X2 (λX8 : (set → set → set → set setsum ∅ ∅ ) (λX8 : set → (set → set → set → set ∅ ) (X6 ∅ False ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → ((set → set → set → (set → set → set ∀X7 : (((set → set → set → set → (set → set → set → (set → set → set → (set → set → set X1 (λX8 : (((set → set → set → set → (set → set → set → set → set → set setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (X5 (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) ) (λX8 : (set → set → set Inj1 (setsum ∅ (X6 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ) (X5 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (Inj0 X4 (λX8 : set ⇒ X6 (X5 (λX9 : set ⇒ λX10 : set ⇒ Inj0 X9 ) (λX9 : set → set setsum (Inj1 X8 (Inj1 (setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 (Inj0 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : (((set → set → set → set → (set → set → set → set → set → set ∅ ) (λX8 : (set → set → set Inj0 X5 ) (X6 (λX8 : (set → set → set → set λX9 : set → set setsum (X9 (X8 (λX10 : set ⇒ ∅ ) ∅ ∅ ) ∅ (X6 (λX8 : (set → set → set → set λX9 : set → set setsum (X6 (λX10 : (set → set → set → set λX11 : set → set X10 (λX12 : set ⇒ ∅ ) ∅ ) (setsum ∅ ∅ ∅ ) (setsum (setsum X4 ∅ (setsum (Inj0 ∅ ∅ (λX8 : set ⇒ Inj0 (setsum ∅ (Inj0 (Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set , (setsum ∅ (setsum X4 (setsum ∅ ∅ ∈ Inj1 (setsum ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set → set X8 ) ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set setsum X6 (setsum (Inj1 ∅ ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ (setsum (setsum (Inj0 X7 X7 (Inj1 (Inj0 ∅ ∈ setsum (X5 (λX8 : set ⇒ ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcLagF1ffBZgHwPaxSYNZqgopsK2zsnSQZ )
∀X0 : (set → set → set → (set → set → set → prop ∀X1 : (set → set → ((set → set → set → (set → set → set → set → (((set → set → set → set → ((set → set → set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → (set → set → set → set → set → (set → (set → set → (set → set → set → prop ∀X3 : (((((set → set → set → set → set → (set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → (set → set → set → set → set → set X8 (λX9 : (set → set → set → set X7 ) (λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ (X6 (λX9 : (set → set → set → set Inj0 (setsum ∅ ∅ ) ) (Inj1 ∅ ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X3 (λX8 : (((set → set → set → set → set → (set → set → set → set → set → set ∅ ) X6 False ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → (set → set → set → set Inj1 (setsum (Inj0 (setsum ∅ ∅ (Inj0 X5 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set X9 X8 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : ((set → set → (set → set → set → set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X2 (λX8 : (((set → set → set → set → set → (set → set → set → set X8 (λX9 : (set → set → set ∅ ) (Inj0 ∅ (λX9 : set ⇒ Inj1 (Inj1 X9 ) ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set X9 ∅ ) (Inj0 (setsum (setsum ∅ (setsum ∅ ∅ (Inj1 ∅ ∈ Inj1 (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ (Inj1 ∅ ) X5 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X9 (λX12 : set ⇒ X10 ) ) (setsum (setsum X5 ∅ ∅ False ) → (∀X4 : (set → set → set → ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj1 X9 (setsum X6 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set (X4 (λX8 : set ⇒ X7 (λX9 : (set → set → set X7 (λX10 : (set → set → set Inj0 ∅ ) ) ) ∈ Inj1 (setsum (Inj1 (Inj1 ∅ X6 → X0 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X3 (λX8 : (((set → set → set → set → set → (set → set → set → set → set → set ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKVtGBBf5TdvcMYXfhGhrkDB7yVhaPeSUR )
∀X0 : (set → (set → (set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → (set → (set → set → set → set → (((set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → (set → set → set → prop ∀X3 : ((((set → set → set → set → set → set → set → set → set → ((set → (set → set → set → set → (set → set → set → set → (((set → set → set → set → set → set → (set → set → prop (∀X4 : set → set ∀X5 : (((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → set → set → set ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (Inj0 X11 ) (λX8 : (set → set → set → set X5 (λX9 : (set → set → set Inj1 X6 ) (λX9 : set ⇒ Inj1 (Inj0 (setsum ∅ ∅ ) ) (X4 (setsum ∅ X7 (λX8 : set ⇒ Inj0 X8 ) ) → (∀X4 : (set → set → set ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → set → set → set Inj0 (Inj0 (setsum (X8 (λX9 : set → set → set ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → set ∅ ) (setsum ∅ (Inj1 ∅ (λX8 : set ⇒ X7 ) (X5 X6 (Inj0 (X5 (Inj0 ∅ X7 (Inj0 ∅ X6 (Inj1 X6 (Inj1 ∅ ∈ setsum ∅ (setsum X7 (setsum (X4 (λX8 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ setsum ∅ (setsum (Inj1 X7 X6 ) (setsum X5 ∅ (setsum (setsum (setsum X5 X7 X5 (Inj0 (setsum ∅ (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set , (Inj1 X4 ∈ Inj1 (Inj1 ∅ → X2 (λX8 : set ⇒ Inj0 ∅ ) (Inj1 (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ X4 (λX8 : set ⇒ λX9 : set ⇒ X6 ∅ (λX10 : set → set Inj1 X7 ) ∅ ) X2 (λX8 : set ⇒ X6 (Inj0 (Inj1 X7 (λX9 : set → set ∅ ) (setsum (Inj1 (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) (X6 (Inj1 (setsum (X6 ∅ (λX8 : set → set ∅ ) ∅ (setsum ∅ ∅ (λX8 : set → set Inj0 (Inj1 (Inj1 ∅ ) (Inj1 ∅ (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ X7 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : ((set → set → set → set → set setsum (X8 (λX9 : set → set → set setsum ∅ (Inj0 ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum (X8 (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ (setsum X9 (setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → (set → set → set ∀X7 : (set → set → set X1 (λX8 : ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum (X6 (λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ Inj0 (X8 (λX11 : set ⇒ ∅ ) ∅ ) (Inj0 (X7 (λX10 : set ⇒ X7 (λX11 : set ⇒ ∅ ) ) ) False ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set (Inj1 X4 ∈ X6 (Inj1 (Inj0 (setsum ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set → (set → set → set setsum ∅ (Inj0 X8 ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set X6 ) (setsum ∅ (setsum ∅ ∅ X1 (λX8 : ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ (X7 (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMbo4RtLMRgcJJSxCq1K89teALqJWLcg3mi )
∀X0 : (((set → set → set → set → set → set → (set → set → (set → set → prop ∀X1 : ((set → (set → set → set → (((set → set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → set → ((set → (set → set → set → set → ((set → set → set → set → set → set → (((set → set → set → set → (set → set → set → ((set → set → set → prop ∀X3 : ((set → set → set → (set → set → set → set → set → set → prop (∀X4 : set → set → (set → set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set ∅ ) (Inj0 (X6 (X4 (Inj0 ∅ (Inj1 ∅ (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set → set setsum (X8 ∅ (Inj0 ∅ ) (Inj0 (setsum (Inj0 (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj1 (setsum (setsum (X7 ∅ ∅ (Inj1 (Inj0 ∅ ∈ Inj1 X6 → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set X10 (setsum (Inj1 (Inj1 ∅ (X7 (X8 ∅ X9 ) (Inj1 (setsum ∅ X4 (Inj0 X5 X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set Inj0 X9 ) (Inj1 ∅ X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set → set X2 (λX8 : set → set → set → set → set Inj1 (X8 ∅ (Inj0 (setsum ∅ ∅ (X7 (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ X8 (Inj0 (X7 (setsum ∅ ∅ (λX11 : set ⇒ ∅ ) (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set X6 (λX9 : set ⇒ λX10 : set → set ∅ ) ) X2 (λX8 : set → set → set → set → set Inj0 ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum ∅ (Inj1 ∅ ) (λX8 : set → set Inj0 (X6 (λX9 : set ⇒ λX10 : set → set Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → (set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : ((set → set → set → set → set → (set → set → set → set X2 (λX8 : set → set → set → set → set setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ (X8 ∅ ∅ ∅ ∅ (setsum (X7 (λX9 : set → set → set λX10 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X8 ∅ ∅ ∅ ∅ ) (Inj1 (setsum ∅ ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ X8 ∅ (λX11 : set ⇒ X11 ) (setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X6 (λX9 : (set → set → set λX10 : set ⇒ X10 ) (setsum ∅ ∅ ) X2 (λX8 : set → set → set → set → set X8 ∅ (setsum (X6 (λX9 : (set → set → set λX10 : set ⇒ X8 ∅ ∅ ∅ ∅ ) (X6 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X8 ∅ ∅ ∅ ∅ ) (λX9 : set ⇒ X6 (λX10 : (set → set → set λX11 : set ⇒ ∅ ) ∅ ) (setsum ∅ ∅ ∅ (X8 ∅ (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ (Inj1 ∅ (Inj0 (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set X9 (setsum (setsum (setsum ∅ ∅ (X7 (λX10 : set → set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (X8 (λX10 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → set → (set → set → set → set (Inj1 (Inj1 ∅ ∈ Inj0 (Inj0 ∅ → X1 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set → set λX10 : set → set → set setsum (X10 ∅ (X10 (Inj1 ∅ (X7 ∅ ∅ (λX11 : set ⇒ ∅ ) ∅ (setsum ∅ (X10 ∅ (setsum ∅ ∅ ) ∅ X1 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set → set λX10 : set → set → set Inj0 (X8 (setsum ∅ (Inj1 ∅ (λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (setsum (setsum (Inj1 (setsum ∅ ∅ (Inj0 (X6 ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set (Inj1 X6 ∈ Inj0 ∅ → X1 (λX8 : set → (set → set → set λX9 : ((set → set → set → set → set → set λX10 : set → set → set ∅ ) (Inj0 (setsum X4 X4 X2 (λX8 : set → set → set → set → set setsum (setsum (X7 (λX9 : set → set → set ∅ ) (Inj0 (setsum ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : (set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : (set → set → set → (set → set → set ∀X5 : (set → set → set ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : (set → set → set → set → set X5 (λX9 : set ⇒ X7 ) ) (λX8 : set ⇒ setsum (Inj1 (Inj0 (setsum ∅ ∅ X7 ) (λX8 : set ⇒ Inj1 (Inj1 (Inj0 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : (set → set → set → set → set X5 (λX9 : (set → set → set setsum ∅ (setsum (Inj1 ∅ (Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X10 ) ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ Inj0 (setsum X8 (setsum ∅ (Inj0 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKAQqvTJ4ndSHr1ZQDaWy7swgUsisvBHaN )
∀X0 : (set → ((set → set → set → set → set → (set → set → set → (set → set → (set → set → prop ∀X1 : ((set → set → set → (set → (set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : ((set → ((set → set → set → set → set → (set → set → set → set → set → prop (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → ((set → set → set → set setsum (Inj0 (setsum (Inj0 ∅ ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (Inj0 (Inj0 ∅ ) ) → (∀X4 : ((set → set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set → ((set → set → set → set X3 (λX8 : set → ((set → set → set → set Inj0 (setsum (setsum (Inj1 ∅ (X7 ∅ (λX9 : set → set ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 X10 (setsum (Inj0 (Inj1 ∅ X8 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj1 (Inj1 (setsum X6 ∅ ∈ X4 → X2 (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (setsum (Inj1 X5 (setsum (setsum ∅ ∅ X5 ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set → set (setsum (Inj0 (X5 (setsum ∅ ∅ ∅ ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ ∅ ) (setsum ∅ (Inj1 ∅ (Inj0 (X7 ∅ X2 (λX8 : set ⇒ Inj1 (Inj1 (Inj1 (X5 ∅ ∅ ) ∅ ∅ ) → (∀X4 : (set → set → (set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set setsum (setsum X7 (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) (Inj0 (setsum (X5 (Inj1 ∅ (setsum ∅ (Inj1 ∅ (setsum (X5 ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : (((set → set → set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set Inj1 (setsum (X5 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X10 ) (λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set X7 ) (setsum ∅ (setsum X6 (Inj0 (setsum ∅ ∅ (setsum ∅ X6 (setsum (setsum ∅ (Inj0 (Inj1 ∅ (X5 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ ∈ setsum (setsum (X4 (λX8 : set ⇒ setsum ∅ ∅ ) X6 (setsum (setsum (Inj0 ∅ (Inj0 ∅ (Inj0 ∅ ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set X1 (λX8 : set → set setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 (X7 (λX8 : (set → set → set ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : (set → set → set Inj0 (Inj1 (Inj0 (Inj0 ∅ ) (Inj1 (Inj0 (X5 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X7 (λX9 : (set → set → set ∅ ) ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → set X8 ) (Inj0 (X7 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X5 ) (λX8 : set ⇒ setsum ∅ X8 ) (X5 ∈ X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGu18729Jjg3NLr97zqEr6b5KNMbkxXxSi )
∀X0 : ((set → (set → set → set → set → set → (set → set → ((set → set → set → set → (set → set → ((set → set → set → (set → set → set → set → set → set → prop ∀X1 : (((set → set → (set → set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : ((((set → set → (set → set → set → set → set → set → (set → (set → set → (set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj0 X7 → X3 (λX8 : ((set → set → (set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (Inj1 ∅ X5 ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → (set → set → set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) X3 (λX8 : ((set → set → (set → set → set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ X7 ) ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : (set → set → set → set → set → (set → set → set ∀X6 : set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (setsum X7 (Inj0 (X6 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → (set → set → (set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ ∅ ) (Inj0 ∅ (X7 ∅ X1 (λX8 : (set → set → (set → set → set λX9 : set ⇒ setsum (setsum (X8 (λX10 : set ⇒ X7 ∅ ) (λX10 : set ⇒ X10 ) ∅ ∅ ) (Inj1 (setsum (X7 (Inj1 ∅ (Inj1 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum X9 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X6 ∈ setsum (setsum X5 ∅ ∅ → X1 (λX8 : (set → set → (set → set → set λX9 : set ⇒ Inj1 (Inj0 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set X1 (λX8 : (set → set → (set → set → set λX9 : set ⇒ Inj1 (Inj1 ∅ ) (Inj0 X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (Inj0 X10 (setsum (Inj1 ∅ (setsum (X8 ∅ (X7 ∅ ) (X6 (λX8 : set ⇒ X5 ) X2 (λX8 : set ⇒ X7 X8 ) X5 X5 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set → (set → set → set → set X0 (λX8 : set → (set → set → set → set → set λX9 : set → set λX10 : (set → set → set Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X9 X10 ) (Inj0 (Inj1 ∅ (setsum (Inj1 ∅ ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set → (set → set → set → set → set λX9 : set → set λX10 : (set → set → set Inj0 ∅ ) (λX8 : set ⇒ setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ Inj1 (setsum (setsum (setsum ∅ ∅ X7 (X9 (Inj0 ∅ ) (X4 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 (Inj1 X5 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TML1JMHfPJJNmssarrhySerdqXS12xtmS6y )
∀X0 : (set → ((set → set → (set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → set → set → ((set → set → set → set → set → (set → set → set → prop ∀X2 : (((set → set → set → (((set → set → set → set → set → (((set → set → set → (set → set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → ((set → set → set → prop ∀X3 : ((((set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set (Inj1 (X4 (Inj1 (X7 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ∅ ∈ Inj0 ∅ → X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set setsum (setsum (X8 (λX11 : (set → set → set → set Inj0 ∅ ) ∅ (X7 (λX11 : (set → set → set λX12 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (X8 (λX11 : (set → set → set → set setsum ∅ (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ ∅ ) X6 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 ∅ ) X3 (λX8 : ((set → set → set → (set → set → set → set → set X7 (λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X6 ) (X7 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , (Inj0 (Inj1 (setsum X7 ∅ ∈ Inj1 (setsum X7 ∅ → X3 (λX8 : ((set → set → set → (set → set → set → set → set Inj0 (X5 (setsum (Inj0 ∅ (Inj1 ∅ (λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) ∅ X3 (λX8 : ((set → set → set → (set → set → set → set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ ∅ (X8 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → (set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : ((set → set → set → set → set X2 (λX8 : (set → set → set λX9 : ((set → set → set → set ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set X7 (λX10 : set → set λX11 : set ⇒ Inj1 X11 ) ) (λX8 : set → set Inj0 (Inj1 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : (((set → set → set → set → set → (set → set → set (Inj1 (X6 (Inj1 (Inj0 ∅ ∈ Inj1 (Inj1 ∅ → X2 (λX8 : (set → set → set λX9 : ((set → set → set → set X6 (Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 X10 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 X8 ) (λX8 : set → set X6 ∅ ) X2 (λX8 : (set → set → set λX9 : ((set → set → set → set X7 (λX10 : (set → set → set λX11 : set ⇒ Inj1 ∅ ) (λX10 : set ⇒ ∅ ) ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum ∅ X10 X10 ) (λX8 : set ⇒ λX9 : set → set Inj1 (Inj0 ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (setsum ∅ ∅ X7 ) ∈ setsum (Inj1 X5 (Inj0 X7 → X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set setsum (X8 (λX11 : (set → set → set → set Inj1 X9 ) X7 (X10 (λX11 : set ⇒ X8 (λX12 : (set → set → set → set setsum ∅ ∅ ) ∅ ) ) (Inj0 X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → (set → set → set → set → set → set X1 (λX8 : (((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set ∅ ) (setsum (setsum ∅ (X7 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 ∅ (setsum ∅ ∅ (setsum (Inj0 X4 X5 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (Inj0 X5 ∈ X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (Inj0 (setsum (setsum (setsum ∅ ∅ X4 (Inj0 X4 ) → (∀X4 : ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set X6 (λX10 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (setsum (X9 (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ X10 ) (λX10 : set → set ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMgbfVv9WP66e7Ltfj4ZNswQ4ahijXyADc )
∀X0 : (set → set → set → prop ∀X1 : (set → (set → set → set → (set → ((set → set → set → set → set → set → set → set → set → prop ∀X2 : ((set → (set → set → set → ((set → set → set → (set → set → set → set → set → set → set → (((set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → set → ((set → set → set → (set → set → set → set → (set → (set → set → set → set → set → prop (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ∈ setsum (Inj0 (X7 (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (setsum (Inj1 ∅ X6 (X7 (Inj1 ∅ → X3 (λX8 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set λX9 : set → (set → set → set setsum (X8 (λX10 : (set → set → set → set ∅ ) (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ (setsum (X9 ∅ (λX10 : set ⇒ ∅ ) (setsum (Inj0 ∅ X6 ) ∅ ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set → set ∀X7 : (set → set → set → set (Inj0 (setsum (X7 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ∅ ∈ Inj1 (Inj0 (X7 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ → X3 (λX8 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set λX9 : set → (set → set → set X6 (setsum (setsum (X8 (λX10 : (set → set → set → set ∅ ) (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (Inj1 ∅ (setsum (X9 ∅ (λX10 : set ⇒ ∅ ) ∅ ) ∅ X2 (λX8 : set → (set → set → set λX9 : (set → set → set → (set → set → set → set λX10 : set ⇒ Inj1 (Inj0 ∅ ) ∅ (λX8 : (set → set → set λX9 : set ⇒ Inj0 (Inj1 X9 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → (set → set → set λX9 : (set → set → set → (set → set → set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : (set → set → set λX9 : set ⇒ X6 ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 ∅ → X2 (λX8 : set → (set → set → set λX9 : (set → set → set → (set → set → set → set λX10 : set ⇒ Inj0 (X8 (X8 X7 (λX11 : set ⇒ setsum ∅ ∅ ) (λX11 : set ⇒ X8 ∅ (λX12 : set ⇒ ∅ ) ) ) (setsum (setsum (X6 (λX8 : set → set Inj0 ∅ ) (Inj1 (X4 (λX8 : (set → set → set → set ∅ ) (setsum (Inj1 (X5 ∅ ∅ (λX8 : (set → set → set λX9 : set ⇒ X7 ) X2 (λX8 : set → (set → set → set λX9 : (set → set → set → (set → set → set → set λX10 : set ⇒ Inj0 ∅ ) ∅ (λX8 : (set → set → set λX9 : set ⇒ X6 (λX10 : set → set X9 ) ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set → set ∀X7 : set → set (X5 ∈ Inj1 (Inj0 (Inj0 X5 → X1 (λX8 : set ⇒ λX9 : set → set X9 (setsum (setsum (setsum ∅ ∅ (X9 ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ X8 ) (setsum (setsum (X7 (Inj0 ∅ (Inj1 (Inj1 ∅ (Inj1 (Inj0 ∅ (setsum ∅ X5 (Inj1 X5 X1 (λX8 : set ⇒ λX9 : set → set setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ Inj0 (X7 (X7 ∅ ) (setsum X5 ∅ (setsum (setsum (Inj1 (setsum ∅ ∅ (Inj0 (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (setsum X5 (X7 (Inj0 ∅ X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set (Inj1 ∅ ∈ X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ λX9 : set → set X6 ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ Inj0 (setsum (setsum X8 (setsum ∅ ∅ ∅ ) X5 ∅ X5 X0 (λX8 : set ⇒ setsum ∅ X5 ) ∅ ) → (∀X4 : (set → set → ((set → set → set → set ∀X5 : set → (set → set → set → set → set ∀X6 : ((set → set → set → set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → ((set → set → set → (set → set → set → set λX9 : set → (set → set → set Inj0 (setsum (X9 (X6 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) X7 ) (Inj0 ∅ X0 (λX8 : set ⇒ setsum (X6 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X8 ) (setsum ∅ (Inj1 (Inj1 ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ X8 ) (setsum (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) X5 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMEmi9k1e3G7HMohKN6QsX47RxSWdcHF9Qd )
∀X0 : ((set → set → set → set → set → prop ∀X1 : (((set → (set → set → set → set → set → (set → set → prop ∀X2 : (set → set → ((set → set → set → (set → (set → set → set → set → (set → set → set → prop ∀X3 : (((set → set → set → (set → set → set → set → (set → set → prop (∀X4 : set → ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X1 (λX8 : (set → (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ Inj1 (Inj0 ∅ ) X3 (λX8 : (set → set → set → (set → set → set Inj1 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → set → (set → set → set Inj1 (setsum (Inj1 (Inj1 ∅ (setsum ∅ (X8 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (setsum (Inj0 ∅ (Inj0 ∅ (Inj0 (Inj0 ∅ ) X3 (λX8 : (set → set → set → (set → set → set Inj0 (X8 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (λX9 : set ⇒ Inj1 (Inj1 ∅ ) ) (λX8 : set ⇒ Inj1 (setsum (Inj1 (setsum ∅ ∅ ∅ ) ) → (∀X4 : set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set → set → set X5 (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ (Inj1 ∅ ) (X4 ∅ (X7 (setsum ∅ (setsum ∅ ∅ X2 (λX8 : set ⇒ X8 ) (λX8 : set → set Inj0 (setsum ∅ (Inj0 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ (X5 (X4 (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj0 X4 → X2 (λX8 : set ⇒ setsum X8 X7 ) (λX8 : set → set X7 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) (setsum (setsum (Inj1 ∅ ∅ X5 X0 (λX8 : set → set → set X5 ) (setsum (Inj0 ∅ X4 ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : (set → set → set (Inj0 (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ∈ X5 (λX8 : set → set setsum (Inj0 (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) → X1 (λX8 : (set → (set → set → set → set setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum X8 (X7 (λX9 : set ⇒ X7 (λX10 : set ⇒ X8 ) ) ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : (set → set → (set → set → set → set → set ∀X7 : (set → (set → set → set → set X1 (λX8 : (set → (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ∈ Inj1 (setsum (X6 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ X7 ) (λX8 : set → set X7 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (setsum X8 ∅ ) (λX8 : set ⇒ X5 ) (Inj1 ∅ X0 (λX8 : set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set → set Inj0 (setsum ∅ X5 ) (Inj0 (setsum (Inj0 (Inj0 ∅ (Inj0 (Inj1 ∅ X2 (λX8 : set ⇒ X8 ) (λX8 : set → set setsum ∅ (X8 (setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXwLBWpHaJV9z3z3KHfBp7cfXdk4eNm4zy )
∀X0 : (set → set → set → (((set → set → set → set → set → prop ∀X1 : (set → set → (set → (set → set → set → ((set → set → (set → set → set → ((set → set → set → set → (set → set → prop ∀X2 : (set → (((set → set → set → set → set → set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → ((set → set → set → set → set → set → (set → set → set → (set → set → set → prop (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set X0 (λX8 : set ⇒ setsum (X7 (λX9 : (set → set → set ∅ ) (Inj1 (X7 (λX9 : (set → set → set ∅ ) ) ∅ (λX8 : (set → set → set → set ∅ ) X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set → set λX11 : set ⇒ X8 ) (λX8 : set ⇒ X5 ) X6 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set → set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set → set λX11 : set ⇒ X8 ) (λX8 : set ⇒ setsum (setsum (Inj1 ∅ ∅ (Inj0 (X7 ∅ (Inj1 ∅ ∅ X6 ) (Inj0 (Inj0 (setsum (setsum ∅ ∅ X6 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 (setsum X8 ∅ ) X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set → set λX11 : set ⇒ setsum (setsum (Inj1 ∅ X11 (setsum X8 (setsum (setsum ∅ ∅ X11 ) (λX8 : set ⇒ ∅ ) X5 (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : ((set → set → set → set → set setsum (Inj1 (Inj1 X8 ∅ ) (Inj0 (Inj0 ∅ (X5 (λX8 : set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : ((set → set → set → set → set X6 (λX10 : (set → set → set → set X7 ∅ ) ) (X6 (λX8 : (set → set → set → set Inj1 ∅ ) (setsum (Inj1 (X7 X4 X4 (Inj1 (Inj1 (setsum ∅ (Inj1 ∅ ∈ Inj0 (Inj0 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X2 (λX8 : set ⇒ λX9 : ((set → set → set → set → set X7 (λX10 : set ⇒ X9 (λX11 : set → set setsum X10 (setsum ∅ ∅ ) (Inj0 (Inj0 ∅ ) ) ∅ (setsum (X7 (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (Inj1 X5 X1 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set → set X8 ) (λX8 : set → set λX9 : set → set X8 (setsum ∅ (X7 (λX10 : set ⇒ X9 ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ setsum (Inj1 ∅ (setsum ∅ ∅ ) (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → set → set → set ∀X7 : (set → set → set → set X1 (λX8 : set ⇒ Inj0 (setsum X8 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set → set Inj0 (setsum (Inj1 ∅ (X9 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (setsum ∅ ∅ ∈ X4 → X0 (λX8 : set ⇒ Inj1 (Inj1 (setsum X6 (Inj1 ∅ ) ∅ (λX8 : (set → set → set → set Inj0 (Inj0 ∅ ) X0 (λX8 : set ⇒ X8 ) (Inj1 ∅ (λX8 : (set → set → set → set setsum ∅ ∅ ) ) → (∀X4 : (set → set → ((set → set → set → set → (set → set → set ∀X5 : (((set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ Inj1 X6 ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (λX9 : (set → set → set ∅ ) (λX9 : set → set X9 ∅ ) ) (λX8 : (set → set → set → set ∅ ) (setsum ∅ X7 ∈ Inj1 (setsum ∅ (X4 (λX8 : set ⇒ X5 (λX9 : (set → set → set ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPam4CY6CkY4M4eJTKyKs9PRUkQGZXcUBX )
∀X0 : (set → set → set → (set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → (set → (set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → ((set → set → set → (set → set → set → set → ((set → set → (set → set → (set → set → set → set → prop ∀X3 : ((set → set → set → set → ((set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set → set ∅ ) (λX8 : set → set setsum X5 (setsum (X6 (λX9 : (set → set → set → set setsum ∅ ∅ ) (X8 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set → set → set ∅ ) (λX8 : set → set ∅ ) (X6 ∈ Inj1 X5 ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : set , (Inj0 (setsum (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (Inj0 (Inj1 ∅ ∈ X7 → X2 (λX8 : (set → (set → set → set → set → set λX9 : (set → set → set → (set → set → set setsum (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj0 ∅ (X6 (λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ X11 ) ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum (setsum (setsum X11 (setsum ∅ ∅ (setsum (X8 ∅ ∅ ∅ ) X2 (λX8 : (set → (set → set → set → set → set λX9 : (set → set → set → (set → set → set Inj0 (setsum (Inj0 (X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : (set → (set → set → set → set X2 (λX8 : (set → (set → set → set → set → set λX9 : (set → set → set → (set → set → set X7 (λX10 : set ⇒ λX11 : set → set X8 (λX12 : set ⇒ λX13 : set → set λX14 : set ⇒ X11 (setsum ∅ ∅ ) ) ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum (Inj1 (X10 ∅ ∅ ) False ) → (∀X4 : ((set → set → set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) X5 (λX8 : set ⇒ λX9 : set → set setsum ∅ (Inj0 (Inj0 X6 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ (Inj1 X9 ) ∅ (λX8 : set ⇒ λX9 : set → set X8 ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (setsum (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum ∅ (setsum ∅ ∅ (setsum (Inj1 X7 (setsum (Inj0 ∅ (Inj1 ∅ (X4 (Inj1 (setsum (Inj1 ∅ (X4 ∅ ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj0 (Inj1 (X11 ∅ (X11 X12 ) (setsum (Inj0 (X5 (setsum ∅ ∅ (setsum ∅ X7 X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ (Inj1 (X11 (X11 ∅ ) ∅ (Inj1 ∅ X3 (λX8 : set → set → set Inj1 ∅ ) (λX8 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUy8L2kHL8r8p5XSKCmBRL77A3CcEXwC2Z )
∀X0 : (((((set → set → set → set → (set → set → set → set → set → set → set → (set → set → set → set → (set → set → prop ∀X1 : (set → set → (((set → set → set → set → set → set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → set → set → set → set → set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set ∀X7 : (((set → set → set → set → set X0 (λX8 : (((set → set → set → set → (set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ setsum (Inj1 ∅ (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (X5 ∅ ) X3 (λX8 : set ⇒ λX9 : ((set → set → set → set X8 ) (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , (Inj1 (setsum (setsum ∅ ∅ (setsum (Inj0 ∅ X7 ∈ setsum (setsum (Inj1 (Inj1 ∅ (Inj1 X7 (X6 X7 → X3 (λX8 : set ⇒ λX9 : ((set → set → set → set setsum (setsum (X6 (X6 ∅ (Inj1 (setsum ∅ ∅ X7 ) (setsum X4 (Inj0 (setsum ∅ X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ setsum ∅ (X5 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ setsum X10 (setsum ∅ ∅ ) ) (λX8 : (set → set → set → set → set setsum (Inj0 (Inj1 (setsum ∅ ∅ (X6 ∅ ) (setsum (setsum (setsum ∅ (Inj0 ∅ (X6 (Inj1 ∅ ∅ (λX8 : set ⇒ X6 ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set → set (X7 (setsum ∅ (Inj0 ∅ ∈ setsum (setsum X5 ∅ (setsum (X4 ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ∅ → X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 (setsum ∅ (Inj1 X12 (λX13 : set ⇒ ∅ ) X11 ) ∅ (setsum X5 (setsum (setsum (Inj1 ∅ (Inj0 ∅ (Inj1 (Inj1 ∅ (setsum (X4 (X4 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X6 (λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ) (setsum ∅ ∅ (Inj0 (X7 (setsum ∅ (Inj1 ∅ ) → (∀X4 : ((set → set → set → set → ((set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj0 ∅ (Inj1 (setsum X6 ∅ ∅ (Inj1 (Inj0 (X5 (Inj1 ∅ (Inj0 (Inj1 ∅ ∈ X5 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj0 (X7 (Inj1 (X7 ∅ ∅ X4 ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum X4 ∅ X1 (λX8 : set ⇒ Inj1 (X7 (setsum (setsum ∅ ∅ X5 X8 ) (λX8 : (set → set → set → set → set X6 ∅ (X8 (λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) (Inj0 (setsum ∅ ∅ (X6 ∅ (Inj0 ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj1 (Inj0 (X7 (Inj1 ∅ ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set → set setsum ∅ X7 ) ∅ (λX8 : set ⇒ Inj1 (Inj1 (setsum ∅ (X5 ∅ ) (Inj1 (setsum (Inj0 ∅ ∅ ∈ setsum (X5 (X4 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set (setsum ∅ ∅ ∈ Inj0 (setsum ∅ (setsum ∅ X4 → X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 (Inj1 ∅ (λX13 : set ⇒ ∅ ) X10 ) ∅ (Inj1 ∅ ∅ (setsum (Inj1 ∅ (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ X0 (λX8 : (((set → set → set → set → (set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ (setsum (setsum (setsum ∅ ∅ ∅ (X7 (λX11 : set ⇒ λX12 : set ⇒ X9 ∅ ) ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : (set → set → set X0 (λX8 : (((set → set → set → set → (set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ setsum X10 (X8 (λX11 : (set → set → set → set λX12 : set → set ∅ ) (Inj0 ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum X5 (Inj0 (setsum X5 X8 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUekq3Pt6LR324GQ9qcPVGgsTyrcveznSZ )
∀X0 : ((set → set → ((set → set → set → (set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → (set → set → set → set → set → (set → set → prop ∀X2 : ((((set → set → set → set → ((set → set → set → set → set → set → set → set → (set → (set → set → set → set → ((set → set → set → prop ∀X3 : (((set → set → set → set → set → set → ((set → set → set → set → (set → set → set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set → set (Inj0 (setsum X4 (Inj1 (Inj0 ∅ ∈ Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X10 ) (setsum (setsum ∅ ∅ (setsum (setsum ∅ ∅ X4 (X7 ∅ (λX8 : set ⇒ Inj1 (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (X6 ∅ ) X3 (λX8 : (set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → (set → set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : (set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → ((set → set → set → set → set → set → set ∀X7 : ((set → set → set → set X2 (λX8 : ((set → set → set → set → ((set → set → set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (setsum (X6 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (X7 (λX8 : set → set X8 ∅ ) X4 X4 (λX8 : set → set X5 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ setsum ∅ X4 → X2 (λX8 : ((set → set → set → set → ((set → set → set → set → set → set → set Inj1 (Inj0 (X8 (λX9 : set → set λX10 : set ⇒ X7 ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) X7 ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ X8 ) (setsum X6 (setsum ∅ (Inj0 ∅ (λX8 : set → set setsum (X5 (λX9 : set ⇒ ∅ ) X7 ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 ∅ ) ∅ (X5 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 (setsum ∅ ∅ → X3 (λX8 : (set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum ∅ ∅ X8 ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum (Inj1 (Inj0 (Inj1 ∅ X9 ) (setsum ∅ X7 ∅ (λX8 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ X7 (Inj1 (Inj0 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set → (set → set → set → set ∀X6 : (set → set → (set → set → set → set → set ∀X7 : set → ((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum (Inj1 (Inj1 (setsum ∅ ∅ ∅ ) (Inj0 (X6 (λX8 : set ⇒ setsum (Inj1 ∅ (X6 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set ⇒ setsum ∅ (setsum ∅ ∅ ) ∅ (setsum ∅ (setsum ∅ ∅ (Inj1 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) X2 (λX8 : ((set → set → set → set → ((set → set → set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) ∅ (λX8 : set → set ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : (set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj1 (X9 (λX13 : set ⇒ setsum ∅ X10 ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X0 (λX8 : set → set λX9 : (set → set → set → (set → set → set → set X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ X9 (λX11 : set ⇒ λX12 : set ⇒ X11 ) (λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ ∅ ) (setsum ∅ (Inj1 (setsum ∅ ∅ ) (setsum ∅ (setsum ∅ (Inj0 ∅ (X6 (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set λX9 : (set → set → set → (set → set → set → set ∅ ) (setsum (Inj0 ∅ (Inj1 ∅ (X4 (λX8 : set → set → set λX9 : set → set X9 (X8 (setsum ∅ ∅ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TML63VSyTovaCTwzRnCmV1Qgjo5hk7KwDcu )
∀X0 : ((set → set → set → set → ((set → set → set → set → set → prop ∀X1 : (set → set → ((set → (set → set → set → set → set → prop ∀X2 : (set → set → ((((set → set → set → set → (set → set → set → set → prop ∀X3 : ((((set → set → set → set → set → (((set → set → set → (set → set → set → ((set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (setsum ∅ (Inj0 (Inj0 ∅ (setsum (Inj1 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ∈ setsum (setsum (Inj1 X5 (X4 ∅ (Inj0 (Inj0 (Inj1 ∅ → X3 (λX8 : ((set → set → set → set → set λX9 : ((set → set → set → (set → set → set λX10 : (set → set → set Inj1 (setsum X7 ∅ ) (X6 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj0 ∅ X7 (setsum (setsum (Inj1 ∅ (setsum (Inj0 ∅ (X6 ∅ (Inj0 (setsum X5 ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → (set → set → set → (set → set → set → set (Inj1 (X6 ∅ ∈ X7 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X7 (λX9 : set → set λX10 : set ⇒ Inj0 (X9 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX9 : set ⇒ setsum X8 X8 ) (Inj0 ∅ ) (X6 (Inj1 ∅ → X3 (λX8 : ((set → set → set → set → set λX9 : ((set → set → set → (set → set → set λX10 : (set → set → set ∅ ) ∅ ∅ ∅ X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : (set → set → set Inj0 (X8 (Inj1 (setsum ∅ ∅ ∅ ) (X7 (λX8 : set → set λX9 : set ⇒ X6 X9 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 X9 ) (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (X4 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X6 ∅ (λX9 : set → set X8 ) X5 ∅ ) (λX8 : ((set → set → set → set → (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set → set X9 ) ) (λX8 : ((set → set → set → set → (set → set → set Inj1 X7 ) False ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X5 (Inj1 (setsum ∅ (Inj0 ∅ (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set → (set → set → set → set Inj1 (setsum ∅ (Inj0 (Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set ∀X6 : set → set ∀X7 : set , (Inj0 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ∈ X7 → X1 (λX8 : set ⇒ Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum X8 ∅ ) (λX8 : set → (set → set → set → set Inj1 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (X6 ∅ ) X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : (set → set → set Inj1 (Inj0 (Inj0 ∅ ) (setsum (X5 (λX8 : (set → set → set X5 (λX9 : (set → set → set X8 (λX10 : set ⇒ ∅ ) ) ) (X4 (Inj0 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → ((set → set → set → set (Inj0 ∅ ∈ Inj0 ∅ → X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : (set → set → set X7 (λX11 : (set → set → set setsum ∅ (Inj1 (X8 ∅ ∅ ) (λX11 : set → set setsum (Inj1 (X8 ∅ ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : (set → set → set Inj0 (Inj1 ∅ ) (X6 ∅ (Inj0 (Inj1 (Inj0 (setsum ∅ ∅ ∈ Inj0 (setsum (Inj1 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMc9ND2N8yTvgHyAdQBt5DAPUqcz2SB19ks )
∀X0 : (set → set → set → set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → (set → (set → set → set → set → prop ∀X3 : ((set → set → (set → set → set → set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : (set → set → set → set X1 (λX8 : set → set X6 (X7 (λX9 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (Inj1 ∅ X3 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set Inj1 (setsum (X10 (Inj1 ∅ ∅ (Inj1 (setsum ∅ ∅ ) (setsum (setsum (setsum ∅ ∅ (setsum (X6 ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (setsum ∅ (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set setsum ∅ X7 ) ∅ X3 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set setsum (Inj1 (Inj0 X9 (Inj1 (setsum (Inj1 ∅ (X8 ∅ ∅ (λX11 : set ⇒ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → ((set → set → set → set → (set → set → set ∀X7 : (set → (set → set → set → ((set → set → set → set → set → set (X4 ∈ Inj0 ∅ → X3 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set → set X9 ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) (X7 (λX8 : set ⇒ λX9 : set → set Inj0 (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ Inj1 ∅ ) ) (λX8 : set → set ∅ ) (X5 (X5 (setsum ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (X9 (Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X10 (X10 (Inj1 (Inj0 ∅ ) (Inj1 (X6 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set → set X1 (λX8 : set → set X5 (λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) (setsum (X5 (λX9 : set → set λX10 : set ⇒ X7 ∅ ∅ ) (setsum ∅ ∅ (X5 (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (X5 (λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 ∅ (setsum ∅ ∅ (setsum (X5 (λX9 : set → set λX10 : set ⇒ X8 ∅ ) ∅ (Inj0 ∅ (Inj0 (setsum ∅ ∅ ) (Inj0 ∅ X1 (λX8 : set → set setsum (Inj1 (Inj0 ∅ ∅ ) (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set X7 ) (setsum X4 (setsum X7 ∅ X0 (λX8 : set ⇒ Inj0 ∅ ) X6 ∅ (Inj1 (Inj0 (X5 (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ setsum (setsum (Inj1 (Inj1 ∅ (setsum (setsum ∅ ∅ X8 X8 ) (setsum (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ (Inj0 (setsum X7 ∅ (Inj1 X4 X6 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNSfYRRc4T8gca53oaRWAqcAMmahK9LAWX )
∀X0 : (set → (set → set → set → (set → set → set → set → prop ∀X1 : (((set → set → (set → set → set → set → set → (set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → (((set → set → set → set → (set → set → set → set → set → set → set → (set → set → (set → set → set → set → set → prop ∀X3 : (set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set → set → set → set (setsum (Inj1 (Inj1 ∅ ∅ ∈ setsum X5 (setsum (setsum ∅ ∅ ∅ → X3 (λX8 : set ⇒ X5 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ Inj0 (Inj0 (setsum (Inj0 ∅ ∅ ) X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj1 ∅ ) X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) X7 ) → (∀X4 : (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (setsum X10 X10 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (Inj1 X9 ∅ ) X6 ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 (Inj1 ∅ ∈ setsum (Inj0 (setsum X7 ∅ (Inj1 (setsum ∅ ∅ → X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ∅ X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 X11 ) (Inj1 X4 ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : (set → set → set ∀X6 : (set → set → set ∀X7 : set → set → (set → set → set (Inj0 (Inj1 (X6 (λX8 : set ⇒ ∅ ) ∈ Inj0 (setsum (X4 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (Inj1 ∅ (Inj0 ∅ → X1 (λX8 : (set → set → (set → set → set → set X5 (λX9 : set ⇒ setsum X9 (Inj1 ∅ ) ) (λX8 : set ⇒ ∅ ) (setsum (X4 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set → set ∅ ) (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) (setsum (setsum X6 ∅ X7 X1 (λX8 : (set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ Inj0 X8 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set λX9 : ((set → set → set → set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X9 ) (setsum (X6 (setsum ∅ ∅ ∅ X0 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set → set setsum (Inj1 (setsum (setsum ∅ ∅ (X9 ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : (((set → set → set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set → set ∅ ) ∅ (X4 (Inj1 (X4 (Inj1 ∅ (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (Inj0 (setsum ∅ (Inj0 ∅ (λX8 : set ⇒ Inj0 (X6 (X7 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) ) (X7 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) ∈ setsum (setsum (Inj1 ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMbzXQdySnQQ3GH2ATWB6tefoHS2DwXyEhw )
∀X0 : ((set → set → set → set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → set → set → set → prop ∀X2 : (set → set → ((((set → set → set → (set → set → set → set → set → (set → set → set → (set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set (Inj1 (setsum (Inj1 X4 (setsum (setsum ∅ ∅ (Inj1 ∅ ∈ setsum (Inj0 (X6 (X7 ∅ (Inj1 (setsum ∅ X4 → X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum X9 X9 ) ∅ X3 (λX8 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) (Inj1 (setsum X5 (setsum (Inj0 ∅ (Inj1 ∅ ) → (∀X4 : ((set → set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (setsum ∅ (setsum (X6 (setsum ∅ ∅ (λX8 : set → set setsum ∅ ∅ ) (X4 (λX8 : set → set λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) X1 (λX8 : set → set → set → set ∅ ) (setsum (setsum (setsum (X6 ∅ (λX8 : set → set ∅ ) (X6 ∅ (λX8 : set → set ∅ ) ∅ ∅ (X6 ∅ (λX8 : set → set X6 (setsum ∅ ∅ (λX9 : set → set setsum (setsum ∅ ∅ ∅ ) ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (Inj1 (setsum (setsum X7 (X4 (λX8 : set ⇒ ∅ ) (setsum X5 ∅ X2 (λX8 : set ⇒ setsum (setsum (Inj1 (Inj0 ∅ ∅ X7 ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj1 (Inj0 X8 ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) (λX8 : set ⇒ X5 X8 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set X3 (λX8 : set ⇒ X8 ) (Inj0 X6 X1 (λX8 : set → set → set → set ∅ ) ∅ (Inj0 (Inj1 (setsum (setsum ∅ ∅ X5 ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set → set → set → set setsum X5 (X6 ∅ ) (X4 (X4 (Inj0 (setsum ∅ ∅ (λX8 : set → set Inj0 (setsum ∅ ∅ ) (λX8 : set → set Inj1 (Inj0 (X8 ∅ ) (Inj0 ∅ X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X11 ) (setsum X7 (Inj0 (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 X4 ∈ setsum (Inj1 ∅ ∅ → X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 ) X7 ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set → set X0 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum X9 (Inj1 ∅ ) ∅ (X6 ∈ Inj0 (Inj0 X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSE6etr16K9Y5Q7B89bRbJyBgt9PXemBQY )
∀X0 : (set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → set → ((((set → set → set → (set → set → set → set → set → prop ∀X3 : (set → (set → (set → set → set → set → set → ((((set → set → set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (Inj1 (X5 (λX8 : (set → set → set → set λX9 : set → set setsum (setsum ∅ ∅ (X6 ∅ ) (setsum ∅ X7 X3 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ Inj1 (Inj0 (X9 (Inj1 ∅ (λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set → set setsum ∅ (X9 (λX10 : set ⇒ setsum X7 (Inj0 ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : ((set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ X7 (λX11 : set → set → set ∅ ) ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set → set X6 (λX10 : set → set λX11 : set ⇒ X11 ) (X7 (λX10 : set → set → set ∅ ) ) False ) → (∀X4 : (set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (Inj0 X6 ∈ X4 (λX8 : set ⇒ X6 ) → X2 (λX8 : (((set → set → set → set → set → set → set ∅ ) (λX8 : ((set → set → set → (set → set → set → set X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X2 (λX8 : (((set → set → set → set → set → set → set X7 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X7 X5 (Inj0 ∅ (λX9 : set ⇒ X8 (λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) ) ∅ (λX9 : set ⇒ X9 ) ) (λX8 : ((set → set → set → (set → set → set → set X8 (λX9 : set → set X6 ) (λX9 : set ⇒ setsum (setsum ∅ X6 X6 ) ∅ ) X2 (λX8 : (((set → set → set → set → set → set → set Inj1 (setsum X6 (Inj1 ∅ ) (λX8 : ((set → set → set → (set → set → set → set X7 (setsum (setsum (Inj1 ∅ (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ (setsum (X7 ∅ X6 (λX9 : set ⇒ ∅ ) (Inj0 ∅ (λX9 : set ⇒ X7 ∅ (Inj0 (X8 (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ) ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj1 ∅ ∈ Inj1 (setsum (Inj1 ∅ (setsum (X5 (λX8 : set → set ∅ ) ∅ → X1 (λX8 : set ⇒ Inj0 (Inj1 (setsum (setsum ∅ ∅ X6 ) (Inj0 (setsum (Inj1 (setsum ∅ ∅ (X4 ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (setsum X7 (Inj1 (X5 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ∈ Inj0 X6 → X1 (λX8 : set ⇒ ∅ ) (setsum X4 (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : (set → set → set → set X7 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set → (set → set → set ∀X7 : set , (setsum (setsum (Inj1 (Inj1 ∅ ∅ (setsum ∅ (X6 (Inj1 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) ∈ Inj0 (Inj0 (Inj0 (setsum ∅ ∅ → X0 (λX8 : set ⇒ Inj1 X8 ) (X6 (Inj0 ∅ (λX8 : set ⇒ setsum (Inj1 ∅ (setsum X8 (Inj1 ∅ ) (setsum X7 (Inj0 ∅ ) → (∀X4 : set → (set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (X5 (λX8 : (set → set → set → set X5 (λX9 : (set → set → set → set X8 (λX10 : set ⇒ X7 ) (Inj1 ∅ ) ) (setsum (X6 (λX8 : set → set ∅ ) (setsum (Inj0 (X6 (λX8 : set → set ∅ ) (setsum (Inj0 ∅ ∅ ∈ X5 (λX8 : (set → set → set → set Inj0 (Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMW7hSzKH9NYRiuATyJMLRYkq8aAUwDU4js )
∀X0 : (set → set → set → ((((set → set → set → set → set → (set → set → set → set → set → set → (set → set → prop ∀X1 : (((set → (set → set → set → (set → set → set → set → set → set → ((((set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → prop ∀X3 : ((set → (set → set → set → set → set → set → set → set → prop (∀X4 : (((set → set → set → set → set → ((set → set → set → (set → set → set ∀X5 : (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ → X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X6 ) → (∀X4 : (set → set → set ∀X5 : set → set → set ∀X6 : set → set → set → set ∀X7 : set → set X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 ∅ (λX11 : set ⇒ X10 ) (X7 (setsum (X7 ∅ ∅ ) (X5 (Inj0 (X4 (λX8 : set ⇒ Inj0 ∅ ) (setsum (Inj1 ∅ (Inj0 (X6 ∅ ∅ ∅ False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (setsum (setsum (Inj0 ∅ ∅ X4 ∈ Inj0 (Inj0 (Inj1 ∅ → X2 (λX8 : (((set → set → set → set → set Inj1 ∅ ) (setsum ∅ (X7 (Inj0 (Inj0 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : (set → set → set → set X2 (λX8 : (((set → set → set → set → set setsum ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ ) ∅ (Inj1 (Inj1 (setsum ∅ (Inj1 ∅ ∈ setsum (setsum (X4 (λX8 : set ⇒ Inj1 ∅ ) (Inj1 ∅ (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ X6 → X1 (λX8 : (set → (set → set → set → (set → set → set → set λX9 : set ⇒ setsum (setsum X7 (Inj1 (setsum ∅ ∅ (X8 (λX10 : set ⇒ λX11 : set → set Inj0 (X11 ∅ ) (λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 ∅ ) ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set X8 (λX11 : set → set setsum (setsum (X9 ∅ (Inj0 ∅ (X9 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → (set → set → set → (set → set → set → set λX9 : set ⇒ Inj0 (Inj0 (setsum ∅ X9 ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set setsum ∅ (X8 (λX11 : set → set ∅ ) ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (setsum ∅ (Inj0 (Inj1 ∅ ∈ X4 → X0 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj1 (Inj1 (Inj1 (Inj1 ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → set → set → (set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 (X6 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj1 ∅ (λX10 : set ⇒ setsum ∅ ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (Inj0 ∅ (λX8 : set ⇒ X8 ) X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum X10 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X8 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTc7CqcokpQFamwpuKWdf4oxFWtb9jyMTz )
∀X0 : (set → set → set → set → ((set → (set → set → set → set → set → set → set → prop ∀X1 : (set → ((set → set → set → set → set → set → (set → set → set → set → set → (set → (set → set → set → set → set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → (set → set → set → (set → set → set ∀X7 : set → set (X5 (X5 (Inj0 (X7 ∅ ∈ Inj1 (X6 (λX8 : set → set → set λX9 : set → set setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X5 (Inj1 ∅ ) → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum ∅ X9 ) ∅ (X7 (Inj1 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ X6 ) (setsum (Inj1 ∅ (X7 X5 ∅ ∅ (setsum (setsum (setsum X5 (X7 ∅ ∅ X6 (Inj0 ∅ (setsum X4 (Inj1 ∅ ∈ setsum (setsum (Inj0 X4 (Inj0 (Inj1 ∅ X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → (set → set → set ∀X7 : set , (Inj0 X5 ∈ Inj0 (setsum ∅ (setsum X5 (setsum ∅ ∅ → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ ∅ ) (Inj1 (setsum (setsum ∅ (Inj1 ∅ (X6 (λX8 : (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ X5 ) ∅ (setsum (Inj1 (Inj0 (setsum ∅ ∅ (Inj1 (Inj1 ∅ X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (X9 (λX10 : set ⇒ X9 (λX11 : set ⇒ X11 ) ) (Inj1 X7 ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → (set → set → set (X4 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (Inj0 (X6 ∅ ) (setsum (X7 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) ∅ ∈ Inj0 (setsum (Inj1 (Inj1 ∅ X5 → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set X8 ) X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ ∅ ) (setsum (X4 (λX8 : set ⇒ setsum X5 (setsum ∅ ∅ ) (setsum (X4 (λX8 : set ⇒ ∅ ) ∅ (X6 ∅ (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ (X6 ∅ (Inj0 (Inj1 (Inj1 (X6 ∅ (Inj0 (setsum (Inj0 (setsum ∅ ∅ (setsum (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set (setsum ∅ ∅ ∈ Inj1 (Inj0 (X5 (Inj0 ∅ → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ setsum ∅ ∅ ) X4 (X7 (λX8 : set ⇒ ∅ ) X4 X1 (λX8 : set ⇒ λX9 : (set → set → set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) (Inj1 (Inj0 (X5 (Inj1 ∅ (X5 ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set → set → set ∀X7 : set , (X7 ∈ X7 → X1 (λX8 : set ⇒ λX9 : (set → set → set → set → set → set λX10 : set → set λX11 : set ⇒ setsum X8 (Inj0 (Inj0 (setsum ∅ ∅ ) (setsum (Inj0 (setsum ∅ (setsum ∅ ∅ X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (setsum (X6 ∅ (Inj0 ∅ (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (Inj0 (Inj1 (setsum ∅ ∅ X1 (λX8 : set ⇒ λX9 : (set → set → set → set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj1 (Inj1 (setsum ∅ ∅ (setsum (X10 (setsum ∅ ∅ ∅ ) (setsum (Inj1 (Inj1 (Inj0 ∅ (X5 (Inj1 (Inj0 ∅ (setsum (Inj1 ∅ (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (X5 X7 X7 (setsum (Inj0 (setsum (Inj0 ∅ (X6 ∅ ∅ ∅ X7 ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : (set → set → ((set → set → set → (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : set ⇒ X8 (X8 (setsum (setsum ∅ ∅ (X8 ∅ (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) (X6 (setsum ∅ ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ X7 (λX11 : set ⇒ X10 ) (λX11 : set → set ∅ ) (λX11 : set ⇒ Inj1 ∅ ) ) ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (setsum (Inj1 ∅ (X7 ∅ (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) (λX8 : set → (set → set → set → set λX9 : set ⇒ X9 ) (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 X10 ) (λX8 : set → (set → set → set → set λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQBBuKR93kc2gFVPqfoTQXBoBqTzwBte1Q )
∀X0 : (set → set → set → (((set → set → set → set → set → set → prop ∀X1 : ((set → set → set → (((set → set → set → set → (set → set → set → set → set → set → (set → set → set → set → set → prop ∀X2 : (set → set → set → set → ((set → set → set → (set → set → set → prop ∀X3 : (((((set → set → set → (set → set → set → set → (set → set → set → set → (((set → set → set → (set → set → set → set → (set → set → set → prop (∀X4 : (set → (set → set → set → (set → set → set → set → set ∀X5 : ((set → set → set → (set → set → set → ((set → set → set → (set → set → set ∀X6 : set → set → set ∀X7 : set → set (Inj1 ∅ ∈ Inj1 (Inj0 ∅ → X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set setsum (setsum (Inj0 (Inj1 ∅ (setsum (Inj0 ∅ (X8 (λX9 : (set → set → set λX10 : set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) (X5 (λX9 : set → set → set λX10 : set → set X7 (Inj1 ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (λX8 : (set → set → set → (set → set → set setsum (Inj0 (X5 (λX9 : set → set → set λX10 : set → set X7 ∅ ) (λX9 : set → set setsum ∅ ∅ ) (λX9 : set ⇒ X9 ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set setsum (setsum (Inj0 (X7 (λX9 : set → set λX10 : set ⇒ ∅ ) X5 X5 ) (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum X11 (Inj1 ∅ ) ) ) → (∀X4 : set → set → (set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set ∅ ) (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X2 (λX8 : set ⇒ Inj1 X7 ) ∅ (Inj1 (setsum (setsum ∅ X7 (Inj0 ∅ (λX8 : set → set Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ (X6 (setsum (setsum ∅ ∅ X8 ) (setsum ∅ (setsum (setsum X7 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set → set → set → set → set (X6 (λX8 : set ⇒ X6 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ) ∈ setsum (Inj0 (X7 (Inj0 ∅ ∅ ∅ (X6 (λX8 : set ⇒ ∅ ) (Inj0 ∅ → X2 (λX8 : set ⇒ Inj1 ∅ ) (X6 (λX8 : set ⇒ X6 (λX9 : set ⇒ Inj0 (Inj0 ∅ ) ) (setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ (λX8 : set → set Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (X7 X4 ∅ X4 ∅ X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set X8 (λX9 : (set → set → set λX10 : set → set X8 (λX11 : (set → set → set λX12 : set → set setsum ∅ (X9 (λX13 : set ⇒ ∅ ) ) (X8 (λX11 : (set → set → set λX12 : set → set X11 (λX13 : set ⇒ ∅ ) ) (setsum ∅ ∅ (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ) (Inj0 (Inj1 (Inj1 ∅ (λX9 : set ⇒ X6 (λX10 : set ⇒ Inj1 (X7 ∅ ∅ ∅ ∅ ) ) ) (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ (Inj1 (setsum (Inj1 ∅ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set → (set → set → set → set → set X1 (λX8 : set → set → set λX9 : ((set → set → set → set λX10 : set → set → set λX11 : set ⇒ setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X8 ∅ ) (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set → set λX9 : ((set → set → set → set λX10 : set → set → set λX11 : set ⇒ ∅ ) (setsum (Inj1 (X4 (Inj1 ∅ (setsum ∅ (Inj1 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) X6 X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set X8 (λX9 : (set → set → set λX10 : set → set setsum (setsum (X8 (λX11 : (set → set → set λX12 : set → set ∅ ) ∅ (λX11 : set ⇒ ∅ ) ∅ (setsum X7 (X10 ∅ ) (setsum (Inj1 ∅ ∅ (λX9 : set ⇒ setsum ∅ ∅ ) ) (λX8 : (set → set → set → (set → set → set X6 ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) ) → (∀X4 : ((set → set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X3 (λX8 : (((set → set → set → (set → set → set → set → (set → set → set setsum (Inj1 (X7 ∅ (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ∅ ) (λX8 : (set → set → set → (set → set → set Inj1 X6 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 X9 ) X0 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum (X7 (setsum ∅ (setsum ∅ ∅ (λX10 : set → set λX11 : set ⇒ X8 (λX12 : set ⇒ λX13 : set ⇒ Inj1 ∅ ) ) (X7 (setsum ∅ ∅ (λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ) ) → (∀X4 : (set → set → set → set ∀X5 : (set → set → (set → set → set → set ∀X6 : set → set → set ∀X7 : ((set → set → set → set → ((set → set → set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum X8 ∅ X8 ) (λX8 : (set → set → set → set λX9 : set ⇒ X6 (setsum ∅ ∅ (Inj0 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKSLqCBCZuikYh9hrV4iJq9Rwg46e5rLtb )
∀X0 : (set → set → (set → ((set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → set → set → (set → set → prop ∀X2 : (set → set → (set → set → set → (set → set → set → (set → set → set → prop ∀X3 : ((set → set → set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ setsum ∅ ∅ ) (X6 (setsum (Inj0 ∅ ∅ (λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ) (Inj0 (setsum X5 (X7 (λX8 : set ⇒ X5 ) (setsum (setsum (Inj1 ∅ (Inj1 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 (setsum ∅ (Inj0 ∅ (setsum ∅ ∅ (λX8 : set ⇒ X7 (λX9 : set ⇒ Inj0 (Inj1 X8 ) ) X3 (λX8 : set → set → set λX9 : set → set → set → set setsum (Inj1 (X6 ∅ (λX10 : set → set λX11 : set ⇒ X11 ) (X9 ∅ (Inj0 (X6 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) (X7 (λX10 : set ⇒ Inj0 ∅ ) ) (X6 ∅ (λX8 : set → set λX9 : set ⇒ X8 (setsum (X8 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X3 (λX8 : set → set → set λX9 : set → set → set → set X7 (λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ Inj0 ∅ ) ) (setsum (X5 (λX8 : (set → set → set → set X7 (λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) ) (Inj1 (Inj0 (setsum ∅ ∅ (Inj0 ∅ ∈ setsum ∅ X4 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set → set → set λX9 : set → set → set → set X8 ∅ X6 ) (Inj1 (Inj0 (X5 (λX8 : set ⇒ X7 ∅ ) X2 (λX8 : set ⇒ X7 (Inj1 (setsum ∅ (X5 (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 (Inj1 X8 ) ) → (∀X4 : ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set → set (Inj0 ∅ ∈ X6 → X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 (Inj0 (setsum ∅ ∅ ) X0 (λX8 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ ∅ X6 ) (λX8 : set ⇒ λX9 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X5 ∅ (setsum (setsum ∅ (Inj0 ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 (Inj1 X6 ) X1 (λX8 : set ⇒ X5 (Inj0 X7 ∅ ) ∅ (Inj1 (Inj1 (X5 (X5 ∅ ∅ X6 (X5 (Inj1 ∅ (setsum (Inj0 X4 (Inj0 (Inj1 ∅ (λX8 : set ⇒ X7 ) ) → (∀X4 : (((set → set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ Inj0 X8 ) (Inj1 (Inj1 (X6 X7 (λX8 : set → set setsum ∅ ∅ ) X5 (Inj0 (setsum (X4 (λX8 : (set → set → set setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ setsum ∅ ∅ ) False ) → (∀X4 : set → set ∀X5 : (set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj1 (Inj0 (Inj0 (Inj1 ∅ → X0 (λX8 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ λX9 : (set → set → set setsum (Inj1 ∅ (setsum (Inj1 ∅ (Inj1 X7 ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj0 X5 → X0 (λX8 : set ⇒ setsum (setsum X8 ∅ (setsum X7 (setsum X8 X6 ) (λX8 : set ⇒ λX9 : (set → set → set X7 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) X1 (λX8 : set ⇒ Inj1 (Inj0 X8 ) (Inj1 ∅ ∅ X5 (λX8 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGM59iE2CVkXt6Aae68z66UJ9LQBiEnxe4 )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → (set → set → set → set → prop ∀X2 : (set → set → set → set → set → set → set → prop ∀X3 : ((set → (set → set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → (set → set → set → (set → set → set ∀X7 : set , X3 (λX8 : set → (set → set → set → set Inj1 (setsum (Inj0 ∅ (setsum X5 (setsum ∅ ∅ ) (λX8 : set → set → set setsum (X6 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) (setsum (Inj1 (Inj1 ∅ (setsum (Inj0 ∅ (X6 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (setsum X7 (setsum (Inj1 X7 (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set , (setsum (setsum ∅ (X6 ∅ (λX8 : set → set Inj1 ∅ ) (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ X4 ∈ Inj0 (setsum (X6 X5 (λX8 : set → set Inj1 ∅ ) (Inj1 ∅ X5 → X3 (λX8 : set → (set → set → set → set setsum (Inj0 (Inj0 (Inj0 ∅ ∅ ) (λX8 : set → set → set Inj1 ∅ ) (setsum ∅ X5 X3 (λX8 : set → (set → set → set → set X8 (X8 X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ X7 ) ) (λX8 : set → set → set ∅ ) X4 ) → (∀X4 : set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , (Inj1 (Inj1 (X6 (λX8 : (set → set → set ∅ ) (Inj1 ∅ ∈ X4 (Inj0 (X5 ∅ (X5 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj1 (setsum (Inj0 ∅ (Inj1 ∅ ) (Inj0 (setsum (setsum (Inj0 ∅ X7 X7 ) → (∀X4 : (((set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → ((set → set → set → set → (set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X11 ) (X7 (λX8 : set ⇒ λX9 : set → set Inj0 X8 ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 (setsum X4 (Inj0 (Inj0 ∅ ∈ Inj1 X6 → X1 (λX8 : set ⇒ ∅ ) X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (Inj1 X10 X10 ) ) → (∀X4 : (set → set → set ∀X5 : ((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ setsum (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) (Inj1 (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ X7 → X1 (λX8 : set ⇒ X6 ) X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum X8 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum ∅ ∅ ) (Inj1 X6 ) → (∀X4 : (((set → set → set → set → set → (set → set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (X4 (λX8 : (set → set → set → set setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (X5 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 ∅ (setsum X8 (X6 ∅ ) (setsum ∅ X7 (setsum (setsum ∅ (setsum ∅ ∅ (X6 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set (X5 ∈ setsum (setsum (X6 (λX8 : set ⇒ X8 ) (Inj0 (X4 ∅ (setsum (X6 (λX8 : set ⇒ Inj1 ∅ ) (Inj0 ∅ → X0 (λX8 : set ⇒ X8 ) (setsum (Inj1 (setsum (X7 ∅ (setsum ∅ ∅ (setsum ∅ (X7 (Inj0 ∅ X0 (λX8 : set ⇒ X6 (λX9 : set ⇒ Inj0 ∅ ) ) (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNJBLmArsWRcJGVjuCjGT7ttSPeC7RAimH )
∀X0 : (set → (set → (set → set → set → set → set → (set → set → (((set → set → set → set → (set → set → set → prop ∀X1 : ((((set → set → set → (set → set → set → set → set → set → set → prop ∀X2 : ((set → set → set → ((set → set → set → prop ∀X3 : (set → (set → set → set → set → set → set → set → set → (set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → set ∀X7 : set → (set → set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum (Inj0 X12 (X9 ∅ X11 ) (Inj0 (setsum X4 (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set X7 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ X10 ) (X7 ∅ (λX10 : set ⇒ λX11 : set ⇒ X8 ) (λX10 : set ⇒ X10 ) (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : ((set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (setsum (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set → set X7 (X7 ∅ ) False ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : (((set → set → set → set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set (Inj0 (setsum (setsum ∅ (setsum ∅ ∅ X6 ∈ Inj1 (setsum X6 ∅ → X2 (λX8 : set → set ∅ ) (λX8 : set → set Inj0 (setsum ∅ (X8 (setsum ∅ ∅ ) X2 (λX8 : set → set X5 (λX9 : (set → set → set λX10 : set ⇒ X7 (λX11 : set ⇒ X10 ) ) (λX9 : set → set λX10 : set ⇒ X8 ∅ ) (setsum (setsum (setsum ∅ ∅ (X7 (λX9 : set ⇒ ∅ ) X6 ) (λX8 : set → set setsum (X7 (λX9 : set ⇒ X8 (Inj1 ∅ ) (X5 (λX9 : (set → set → set λX10 : set ⇒ Inj0 (X9 (λX11 : set ⇒ ∅ ) ) (λX9 : set → set λX10 : set ⇒ ∅ ) (X5 (λX9 : (set → set → set λX10 : set ⇒ Inj1 ∅ ) (λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set Inj1 X7 ) (λX8 : set → set ∅ ) (X5 (Inj1 (setsum (setsum ∅ ∅ ∅ ∈ Inj1 (X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → set → set X1 (λX8 : ((set → set → set → (set → set → set → set → set X7 (X7 ∅ X5 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , X1 (λX8 : ((set → set → set → (set → set → set → set → set ∅ ) (Inj0 ∅ (X7 ∈ Inj1 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (setsum (setsum (Inj1 (setsum ∅ ∅ (X7 (setsum ∅ ∅ ∅ ∈ Inj1 (setsum X6 (Inj0 X6 → X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set ∅ ) (λX8 : set ⇒ setsum ∅ X6 ) (λX8 : (set → set → set → set λX9 : set → set Inj0 (X8 (λX10 : set ⇒ setsum (X9 ∅ (Inj0 ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → (set → set → set → set setsum (setsum (Inj1 (Inj1 ∅ (setsum (Inj0 ∅ (Inj0 ∅ (X6 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj1 ∅ ∅ ) ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set Inj1 ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ∈ setsum X4 (Inj1 (setsum (Inj0 ∅ (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGaj4s7pByV3Ujt6VnBFtkZA1dm3MuCCK2 )
∀X0 : ((set → set → set → set → set → set → prop ∀X1 : (set → set → (set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → (set → set → set → prop ∀X3 : (set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set → set ∀X7 : set → set → set (X7 (Inj0 ∅ (setsum ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ∈ X4 → X3 (λX8 : set ⇒ X8 ) (Inj1 (Inj0 ∅ (setsum (Inj1 (Inj1 (X6 ∅ (setsum (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj0 ∅ (λX8 : set ⇒ X5 (Inj1 (X5 (Inj0 ∅ ∅ (X5 ∅ ∅ ∅ ∅ ∅ (Inj1 (Inj0 ∅ (setsum (X5 X8 (X5 ∅ ∅ ∅ ∅ (X5 ∅ ∅ ∅ ∅ (Inj0 ∅ X8 (setsum ∅ (Inj0 (X6 ∅ ) (X7 (setsum (Inj0 (Inj1 ∅ (X7 X4 (setsum ∅ ∅ X4 ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ setsum ∅ (setsum X7 (Inj0 ∅ ) (X6 (X5 (setsum (setsum ∅ ∅ (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ ∅ ) ∅ (Inj0 X7 (λX8 : set ⇒ Inj0 (setsum ∅ (X6 (X6 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ (λX9 : set → set λX10 : set ⇒ X8 ) (λX9 : set ⇒ setsum ∅ ∅ ) X8 ) ∅ (Inj0 (X6 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X8 (Inj0 ∅ ) (λX8 : set ⇒ setsum ∅ (setsum ∅ ∅ ) X7 ∈ X4 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) (setsum ∅ (setsum (X4 (λX8 : set ⇒ ∅ ) ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (setsum X4 ∅ ∈ Inj0 (Inj0 (setsum ∅ ∅ → X2 (λX8 : ((set → set → set → set → set Inj0 X7 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ X5 → X2 (λX8 : ((set → set → set → set → set Inj0 (setsum (setsum (setsum ∅ ∅ (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X0 (λX8 : set → set → set → set Inj0 (setsum (setsum ∅ (Inj1 ∅ X7 ) X6 ) → (∀X4 : (((set → set → set → (set → set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set (Inj0 (X7 (setsum X6 ∅ (λX8 : set ⇒ ∅ ) ∈ Inj0 (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) → X2 (λX8 : ((set → set → set → set → set Inj0 (X5 (X8 (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ (Inj1 (Inj1 (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : (((set → set → set → (set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ X5 (λX9 : (set → set → set λX10 : set → set setsum X7 (Inj0 (setsum ∅ ∅ ) (setsum ∅ (X5 (λX9 : (set → set → set λX10 : set → set ∅ ) ∅ (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ (setsum (Inj1 (setsum ∅ ∅ ∅ X0 (λX8 : set → set → set → set X8 (X8 (setsum X6 (setsum ∅ ∅ (setsum (Inj1 ∅ ∅ (setsum (X8 ∅ ∅ ∅ ∅ (setsum (setsum (X8 ∅ ∅ ∅ (setsum ∅ ∅ (Inj0 X6 (Inj0 (setsum ∅ (Inj0 ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → set → set (Inj1 (Inj0 (X6 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) ∈ X7 ∅ (setsum ∅ ∅ → X2 (λX8 : ((set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 (setsum (setsum ∅ (Inj0 ∅ (X7 ∅ (X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) X0 (λX8 : set → set → set → set ∅ ) X5 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set X0 (λX8 : set → set → set → set setsum ∅ (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ ) (setsum (X6 (λX8 : set → set → set Inj0 ∅ ) (Inj0 (setsum ∅ ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 (X7 (λX8 : (set → set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (X7 (λX8 : (set → set → set X5 ) (λX8 : set ⇒ X6 (λX9 : set → set → set ∅ ) ∅ ∅ ∅ ) (Inj0 ∅ X3 (λX8 : set ⇒ setsum (X7 (λX9 : (set → set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ Inj0 ∅ ) ∅ ∅ ) (X4 ∅ (setsum ∅ (Inj0 (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (setsum (setsum X8 (setsum ∅ ∅ (Inj1 ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHFjeF4mLhTnKnYwoDywqbbmQ8AVmRENCL )
∀X0 : (((((set → set → set → set → set → set → set → ((((set → set → set → set → set → ((set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : (set → (set → (set → set → set → ((set → set → set → set → set → (set → set → set → set → set → prop ∀X3 : (set → set → set → (set → set → set → set → (set → set → set → prop (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set X6 (λX9 : (set → set → set ∅ ) (Inj0 (Inj1 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X8 (λX12 : set → set λX13 : set ⇒ Inj0 ∅ ) ) X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : (set → set → set Inj1 (Inj0 (Inj0 ∅ ) X9 ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (Inj1 X10 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (Inj1 (setsum ∅ (X5 (λX8 : (set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) ∈ Inj0 (Inj1 (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ Inj0 (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ ) ∅ (setsum (Inj1 ∅ (Inj1 (setsum (X7 ∅ (setsum ∅ ∅ (X7 (setsum ∅ (X7 ∅ X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ X8 ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set (Inj0 (X5 (λX8 : (set → set → set → set ∅ ) ∈ Inj1 (Inj0 (Inj1 (Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set λX11 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set λX11 : set ⇒ X11 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj0 (setsum (setsum X7 ∅ ∅ → X1 (λX8 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) (setsum (setsum X4 X7 (setsum (setsum (Inj1 ∅ ∅ X6 (Inj0 (setsum ∅ ∅ (setsum X6 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X1 (λX8 : set ⇒ setsum (setsum X8 ∅ (X7 ∅ ) (setsum ∅ (Inj1 ∅ X5 (Inj0 (X7 (setsum ∅ (Inj1 ∅ False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum X11 X11 (setsum (setsum (setsum ∅ ∅ ∅ X8 ) X0 (λX8 : (((set → set → set → set → set → set Inj0 (setsum ∅ (Inj1 (X5 (λX9 : (set → set → set → set ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ Inj0 (Inj0 (X8 (λX12 : set → set λX13 : set ⇒ Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum X4 (setsum (setsum (Inj0 ∅ (X5 ∅ X6 ∈ setsum (Inj1 (Inj0 (Inj0 ∅ (setsum ∅ ∅ → X0 (λX8 : (((set → set → set → set → set → set setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj0 (X5 ∅ (Inj1 (X8 (λX9 : (set → set → set → set ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (Inj1 X9 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTXPUy3UHCJxdskqEKFKjYjEHYC9DLBCWA )
∀X0 : (set → set → set → (set → set → set → ((set → set → set → set → set → prop ∀X1 : (set → (set → set → set → ((set → set → set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : ((set → (set → set → set → (((set → set → set → set → ((set → set → set → set → set → prop ∀X3 : ((set → ((set → set → set → set → set → (set → set → set → set → set → set → prop (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set (Inj1 X6 ∈ Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj0 ∅ ) (λX8 : set → set Inj0 (setsum (Inj1 ∅ (Inj1 (Inj1 ∅ ) ∅ (Inj0 ∅ X3 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set Inj0 (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → ((set → set → set → set → set λX9 : set → set → set → set setsum (Inj0 (Inj0 (setsum ∅ ∅ (X9 (setsum (Inj1 ∅ (X8 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) X6 X6 ) (setsum ∅ (Inj1 ∅ False ) → (∀X4 : (set → set → set → set → set ∀X5 : set → set ∀X6 : (set → (set → set → set → set → (set → set → set ∀X7 : (set → (set → set → set → set X2 (λX8 : set → (set → set → set λX9 : ((set → set → set → set λX10 : (set → set → set Inj1 (Inj1 (Inj0 ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → (set → set → set λX9 : ((set → set → set → set λX10 : (set → set → set X8 ∅ (λX11 : set ⇒ Inj1 (setsum ∅ (setsum ∅ ∅ ) ) (Inj1 (Inj0 X7 False ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ setsum (Inj1 (X4 (X4 ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : (set → set → set λX11 : set ⇒ setsum X11 (Inj0 ∅ ) (X5 ∅ (X5 ∅ (λX8 : set → set λX9 : set ⇒ Inj0 (X6 (λX10 : set ⇒ λX11 : set → set X11 (setsum ∅ ∅ ) ) (Inj1 ∅ ∅ ) → (∀X4 : ((set → set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : (set → set → set λX11 : set ⇒ X9 ∅ ∅ ) (X4 (λX8 : set → set → set setsum ∅ X7 ) ∅ (λX8 : set ⇒ Inj0 (Inj1 (setsum ∅ ∅ ) ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) X7 (Inj0 X7 False ) → (∀X4 : (((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj0 (setsum X5 ∅ ∈ setsum (setsum (X7 X5 ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : (set → set → set λX11 : set ⇒ X11 ) ∅ (X7 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) ∅ ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 X8 ) (λX8 : set → set Inj1 ∅ ) (setsum (X7 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ X6 ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum (setsum (X4 ∅ ∅ (Inj0 ∅ ∅ (Inj1 ∅ (X4 (X4 (setsum ∅ ∅ (X7 ∅ (Inj0 ∅ (Inj1 ∅ (setsum (Inj0 ∅ (Inj1 ∅ (setsum (X4 ∅ ∅ ∅ ∅ (Inj1 ∅ (setsum (Inj0 ∅ ∅ ∈ Inj1 (setsum (setsum (X7 ∅ (setsum ∅ ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (setsum (Inj1 (setsum ∅ ∅ (X11 (X11 ∅ ) (λX8 : set → set Inj1 (X8 X6 ) (Inj1 (X7 (setsum (X4 ∅ ∅ ∅ ∅ X6 (Inj0 X6 X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : (set → set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj0 (setsum (X7 ∅ X5 (λX8 : set → set λX9 : set ⇒ X8 (Inj1 (X8 ∅ ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ (Inj0 (Inj0 ∅ (Inj0 ∅ X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYQ5L7yhMo49irKFBXDL1mFouXppwCbJSX )
∀X0 : (set → set → (set → set → set → prop ∀X1 : (set → set → set → set → ((set → set → set → set → (set → set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → set → (((set → set → set → set → set → set → prop ∀X3 : (((set → set → set → set → set → (((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj1 (Inj0 X10 ) (λX8 : (set → set → set → set → set ∅ ) X3 (λX8 : (set → set → set setsum ∅ (Inj0 (setsum (Inj0 ∅ ∅ ) ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set → (set → set → (set → set → set ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 (setsum (Inj1 (Inj0 ∅ X6 → X3 (λX8 : (set → set → set X5 ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ (λX9 : set ⇒ ∅ ) (setsum (Inj0 (Inj1 ∅ (X8 (λX9 : set ⇒ Inj0 ∅ ) ) (Inj1 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ setsum (Inj0 (setsum ∅ X7 ∅ ) ∅ (X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (setsum ∅ (setsum ∅ (Inj1 ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set → set → set → set ∀X6 : set → set ∀X7 : (((set → set → set → set → set → ((set → set → set → (set → set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ X8 ) (λX8 : (set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (X6 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set → (set → set → set → set ∀X6 : set → set → (set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ (X9 ∅ (λX11 : set ⇒ ∅ ) ∅ ) (λX8 : (set → set → set → set → set ∅ ) X3 (λX8 : (set → set → set ∅ ) (setsum X7 ∅ (λX8 : (set → set → set → set λX9 : set ⇒ setsum (X6 (setsum ∅ (X8 (λX10 : set ⇒ ∅ ) ∅ (setsum (X6 ∅ ∅ (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ (λX10 : set ⇒ setsum (Inj1 ∅ ∅ ) X9 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ Inj0 ∅ → X3 (λX8 : (set → set → set Inj0 ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum (setsum (Inj0 ∅ ∅ (Inj1 X5 ) X6 ∅ (λX8 : set → set λX9 : set ⇒ Inj1 (Inj0 (setsum (Inj1 ∅ ∅ ) (λX8 : set ⇒ Inj1 (setsum (Inj1 (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → (set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (Inj0 (setsum X7 ∅ (setsum (setsum (Inj1 (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum X7 (Inj1 (Inj1 (Inj1 ∅ (X7 ∈ setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : set ⇒ X10 ) (λX8 : (set → set → set → set → set Inj1 ∅ ) X0 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ X8 ) (setsum (X6 (Inj1 (setsum ∅ ∅ (setsum (X6 ∅ ∅ ∅ (setsum (setsum (Inj1 ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum X7 (setsum X4 ∅ ∈ setsum (X6 (X6 ∅ ∅ → X0 (λX8 : set ⇒ Inj1 (Inj1 (setsum (setsum ∅ ∅ X7 ) (λX8 : set ⇒ X6 ∅ ) X5 X0 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ Inj1 X5 ) (setsum ∅ (setsum X4 (Inj0 X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcTmjNdsoVfTspeqdZaz3kKTL33jJY2EbJ )
∀X0 : (((((set → set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → set → (set → set → set → prop ∀X2 : (set → set → set → set → set → prop ∀X3 : (set → set → ((((set → set → set → (set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum ∅ (setsum (Inj1 (Inj1 ∅ ∅ ∈ Inj1 X7 → X0 (λX8 : (((set → set → set → set → set setsum ∅ X7 ) (X6 (X6 ∅ X3 (λX8 : set ⇒ X8 ) (λX8 : ((set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (X9 (λX11 : set ⇒ setsum ∅ (Inj0 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set ∀X7 : (set → (set → set → set → set (setsum ∅ ∅ ∈ setsum (Inj0 (X7 (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) (setsum (Inj0 (X6 (λX8 : set → set → set λX9 : set → set ∅ ) (setsum X5 ∅ → X3 (λX8 : set ⇒ setsum (Inj0 ∅ ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (Inj0 ∅ ) X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ X8 (λX11 : set → set Inj0 (Inj0 ∅ ) (λX11 : set ⇒ X11 ) ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set (setsum ∅ (X4 (setsum (setsum ∅ ∅ (Inj1 ∅ ∈ Inj1 (Inj1 (Inj0 (Inj0 ∅ → X2 (λX8 : set ⇒ X5 ) (X4 (Inj0 (setsum (Inj1 ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set → set X8 ) (Inj0 (Inj1 ∅ ) → (∀X4 : set → set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X2 (λX8 : set ⇒ Inj0 (setsum (Inj0 (X7 (λX9 : set ⇒ ∅ ) ∅ ) (X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X9 X10 ) (Inj0 (Inj0 (Inj1 (X4 ∅ ∅ ∅ ∅ (Inj0 ∅ False ) → (∀X4 : (set → set → set → set ∀X5 : set → set → set → set → set ∀X6 : ((set → set → set → set → set → (set → set → set → set ∀X7 : set , (Inj1 (setsum (X6 (λX8 : set → set → set Inj0 ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (X6 (λX8 : set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ ∈ setsum (setsum (setsum (Inj1 ∅ X7 (Inj1 (Inj1 ∅ (Inj1 (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X2 (λX8 : set ⇒ ∅ ) (setsum (X5 (Inj1 (Inj0 ∅ (setsum ∅ (X6 (λX8 : set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (Inj1 (setsum ∅ ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ (setsum (setsum ∅ (X6 (λX8 : set → set → set ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (X5 ∅ ∅ ∅ ∅ ∅ X7 X1 (λX8 : set → set setsum (X8 (Inj1 ∅ (Inj1 (X8 ∅ ) (setsum ∅ (setsum ∅ ∅ (X5 (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (setsum (Inj1 ∅ ∅ ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set → set → set setsum ∅ ∅ ) (setsum ∅ ∅ (λX10 : set ⇒ setsum ∅ ∅ ) X7 ) (λX8 : set ⇒ λX9 : set ⇒ setsum X7 X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set ∅ ) (Inj1 X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 (Inj0 ∅ ) (setsum X5 X5 ∈ Inj0 (setsum (Inj0 (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (set → set → set ∀X7 ∈ Inj1 ∅ X1 (λX8 : set → set setsum (X5 (λX9 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) ∅ ) ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X0 (λX8 : (((set → set → set → set → set ∅ ) (setsum (setsum (Inj1 (X6 (λX8 : set ⇒ ∅ ) (setsum (Inj1 ∅ (Inj1 ∅ (X6 (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → set setsum (X6 (X5 (λX9 : (set → set → set → set ∅ ) ∅ ) (X6 (Inj1 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUCbhzUhr1jPbBNBJzTiJtVniUxJGSiYrY )
∀X0 : ((set → set → set → (set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : (set → set → set → (set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set X6 ) (λX8 : set ⇒ ∅ ) X3 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) (setsum X5 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : (set → set → set → set X3 (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ (X6 (setsum (X6 ∅ ∅ (X6 ∅ ∅ (setsum ∅ ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set → set (setsum (Inj1 (Inj0 ∅ (X6 (Inj1 (X4 ∅ (λX8 : set → set ∅ ) ∈ Inj0 (setsum (setsum ∅ (setsum ∅ ∅ (X5 (λX8 : set ⇒ Inj0 ∅ ) → X2 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum ∅ (X6 (setsum (Inj1 ∅ (X6 ∅ (λX9 : set → set ∅ ) (λX9 : set → set Inj1 (setsum ∅ ∅ ) ) ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (setsum X8 ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 (X5 (λX9 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (Inj0 X4 ∈ Inj0 (X5 (λX8 : set ⇒ setsum ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set , (setsum (setsum (setsum X5 (Inj1 ∅ ∅ (Inj0 ∅ ∈ Inj1 (setsum (setsum (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X7 ∅ → X1 (λX8 : set → set X6 X5 (λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (Inj1 ∅ (X8 (X8 ∅ ) ) (X6 (Inj0 (Inj1 (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X1 (λX8 : set → set setsum (X8 X7 (Inj0 ∅ ) (setsum (setsum X5 (Inj1 (setsum ∅ ∅ (setsum (setsum (Inj0 ∅ X7 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (setsum ∅ ∅ ∈ X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X7 ) ∅ (λX8 : set ⇒ ∅ ) → X1 (λX8 : set → set Inj0 ∅ ) ∅ X1 (λX8 : set → set X8 (setsum (Inj0 (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) (setsum ∅ (Inj0 (X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set → set → set → set ∀X6 : (set → set → set ∀X7 : ((set → set → set → (set → set → set → ((set → set → set → (set → set → set X0 (λX8 : set → set ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ X7 (λX10 : set → set → set λX11 : set → set ∅ ) (λX10 : set → set Inj1 (setsum ∅ ∅ ) (λX10 : set ⇒ ∅ ) ) ∅ (Inj0 (setsum (Inj1 ∅ X8 (X6 (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set Inj1 (Inj1 X6 ) (λX8 : set ⇒ Inj1 X6 ) (setsum (Inj1 (Inj1 ∅ (setsum X6 ∅ ∈ Inj1 (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X7 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZXZYh8QyhSHj3eK5JcACGdSy6t1xNQpfb )
∀X0 : (set → (((set → set → set → set → set → set → set → prop ∀X1 : ((set → ((set → set → set → set → (set → set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (set → ((set → set → set → set → set → prop ∀X3 : (set → set → (set → (set → set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , (X6 (λX8 : set → set → set ∅ ) ∈ setsum (setsum (Inj0 (Inj0 ∅ (setsum (Inj1 ∅ (Inj0 ∅ (setsum ∅ (X5 (λX8 : set → set → set Inj1 ∅ ) X7 X4 ∅ → X1 (λX8 : set → ((set → set → set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (setsum (Inj0 ∅ (Inj1 (Inj1 ∅ ) X3 (λX8 : set ⇒ X6 (λX9 : set → set → set ∅ ) ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ setsum ∅ (Inj1 (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → set (X4 ∈ X5 (λX8 : set ⇒ ∅ ) ∅ (setsum (setsum ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ ∅ ) X3 (λX8 : set ⇒ setsum (Inj0 (Inj1 ∅ (setsum ∅ (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : (set → set → set X7 ) (Inj1 X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set → set → set → set → set X2 (λX8 : set ⇒ λX9 : (set → set → set Inj0 (Inj1 (Inj0 ∅ ) ∅ False ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (Inj1 ∅ ∈ setsum (Inj1 X5 (Inj1 (Inj0 (setsum ∅ ∅ → X1 (λX8 : set → ((set → set → set → set → (set → set → set → set X8 (setsum (Inj0 (setsum ∅ ∅ ∅ (λX9 : set → set λX10 : set ⇒ setsum (Inj1 X7 (Inj1 (setsum ∅ ∅ ) (λX9 : set ⇒ setsum X9 ∅ ) (Inj1 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X7 ) ) → (∀X4 : set → (set → set → (set → set → set → set ∀X5 : (set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 X7 ) False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ Inj0 (setsum (setsum ∅ (Inj0 ∅ X7 ) X6 X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ ∅ ) (Inj1 ∅ X0 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ setsum (X9 (λX11 : set → set Inj0 (Inj1 ∅ ) ∅ ) (Inj1 (Inj1 (Inj1 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMP69cTt6LGA1BgVZwfym8rMjfiQrGrXfs3 )
∀X0 : (set → set → set → (set → set → ((set → set → set → set → prop ∀X1 : (set → (set → set → ((set → set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → ((set → set → ((set → set → set → set → prop ∀X3 : (set → set → (set → set → (set → set → set → set → set → prop (∀X4 : (((set → set → set → set → (set → set → set → set → (set → set → set → set ∀X5 : set → set → set ∀X6 : set → (set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set → set λX9 : (set → set → set X8 ∅ ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set Inj1 (X10 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ (X5 (X4 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X9 X10 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set setsum (setsum X8 (setsum X9 (Inj1 ∅ (Inj0 ∅ ) ∅ (Inj1 (setsum ∅ ∅ (Inj1 (setsum ∅ (setsum ∅ (X7 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∈ Inj0 (Inj0 (Inj1 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set Inj0 (setsum (Inj0 ∅ (X9 ∅ ) (Inj1 (Inj1 (X7 ∅ (λX8 : set ⇒ ∅ ) (X7 X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum X5 (setsum ∅ ∅ ) (Inj0 X4 X4 X2 (λX8 : set ⇒ X7 (setsum (Inj1 (setsum ∅ ∅ (Inj0 X6 (λX9 : set ⇒ X6 ) ) (λX8 : set → set λX9 : (set → set → set X8 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ setsum ∅ (setsum (setsum X6 ∅ ∅ → X2 (λX8 : set ⇒ X7 ) (λX8 : set → set λX9 : (set → set → set X9 (λX10 : set ⇒ X8 (setsum ∅ (setsum ∅ ∅ ) ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set ∅ ) ∅ (Inj1 (Inj1 (setsum (setsum ∅ ∅ X5 ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set X8 ) (Inj1 (setsum ∅ ∅ ∅ (λX8 : set → set setsum (setsum X7 (X5 (Inj1 ∅ (X8 ∅ ∅ ) (Inj1 (X6 X4 (λX8 : set → set Inj1 (Inj0 ∅ ) ∅ (setsum ∅ (setsum (Inj0 X7 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set Inj1 ∅ ) (setsum X5 ∅ (Inj0 ∅ (λX8 : set → set setsum ∅ (Inj0 ∅ ) ∅ ∅ (Inj1 ∅ ∈ Inj0 X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → (set → set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum ∅ (Inj0 (setsum X8 (X6 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (setsum ∅ ∅ (λX8 : set ⇒ X6 (setsum (setsum (setsum ∅ ∅ X7 (Inj1 X8 (λX9 : set ⇒ Inj1 (Inj0 ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ (setsum (Inj0 (Inj0 ∅ ∅ ∈ Inj0 X7 → X0 (λX8 : set ⇒ setsum X5 (setsum X6 ∅ ) (setsum (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum ∅ (setsum X4 ∅ (λX8 : set ⇒ Inj0 X5 ) (λX8 : set → set λX9 : set ⇒ Inj0 (setsum ∅ (Inj1 X9 ) X2 (λX8 : set ⇒ X7 ) (λX8 : set → set λX9 : (set → set → set setsum (Inj1 ∅ (X8 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMaeSeEK1gTLcHphY3TFsrCx9QLcLUvuoCj )
∀X0 : (set → (set → (set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → (set → set → set → ((set → set → set → (set → set → set → set → prop ∀X2 : ((set → set → set → set → (set → (set → set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → set → (((set → set → set → (set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , (Inj1 (setsum ∅ (X6 (λX8 : set → set → set ∅ ) ∈ Inj0 (Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : set → (set → set → set X6 (λX10 : set → set → set X8 ) ) ∅ X3 (λX8 : set → set → set X7 ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set → set Inj1 (X8 X6 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set → set ∀X7 : set , X3 (λX8 : set → set → set Inj0 (X8 ∅ ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set λX10 : set ⇒ setsum ∅ (Inj0 (Inj0 (X9 (λX11 : set ⇒ ∅ ) ) X2 (λX8 : set → set λX9 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set → set → set X9 (Inj1 (setsum (Inj0 ∅ ∅ (Inj1 (setsum ∅ (setsum ∅ ∅ ) (setsum X7 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set → set → ((set → set → set → set → set ∀X6 : set → (set → set → set ∀X7 : set , (X4 (X4 (Inj1 (Inj0 ∅ ∈ Inj1 (X4 (setsum (Inj0 ∅ (setsum ∅ ∅ → X2 (λX8 : set → set λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set → set X7 ) (Inj0 X7 (λX8 : set → set λX9 : set ⇒ ∅ ) X2 (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set → set → set X8 ) (setsum ∅ X7 (λX8 : set → set λX9 : set ⇒ setsum (setsum (X6 ∅ (λX10 : set ⇒ ∅ ) ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (X6 (X6 X7 (setsum (X6 ∅ ∅ (setsum ∅ ∅ (Inj0 (Inj0 (X6 ∅ ∅ ∈ Inj0 ∅ → X1 (λX8 : ((set → set → set → set → (set → set → set λX9 : (set → set → set λX10 : set → set Inj0 ∅ ) (Inj1 (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) → (∀X4 : set → ((set → set → set → (set → set → set ∀X5 : (set → set → set ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : (set → (set → set → set → set X1 (λX8 : ((set → set → set → set → (set → set → set λX9 : (set → set → set λX10 : set → set setsum ∅ (X7 (λX11 : set ⇒ λX12 : set → set setsum ∅ ∅ ) ) (Inj1 (setsum ∅ (setsum (setsum ∅ ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set X8 ) ∅ ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → (set → set → set → set ∀X7 : ((set → set → set → (set → set → set → (set → set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set X9 (Inj1 (Inj1 ∅ (λX10 : set ⇒ ∅ ) ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWX1Bn7TJw7NUP6mf8waH4cSUsVVDLWUJp )
∀X0 : ((((set → set → (set → set → set → set → (set → set → set → set → set → set → set → set → set → prop ∀X1 : ((((set → set → (set → set → set → set → set → (set → set → set → set → (((set → set → set → (set → set → set → set → ((set → set → set → set → prop ∀X2 : ((set → set → set → set → set → (set → set → (set → set → set → prop ∀X3 : (((set → set → set → set → (((set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set → set ∀X7 : set → set (Inj0 (Inj0 (Inj1 ∅ ∈ Inj1 (X7 (Inj0 ∅ → X3 (λX8 : (set → set → set Inj0 (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → set X5 ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → ((set → set → set → set → set (Inj0 ∅ ∈ setsum X5 (setsum (Inj0 ∅ (Inj1 (Inj0 ∅ → X1 (λX8 : ((set → set → (set → set → set → set → set → (set → set → set setsum (X6 X5 (λX9 : set ⇒ λX10 : set ⇒ Inj1 X10 ) (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set ∅ ) X2 (λX8 : set → set λX9 : set ⇒ Inj1 (X7 ∅ (λX10 : set → set λX11 : set ⇒ X10 ∅ ) ) ∅ (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : set ⇒ X7 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ) ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X5 ∈ Inj0 (X4 (setsum (Inj0 ∅ X6 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ X8 ) → X2 (λX8 : set → set λX9 : set ⇒ setsum ∅ X7 ) (setsum (setsum (Inj1 (Inj1 ∅ ∅ ∅ (λX8 : set ⇒ Inj1 (setsum X7 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X11 ) (setsum (setsum (Inj0 ∅ (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : set → set → set X1 (λX8 : ((set → set → (set → set → set → set → set → (set → set → set X7 (setsum ∅ ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set setsum ∅ (X7 (Inj0 (Inj0 ∅ (Inj0 (Inj1 ∅ ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum ∅ (Inj1 (setsum (Inj1 ∅ X7 ∈ setsum (setsum ∅ ∅ (setsum (setsum X7 (X5 ∅ ∅ → X1 (λX8 : ((set → set → (set → set → set → set → set → (set → set → set Inj1 (X8 (λX9 : set → set λX10 : set → set λX11 : set ⇒ X10 (Inj0 ∅ ) (setsum ∅ (X5 ∅ (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) ) (λX8 : (set → set → set → (set → set → set → set λX9 : (set → set → set Inj0 X6 ) X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X10 ) (Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum ∅ X5 ∈ Inj1 (setsum (Inj0 ∅ (setsum (Inj0 ∅ ∅ → X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 X12 ∅ (Inj1 X12 ) X5 X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 ∅ X11 ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → (set → set → set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , (X6 (λX8 : set ⇒ Inj1 (Inj0 (X5 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) (setsum X7 (setsum (setsum ∅ ∅ X7 (λX8 : set ⇒ X5 (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) (Inj0 ∅ (λX9 : set ⇒ setsum ∅ (X6 (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ ) (setsum (setsum ∅ ∅ ∅ ) (X5 (λX8 : set ⇒ ∅ ) (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (X5 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) (setsum (setsum ∅ ∅ (Inj0 ∅ ∈ X4 → X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum X11 ∅ ) (setsum ∅ (setsum ∅ (setsum (Inj0 ∅ (Inj1 ∅ X0 (λX8 : ((set → set → (set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 (setsum ∅ ∅ ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPMZJkNGyE4h4MUGwNemMUuBYps9BsvUX6 )
∀X0 : ((set → set → (set → (set → set → set → set → (set → set → set → ((set → set → set → set → set → prop ∀X1 : (((set → set → set → set → set → ((set → set → set → set → set → (set → set → set → set → (set → set → prop ∀X2 : (set → set → (set → set → set → set → prop ∀X3 : (set → set → ((set → (set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : (set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X8 (Inj0 (Inj0 (setsum ∅ ∅ (λX12 : set ⇒ ∅ ) ) ) → (∀X4 : set → set → set → set → set ∀X5 : set → set → (set → set → set ∀X6 : ((set → set → (set → set → set → set → set ∀X7 : (set → set → set → set → set → set X3 (λX8 : set ⇒ Inj0 (Inj1 (Inj0 (Inj1 ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X1 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (setsum (Inj0 ∅ (X5 ∅ ∅ (λX9 : set ⇒ ∅ ) ) ∅ (X4 (Inj0 (Inj1 (X4 ∅ ∅ ∅ ∅ (Inj0 (Inj1 (Inj0 ∅ (X7 (λX8 : set ⇒ X6 (λX9 : set → set λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ) (X4 (setsum ∅ ∅ (setsum ∅ ∅ (X7 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (X6 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X7 (λX11 : set ⇒ ∅ ) ∅ ∅ ∅ ) (setsum (X6 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) (X4 ∅ ∅ ∅ ∅ ∅ (λX8 : set ⇒ setsum (setsum (Inj0 ∅ X8 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : ((set → set → set → (set → set → set ∀X7 : set , (Inj1 (Inj0 X7 ∈ setsum (X6 (λX8 : set → set Inj1 (X8 ∅ ) (λX8 : set ⇒ setsum X7 (Inj1 ∅ ) (X6 (λX8 : set → set setsum (Inj1 ∅ ∅ ) (λX8 : set ⇒ setsum X8 X8 ) → X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X7 X8 ) ) → (∀X4 : (set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj0 (Inj0 (Inj0 (X4 (λX8 : set ⇒ ∅ ) ∈ Inj0 (setsum (X5 (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ∅ (Inj1 (X5 (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ) X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , (Inj0 (Inj1 X7 ∈ X5 (Inj0 (setsum ∅ (X5 ∅ → X1 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set setsum (Inj0 ∅ (setsum (setsum (X10 (λX11 : set ⇒ ∅ ) ∅ (Inj1 ∅ (X10 (λX11 : set ⇒ setsum ∅ ∅ ) ∅ ) (λX8 : set ⇒ setsum (Inj0 (Inj1 (setsum ∅ ∅ (setsum X7 (Inj1 (setsum ∅ ∅ ) (setsum ∅ (X5 (X5 ∅ ∅ (λX8 : set ⇒ setsum X8 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 ∅ ) X1 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set setsum (Inj0 (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (setsum (X4 (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum ∅ (X5 ∅ (setsum (X5 (Inj0 ∅ (X4 (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : (((set → set → set → set → set → set → (set → set → set ∀X7 : (((set → set → set → set → set → set X1 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (X6 (λX8 : (set → set → set → set X5 (X6 (λX9 : (set → set → set → set setsum ∅ ∅ ) (setsum ∅ ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set setsum ∅ (Inj0 ∅ ) ) (Inj1 (X6 (λX8 : (set → set → set → set X7 (λX9 : (set → set → set → set ∅ ) ) (X6 (λX8 : (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) (Inj1 (Inj0 (X7 (λX8 : (set → set → set → set ∅ ) ∈ setsum (setsum (X7 (λX8 : (set → set → set → set setsum ∅ ∅ ) (setsum X4 (Inj0 ∅ ∅ ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 : set , (setsum (setsum (setsum (Inj1 ∅ (X4 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) ∅ X6 (setsum (X5 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ∈ setsum ∅ ∅ → X0 (λX8 : set → set λX9 : set → (set → set → set setsum (Inj0 ∅ (X9 ∅ (λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set → set λX9 : set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 (λX10 : set ⇒ ∅ ) X6 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X8 (X8 ∅ ) X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWsKpLX2SnqqWXhvk1uHXiXqeuahuyJdNm )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → (((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : ((set → set → set → set → ((((set → set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set (Inj1 (X6 (X6 (setsum ∅ ∅ ∈ X5 (λX8 : set → set λX9 : set → set setsum (setsum (X9 ∅ (setsum ∅ ∅ (Inj0 ∅ ) → X2 (λX8 : set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (X7 (λX9 : (set → set → set → set ∅ ) (X8 (setsum ∅ ∅ ) (X5 (λX8 : set → set λX9 : set → set X8 (Inj1 (setsum ∅ ∅ ) X3 (λX8 : set → set λX9 : set ⇒ X6 (X8 (X7 (λX10 : (set → set → set → set Inj1 ∅ ) ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ setsum (setsum (X7 (λX10 : (set → set → set → set X7 (λX11 : (set → set → set → set ∅ ) ) (Inj0 ∅ (setsum ∅ (setsum ∅ (Inj1 ∅ ) (X6 ∅ (Inj1 ∅ ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → (set → set → set → set X3 (λX8 : set → set λX9 : set ⇒ setsum ∅ (X8 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ (X5 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum (X8 ∅ ∅ (Inj0 ∅ ) (Inj0 (Inj0 ∅ ∈ Inj1 (setsum ∅ (Inj1 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 ∅ → X1 (λX8 : set ⇒ setsum X8 (Inj1 X6 ) ∅ (λX8 : (set → set → set → set X7 ) X2 (λX8 : set → set setsum (setsum ∅ (setsum ∅ (setsum ∅ ∅ (Inj1 (Inj1 (Inj0 ∅ ) (Inj0 (Inj1 X6 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → ((set → set → set → set → (set → set → set → set X2 (λX8 : set → set ∅ ) (setsum (setsum ∅ X6 ∅ False ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ ) X7 (λX8 : (set → set → set → set Inj0 (setsum (setsum X7 (Inj0 ∅ (X8 (λX9 : set ⇒ Inj1 ∅ ) X5 ) ) → (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X1 (λX8 : set ⇒ setsum (Inj0 (Inj0 (setsum ∅ ∅ (Inj0 ∅ ) (setsum (setsum (X4 (X4 ∅ (Inj1 ∅ (X4 ∅ (λX8 : (set → set → set → set setsum ∅ ∅ ) X1 (λX8 : set ⇒ Inj1 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 (Inj0 (Inj1 X6 (λX8 : (set → set → set → set X5 (λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ (setsum ∅ ∅ ) ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ setsum X8 (setsum ∅ (Inj0 (setsum ∅ ∅ ) X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ X5 ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWtPqvwibeyjTMhaidHFzgTS3vNrtDLxxw )
∀X0 : (set → set → set → set → ((set → set → set → prop ∀X1 : (((set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → (set → set → set → set → set → (set → set → prop ∀X3 : ((set → (set → set → (set → set → set → set → (set → (set → set → set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 ∅ → X3 (λX8 : set → (set → set → (set → set → set → set λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ X7 ) ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → (set → set → (set → set → set → set λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : (set → set → ((set → set → set → (set → set → set → set ∀X5 : set → set → set ∀X6 : (set → set → set ∀X7 : (((set → set → set → set → set → set (setsum ∅ (X7 (λX8 : (set → set → set Inj0 (X7 (λX9 : (set → set → set ∅ ) ∅ ) ∅ ∈ Inj0 (Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (Inj1 ∅ (setsum (setsum ∅ (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ) (Inj0 (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ (Inj1 (X7 (λX8 : (set → set → set ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : (set → (set → set → set → set → ((set → set → set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set , (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ ∈ Inj1 (setsum ∅ (setsum (X4 (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) (X6 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ (setsum (X4 (λX8 : set ⇒ X7 ) (setsum (Inj1 ∅ (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) X3 (λX8 : set → (set → set → (set → set → set → set λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ X7 ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set → set X3 (λX8 : set → (set → set → (set → set → set → set λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum ∅ (Inj1 (setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) X1 (λX8 : (set → set → set λX9 : set ⇒ Inj1 X6 ) (Inj1 (setsum ∅ X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) X7 False ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (Inj1 ∅ (X4 (Inj1 ∅ ∅ (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) X5 ∈ X4 ∅ (Inj1 X7 (λX8 : set ⇒ ∅ ) X5 → X0 (λX8 : set ⇒ X7 ) (Inj1 (Inj0 X7 (setsum ∅ ∅ (λX8 : set → set X5 ) ) → (∀X4 : (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X7 ∈ Inj0 (Inj0 (setsum ∅ X7 → X0 (λX8 : set ⇒ Inj1 (Inj0 (Inj0 (Inj1 ∅ ) (setsum (Inj0 ∅ (X4 (λX8 : set ⇒ setsum X7 (Inj0 ∅ ) X5 (λX8 : set ⇒ setsum (setsum ∅ ∅ X8 ) X5 X7 (λX8 : set → set X5 ) X1 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdHA6wCoXw9XGVUkLCwocEhFbsJVcyhT4a )
∀X0 : (((set → set → set → set → set → set → set → set → ((set → set → set → prop ∀X1 : (set → set → (((set → set → set → (set → set → set → set → set → prop ∀X2 : ((set → ((set → set → set → set → set → set → set → ((((set → set → set → set → set → set → set → set → (set → set → prop ∀X3 : (set → set → (((set → set → set → (set → set → set → set → set → set → set → ((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj0 (Inj1 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 X9 ) (λX8 : set → set → set λX9 : set ⇒ Inj0 ∅ ) (Inj0 ∅ X7 (setsum (Inj0 X4 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 ∅ X3 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X9 X9 ) (λX8 : set → set → set λX9 : set ⇒ setsum (X6 (X6 ∅ (Inj0 (X8 (setsum ∅ ∅ (Inj1 ∅ ) (Inj0 (Inj1 ∅ X4 (X6 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → ((set → set → set → set → set → set X3 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : set → set → set λX9 : set ⇒ setsum ∅ ∅ ) (Inj1 X6 (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ X4 (setsum (setsum (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ∅ ∅ (Inj1 (setsum (Inj0 ∅ (Inj0 ∅ X3 (λX8 : set ⇒ X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 (Inj0 (Inj1 ∅ ) (λX9 : set → set λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set → set λX13 : set ⇒ Inj0 X10 ) (λX11 : set → set λX12 : set ⇒ Inj1 (X9 ∅ ) (Inj1 ∅ ) (Inj0 (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (λX8 : set → set → set λX9 : set ⇒ X9 ) X4 X4 X5 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → set → set ∀X7 : set , (Inj0 (setsum X7 (setsum (Inj0 ∅ (Inj0 ∅ ∈ setsum ∅ (Inj1 X7 → X2 (λX8 : set → ((set → set → set → set → set → set setsum (setsum (setsum ∅ (Inj0 ∅ ∅ ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ Inj1 (Inj1 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum (X5 (Inj1 ∅ ∅ ∈ X6 → X2 (λX8 : set → ((set → set → set → set → set → set setsum X7 (Inj1 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set → set λX12 : set ⇒ X9 ) ) (λX8 : set ⇒ setsum ∅ X6 ) X1 (λX8 : set ⇒ X7 ) (λX8 : (set → set → set → (set → set → set Inj1 ∅ ) X7 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (X7 (setsum (setsum X5 ∅ (Inj1 (Inj1 ∅ (λX8 : set → set ∅ ) (Inj0 (setsum (X4 ∅ (X7 ∅ (λX8 : set → set ∅ ) ∅ ∈ setsum (X4 (setsum (Inj1 ∅ ∅ X6 → X1 (λX8 : set ⇒ Inj1 X8 ) (λX8 : (set → set → set → (set → set → set Inj0 ∅ ) ∅ X1 (λX8 : set ⇒ X5 ) (λX8 : (set → set → set → (set → set → set setsum (setsum (Inj1 (setsum ∅ ∅ ∅ (setsum (setsum X6 ∅ (Inj1 (Inj1 ∅ ) (setsum X6 (setsum (Inj1 ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : ((set → set → set → (set → set → set → ((set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum ∅ (Inj1 (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set X8 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum X7 X7 ) (λX9 : set ⇒ ∅ ) ) ∅ (Inj1 (X5 (X5 (setsum ∅ ∅ ∈ Inj0 (setsum (X5 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum (X8 (λX12 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (setsum (Inj1 ∅ X9 (setsum (Inj0 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set → set ∅ ) X0 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ setsum (Inj1 (setsum (setsum ∅ ∅ ∅ ∅ → X0 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (X8 (λX12 : set ⇒ Inj1 (Inj1 ∅ ) (Inj0 (X8 (λX12 : set ⇒ ∅ ) ∅ ) (λX8 : set → set Inj1 X6 ) X3 (λX8 : set ⇒ Inj1 (setsum ∅ X7 ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum ∅ (X8 (λX12 : set ⇒ λX13 : set ⇒ setsum ∅ ∅ ) (λX12 : set ⇒ setsum ∅ ∅ ) X9 ) (λX8 : set → set → set λX9 : set ⇒ Inj1 (setsum (Inj1 X6 ∅ ) (Inj1 (setsum (Inj0 ∅ (Inj0 ∅ ∅ (Inj0 (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMeQvB6Mj8fMYr979VNaBpNnL5Q5Q3LgZr )
∀X0 : (set → set → (set → set → set → prop ∀X1 : (set → (((set → set → set → set → set → set → set → set → prop ∀X2 : ((set → set → set → set → (set → set → set → (((set → set → set → set → set → ((set → set → set → set → set → (set → set → set → set → prop ∀X3 : ((set → set → (set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set → set X3 (λX8 : set → set → (set → set → set Inj1 ∅ ) (λX8 : set ⇒ setsum X8 (X6 X5 ∅ (λX9 : set ⇒ Inj0 (Inj0 ∅ ) (setsum (Inj1 ∅ (setsum ∅ ∅ ) X4 X3 (λX8 : set → set → (set → set → set Inj0 (setsum (X6 (Inj0 ∅ ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (X8 (X8 ∅ ∅ (λX9 : set ⇒ ∅ ) (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ X7 (setsum ∅ (setsum (setsum ∅ ∅ ∅ ) (setsum X5 ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set → (set → set → set setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ Inj0 X8 ) X5 False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum (X8 (X11 (Inj0 ∅ ∅ ) (λX8 : (set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ setsum (Inj0 (Inj1 X10 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 X8 ) ∅ ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (X8 (setsum (X8 ∅ ∅ ) (λX8 : (set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum ∅ (X8 (λX11 : set ⇒ λX12 : set ⇒ X9 (λX13 : set ⇒ ∅ ) ) (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ) ∅ (Inj1 (setsum (setsum (X5 ∅ (X4 (λX8 : set ⇒ ∅ ) ∅ ∈ X5 (X5 (setsum (setsum ∅ ∅ ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj1 (setsum (setsum (Inj0 ∅ ∅ (Inj0 (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set X6 ) (setsum (setsum X6 (setsum (Inj0 ∅ X7 (X4 (λX8 : set → set setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set setsum (X7 (setsum ∅ ∅ (Inj0 (X7 (Inj0 ∅ ) (Inj1 (Inj0 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 ) (Inj1 (X7 (λX8 : set ⇒ setsum (Inj1 ∅ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : ((set → set → set → set (X5 ∈ X7 (λX8 : set → set setsum (X6 ∅ (Inj0 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (X6 X5 (setsum ∅ ∅ (λX9 : set ⇒ X6 ∅ ∅ (λX10 : set ⇒ ∅ ) ) ) → X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ (X7 (λX9 : set → set Inj1 (setsum ∅ ∅ ) ) (setsum ∅ (Inj1 (Inj0 (Inj1 ∅ X3 (λX8 : set → set → (set → set → set Inj1 (X6 (X8 ∅ (Inj0 ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ X6 X5 (setsum ∅ (setsum (Inj1 ∅ (Inj0 ∅ (λX9 : set ⇒ Inj1 (Inj0 (Inj1 ∅ ) ) (Inj1 X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMN4vMhYdGU8fMm1MLvbG5AGWP4HBQw789F )
∀X0 : (((set → (set → set → set → ((set → set → set → set → (set → set → set → set → set → ((set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → set → (set → ((set → set → set → set → set → set → prop ∀X3 : ((((set → set → set → (set → set → set → (set → set → set → set → set → set → set → set → (((set → set → (set → set → set → set → (set → (set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : ((set → set → set → (set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X12 ) (λX8 : (set → set → (set → set → set setsum (X6 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 X7 ) (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set → set → set → set X3 (λX8 : ((set → set → set → (set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 ∅ X12 ) (λX8 : (set → set → (set → set → set Inj0 X6 ) (λX8 : set ⇒ λX9 : set → set setsum ∅ X8 ) (setsum (Inj1 X4 X6 X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : ((set → set → set → set → set X2 (λX8 : set ⇒ X6 (λX9 : set → set → set λX10 : set ⇒ X7 (λX11 : set → set X10 ) X8 ) ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X9 (λX12 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 (Inj0 ∅ ∅ ) X3 (λX8 : ((set → set → set → (set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum ∅ (setsum X10 ∅ ) (λX8 : (set → set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) X5 ) → (∀X4 : (set → set → set → set ∀X5 : (set → set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → ((set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → set → set → set → set → set X3 (λX8 : ((set → set → set → (set → set → set λX9 : set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum X12 (setsum (setsum X12 (X9 ∅ ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 (X7 (λX8 : (set → set → set → set ∅ ) ∅ (setsum (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ (Inj1 ∅ X1 (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (setsum ∅ ∅ X8 ) (setsum (X7 (λX9 : (set → set → set → set X7 (λX10 : (set → set → set → set ∅ ) ∅ ∅ ∅ ) ∅ X8 (setsum ∅ ∅ (Inj1 (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (X7 (λX9 : (set → set → set → set Inj0 (Inj1 ∅ ) (setsum ∅ (setsum ∅ ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X9 ) (λX9 : set → set setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) (Inj0 ∅ (Inj1 (Inj0 ∅ (setsum (setsum (Inj0 ∅ (Inj0 ∅ (setsum (X7 (λX9 : (set → set → set → set ∅ ) ∅ ∅ ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (X7 (λX8 : (set → set → set → set ∅ ) (setsum (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj0 ∅ (Inj0 ∅ (setsum (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set → (set → set → set X1 (λX8 : set ⇒ setsum ∅ (setsum (X5 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ∅ (setsum (Inj1 ∅ X8 ) (Inj1 (Inj1 (Inj0 (Inj0 ∅ (Inj1 (Inj1 (X7 ∅ ∅ (λX8 : set ⇒ Inj0 ∅ ) ∈ X7 X4 ∅ (λX8 : set ⇒ Inj0 (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : (((set → set → set → set → set → set X0 (λX8 : (set → (set → set → set → ((set → set → set → set λX9 : set → set X6 (λX10 : (set → set → set X7 (λX11 : (set → set → set → set Inj0 (Inj1 ∅ ) ) ) ∅ X5 (λX8 : set → set Inj1 (Inj0 (X6 (λX9 : (set → set → set setsum ∅ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : (set → (set → set → set → ((set → set → set → set λX9 : set → set ∅ ) (setsum ∅ ∅ (Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ (λX8 : set → set Inj1 ∅ ) (X5 (setsum (Inj0 X7 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set → set Inj0 (setsum (setsum ∅ ∅ (X5 ∅ (λX9 : set → set ∅ ) ) ∈ Inj1 X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSNSqyuybbwSKRxCXmreZKeTnUMNmfc1vG )
∀X0 : ((set → (set → set → set → (set → set → set → (set → set → set → (set → set → set → ((set → set → set → set → set → (((set → set → set → set → (set → set → prop ∀X1 : ((set → (set → set → set → set → set → ((set → set → set → set → ((set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → ((set → set → set → set → set → set → set → set → set → prop ∀X3 : ((set → set → set → (set → (set → set → (set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : set → set (setsum (setsum ∅ (X7 ∅ X5 ∈ X7 (setsum (Inj0 (Inj1 ∅ X5 → X3 (λX8 : set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : (set → set → set → set → (set → set → set → set X3 (λX8 : set → set X6 X5 (λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj0 (Inj0 ∅ ) (λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) (setsum X5 (X8 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X1 (λX8 : set → (set → set → set → set Inj0 (X6 (Inj1 ∅ (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX9 : set ⇒ X9 ) ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum ∅ ∅ (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX8 : set → set → set Inj1 ∅ ) (λX8 : set → set ∅ ) (X6 (Inj0 (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ X5 ) X5 X5 ) → (∀X4 : set → set → set → set → set ∀X5 : (set → (set → set → set → set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → ((set → set → set → set → set → set → set ∅ ) (X4 (setsum ∅ (X4 (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ ∅ ∅ ∅ (Inj1 (X4 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set ∀X7 : set → ((set → set → set → (set → set → set X2 (λX8 : (((set → set → set → set → ((set → set → set → set → set → set → set Inj0 (X6 (λX9 : set → set X6 (λX10 : set → set Inj0 ∅ ) (λX10 : set ⇒ X8 (λX11 : (set → set → set ∅ ) (λX11 : set → set λX12 : set ⇒ ∅ ) ∅ ∅ ) (X9 ∅ ) (λX9 : set ⇒ Inj0 (X7 ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ) ∅ ) ∅ False ) → (∀X4 : set → set ∀X5 : (set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → (set → set → set → set X8 X7 (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 X7 ) (λX8 : set → set → set ∅ ) (λX8 : set → set Inj0 ∅ ) X6 (Inj0 ∅ X1 (λX8 : set → (set → set → set → set setsum ∅ (X8 (X8 (Inj0 ∅ (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set → set ∅ ) (λX8 : set → set ∅ ) ∅ (setsum (setsum (setsum (setsum ∅ ∅ X7 ∅ (X4 (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X4 ∈ setsum ∅ (setsum (setsum ∅ (Inj0 ∅ (Inj0 ∅ → X1 (λX8 : set → (set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set → set Inj0 X6 ) (λX8 : set → set setsum (X7 ∅ (Inj1 (Inj1 ∅ ) (setsum ∅ X6 ∅ X0 (λX8 : set → (set → set → set → (set → set → set λX9 : set → set → set λX10 : set → set X7 (Inj0 (setsum (X10 ∅ (X7 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (X8 ∅ (setsum ∅ (setsum (Inj0 ∅ ∅ ) (λX8 : (set → set → set Inj1 ∅ ) (λX8 : set ⇒ setsum X8 X8 ) ) → (∀X4 : (set → set → ((set → set → set → (set → set → set ∀X5 : set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → ((set → set → set → set → set → set → set ∅ ) (Inj1 ∅ X0 (λX8 : set → (set → set → set → (set → set → set λX9 : set → set → set λX10 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 X10 ) (λX8 : (set → set → set setsum (X8 (λX9 : set ⇒ ∅ ) (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set → (set → set → set → (set → set → set λX9 : set → set → set λX10 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set Inj1 ∅ ) (λX8 : set ⇒ ∅ ) X2 (λX8 : (((set → set → set → set → ((set → set → set → set → set → set → set X7 ) (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPHQEgTEunu8xW57DggSNi4DtWJ8A5SkBy )
∀X0 : (set → (set → set → set → set → set → (set → (set → set → set → set → set → set → prop ∀X1 : (set → (set → set → set → set → prop ∀X2 : ((set → set → set → set → set → ((set → set → set → set → set → (set → set → (set → set → set → prop ∀X3 : (((set → set → ((set → set → set → (set → set → set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set ∀X6 : ((set → set → (set → set → set → set ∀X7 : (set → set → set X3 (λX8 : (set → set → ((set → set → set → (set → set → set → set λX9 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (X6 (λX10 : set → set λX11 : set → set ∅ ) (X7 (λX10 : set ⇒ ∅ ) (setsum (Inj0 ∅ ∅ ) (Inj1 (X6 (λX8 : set → set λX9 : set → set ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (X5 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (X7 (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → ((set → set → set → (set → set → set → set λX9 : set ⇒ Inj1 X9 ) (Inj1 ∅ (λX8 : set ⇒ Inj0 (setsum (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ) False ) → (∀X4 : set → set → (set → set → set ∀X5 : ((set → set → set → (set → set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (Inj0 (Inj0 ∅ X2 (λX8 : set → set → set ∅ ) (setsum (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ∅ (λX8 : set → set → set λX9 : set ⇒ X7 (Inj0 (Inj1 (X8 ∅ ∅ ) (λX8 : set ⇒ setsum (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X10 (setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X8 ) (setsum (setsum ∅ ∅ (setsum (Inj0 ∅ (Inj0 ∅ ) (λX8 : set ⇒ X8 ) (Inj1 (Inj0 (setsum (setsum ∅ ∅ (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : set → (set → set → set → set X2 (λX8 : set → set → set ∅ ) (setsum (Inj0 (X6 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ∅ (λX8 : set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (setsum (X6 (λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) X8 ∅ ) (λX8 : set ⇒ Inj1 (Inj1 X8 ) ∅ X3 (λX8 : (set → set → ((set → set → set → (set → set → set → set λX9 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (X8 (λX10 : set ⇒ setsum ∅ ∅ ) (λX10 : set → set setsum ∅ ∅ ) (λX10 : set ⇒ Inj0 ∅ ) (X7 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (X7 (X6 (λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (setsum (setsum ∅ (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ (λX8 : set ⇒ setsum (setsum ∅ (Inj1 (Inj1 ∅ (setsum ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → ((set → set → set → (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ Inj0 (Inj0 (setsum ∅ ∅ ) (λX10 : set → set Inj0 (Inj0 (Inj1 ∅ ) (λX10 : set ⇒ X8 (λX11 : set ⇒ X11 ) (λX11 : set → set ∅ ) (λX11 : set ⇒ ∅ ) (setsum X9 X7 ) ∅ ) (Inj0 X7 (λX8 : set ⇒ ∅ ) X1 (λX8 : set ⇒ λX9 : set → set X8 ) (setsum X7 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set setsum X6 (Inj1 (Inj1 ∅ ) (setsum ∅ ∅ X2 (λX8 : set → set → set ∅ ) ∅ (λX8 : set → set → set λX9 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ X7 ) (λX8 : set ⇒ setsum X6 (setsum (setsum (Inj1 ∅ (X5 ∅ ∅ ∅ ∅ X7 ) (Inj1 ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X7 ∈ X6 → X0 (λX8 : set ⇒ λX9 : set → set → set ∅ ) (setsum X5 ∅ (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum (setsum X5 X5 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set → set X8 ) X4 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (setsum (Inj1 (setsum (X5 ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ X7 (setsum ∅ ∅ (X5 (setsum (Inj0 (Inj0 ∅ (setsum ∅ ∅ (X5 (setsum X4 (Inj1 ∅ X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X7 ) X1 (λX8 : set ⇒ λX9 : set → set setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (Inj0 ∅ (setsum (setsum X6 (Inj1 ∅ (setsum X6 X6 ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNpMfoGENZLXEr3Ci12cuo5pWy8YmCdmCo )
∀X0 : (set → set → ((((set → set → set → (set → set → set → set → set → ((set → set → set → set → (set → set → set → prop ∀X1 : ((set → (set → set → set → set → set → set → (((set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → (set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum (Inj0 (setsum (Inj1 ∅ X4 ∅ ∈ X4 → X3 (λX8 : set ⇒ Inj0 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set X8 (λX9 : set → set setsum (X8 (λX10 : set → set Inj1 ∅ ) X6 ) ) ) → (∀X4 : (((set → set → set → set → set → ((set → set → set → set → set → set ∀X5 : (((set → set → set → set → set → set → set → (set → set → set → set ∀X6 : (((set → set → set → set → (set → set → set → set → (set → set → (set → set → set → set ∀X7 : (set → set → set (X7 (λX8 : set ⇒ setsum (Inj0 (X5 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) ∈ setsum (Inj0 (setsum (setsum ∅ ∅ ∅ (setsum (setsum (setsum ∅ ∅ ∅ (setsum (setsum ∅ ∅ (X6 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ → X3 (λX8 : set ⇒ setsum (setsum (Inj1 ∅ (setsum X8 (Inj0 ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set setsum (Inj1 (setsum (X8 (λX9 : set → set ∅ ) (setsum ∅ ∅ (Inj0 ∅ ) X0 (λX8 : set ⇒ Inj0 (X6 (λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 X9 ) (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) (X7 (λX9 : set ⇒ X9 ) ) (λX8 : ((set → set → set → (set → set → set → set X7 (λX9 : set ⇒ setsum (X6 (λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) (λX10 : set ⇒ X7 (λX11 : set ⇒ ∅ ) ) (λX10 : set ⇒ Inj1 ∅ ) ∅ (setsum ∅ (Inj1 ∅ ) ) (λX8 : set → set Inj0 (X7 (λX9 : set ⇒ setsum X9 ∅ ) ) (Inj1 (Inj1 (X5 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum X8 ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ Inj0 (setsum (Inj0 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : ((set → set → set → (set → set → set → set Inj1 ∅ ) (λX8 : set → set X5 ) (setsum (Inj0 ∅ (X4 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) ∅ X2 (λX8 : set ⇒ setsum (Inj0 (setsum (X7 (λX9 : set ⇒ ∅ ) (X7 (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ X6 ) ) → (∀X4 : (set → set → set ∀X5 : (set → set → set → (set → set → set ∀X6 : (set → (set → set → set → (set → set → set → set ∀X7 : set , (X4 (λX8 : set ⇒ Inj1 X7 ) ∈ Inj1 (X6 (λX8 : set ⇒ λX9 : set → set setsum (X6 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (X9 ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ Inj0 ∅ ) (X5 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) ) (Inj0 ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X0 (λX8 : set ⇒ setsum (setsum (Inj1 ∅ (Inj1 (Inj0 ∅ (Inj1 (Inj0 (X6 (λX9 : set ⇒ λX10 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : ((set → set → set → (set → set → set → set ∅ ) (λX8 : set → set Inj1 ∅ ) (setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ (λX8 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) (setsum ∅ (X5 (λX8 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : ((set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → (set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (λX9 : set → set setsum (X9 (setsum ∅ ∅ ∅ ) (λX9 : set → set setsum (Inj1 (X7 (λX10 : (set → set → set ∅ ) (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ ) ) X1 (λX8 : set → (set → set → set → set → set Inj1 ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set → set X8 (λX11 : set ⇒ X10 (setsum (X10 ∅ (Inj0 ∅ ) ) (Inj1 (X7 (λX8 : (set → set → set X5 (λX9 : set → set Inj0 ∅ ) (λX9 : set → set X6 ) ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X1 (λX8 : set → (set → set → set → set → set setsum (setsum (X8 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) ∅ (setsum ∅ ∅ (Inj1 (Inj1 ∅ (Inj1 (setsum (X8 ∅ (λX9 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set → set Inj0 (Inj1 (X10 (X10 ∅ ) (Inj0 X4 False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X7 ∅ ∈ Inj1 (Inj1 (Inj0 ∅ → X1 (λX8 : set → (set → set → set → set → set ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) (Inj1 ∅ X0 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → (set → set → set → set setsum ∅ X6 ) (λX8 : set → set setsum (Inj1 ∅ (X8 (setsum (Inj0 ∅ (setsum ∅ ∅ ) X5 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → (set → set → set → set X5 ∅ ) (λX8 : set → set Inj1 (setsum X7 ∅ ) (Inj1 ∅ (λX8 : set ⇒ setsum X7 (Inj0 X8 ) (Inj1 (setsum (setsum ∅ (X5 ∅ X4 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQXLQTgRhcRcdYCvvBr6rwBVgk2mX4Yrcn )
∀X0 : (set → set → set → set → prop ∀X1 : ((set → set → (set → set → set → set → (((set → set → set → set → set → set → set → (set → set → set → prop ∀X2 : (set → set → ((((set → set → set → set → set → set → (set → set → set → set → set → prop ∀X3 : ((set → set → set → set → set → set → set → prop (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X3 (λX8 : set → set → set → set λX9 : set ⇒ X9 ) (X6 (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → set → set → set ∀X6 : ((set → set → set → (set → set → set → set → set ∀X7 : set → set X3 (λX8 : set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ (X4 (X5 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) (Inj1 (X4 (Inj0 ∅ (X7 ∅ (λX8 : set ⇒ X6 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) ∈ Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → set X0 (λX8 : set ⇒ Inj1 X5 ) (setsum (X4 ∅ (setsum X5 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 (Inj0 (Inj1 ∅ (setsum (Inj1 (Inj0 (setsum ∅ ∅ (X4 ∅ (Inj1 ∅ X5 X2 (λX8 : set ⇒ X7 (Inj1 ∅ ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set X8 (λX10 : set → set λX11 : set ⇒ X8 (λX12 : set → set λX13 : set ⇒ X12 X13 ) (X10 (X8 (λX12 : set → set λX13 : set ⇒ ∅ ) ∅ ) ∅ ) (setsum X5 (setsum (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set ∅ ) (setsum X4 X7 X0 (λX8 : set ⇒ setsum ∅ X5 ) X4 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set Inj0 (setsum (setsum (Inj1 ∅ ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum (setsum ∅ (X8 ∅ (Inj0 X10 (Inj1 ∅ ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) (Inj1 (X6 X7 ∅ X5 (X6 (Inj0 ∅ ∅ (setsum ∅ ∅ ∅ ∈ Inj1 X4 ) → (∀X4 : set , ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set X8 (λX10 : set → set λX11 : set ⇒ X11 ) ∅ ) (setsum X6 (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ X7 (λX11 : (set → set → set λX12 : set → set λX13 : set ⇒ X11 (λX14 : set ⇒ ∅ ) ) ∅ ) (Inj1 X6 X0 (λX8 : set ⇒ X7 (λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ X9 (λX12 : set ⇒ X9 (λX13 : set ⇒ ∅ ) ) ) X8 ) (setsum (setsum X6 (Inj0 ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) ∅ (setsum (setsum (Inj1 (setsum ∅ ∅ (X5 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ X6 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ) X7 ∅ X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (Inj1 ∅ X10 ) (λX8 : (set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNBBAoTUVh5mvy7zW5exknRM9YMu6UNfxK )
∀X0 : ((set → set → (set → set → set → set → set → (set → set → set → (((set → set → set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → (set → set → set → (set → set → set → prop ∀X2 : (set → set → set → set → set → set → prop ∀X3 : (set → set → (((set → set → (set → set → set → set → set → prop (∀X4 : (set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : set ⇒ setsum X8 (setsum (X6 (setsum ∅ ∅ X5 ) (λX8 : (set → set → (set → set → set → set Inj0 (setsum (setsum ∅ (setsum ∅ ∅ (setsum (X8 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : ((set → set → set → set → set X3 (λX8 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : (set → set → (set → set → set → set X5 (λX9 : set ⇒ λX10 : set → set ∅ ) ) False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set (X4 ∈ Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum (Inj0 X8 (Inj0 ∅ ) (Inj0 (Inj0 ∅ ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) (Inj1 ∅ X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : (set → set → set → set X8 (λX9 : set ⇒ ∅ ) ∅ ) (Inj1 ∅ (λX8 : set ⇒ Inj1 (Inj0 ∅ ) (setsum (setsum X7 ∅ (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set (setsum (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ∈ X5 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ setsum X9 X8 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (Inj1 X8 X9 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (Inj0 ∅ (setsum (setsum (X4 ∅ ∅ X7 ∈ Inj0 (setsum (setsum (X4 ∅ X5 (X4 X5 → X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ (X6 (X6 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum X8 (Inj0 (setsum ∅ ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : (set → set → (set → set → set → set ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , (X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∈ X7 → X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ X6 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (setsum (X6 ∅ (setsum ∅ ∅ (Inj0 X7 ) (λX8 : (set → set → set → set setsum ∅ (X6 (Inj1 (setsum ∅ ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj0 (X5 X7 (λX9 : set → set Inj1 X7 ) (λX9 : set ⇒ setsum (Inj0 ∅ X9 ) ) (X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → ((set → set → set → set → set ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : (set → (set → set → set → set → (set → set → set → set → set (Inj0 (setsum (setsum (X6 ∅ ∅ (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ (Inj0 ∅ ∈ setsum (X6 (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ∅ (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum X10 ∅ ) → X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ X8 (setsum (X6 ∅ ∅ X9 (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX10 : set ⇒ setsum (X7 (λX11 : set ⇒ λX12 : set → set λX13 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ∅ ∅ ) (Inj0 ∅ (Inj0 (X8 ∅ ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ Inj1 (setsum (X8 ∅ ∅ (λX11 : set ⇒ ∅ ) X10 ) ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ X9 ) (X6 ∅ ∅ (setsum ∅ ∅ (Inj0 (setsum (setsum ∅ ∅ (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : (set → set → set → set Inj0 ∅ ) (setsum ∅ (setsum (setsum (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ (setsum (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ Inj0 (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X12 ) (λX10 : set ⇒ X7 (λX11 : set ⇒ λX12 : set → set λX13 : set ⇒ X12 ∅ ) (λX11 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ X10 ) (setsum ∅ (X6 ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 X9 ) (λX8 : (set → set → set → set X8 (λX9 : set ⇒ ∅ ) (X5 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMd3WtHdk5DnekmazsUSg3fGzvbnkEZThBU )
∀X0 : ((set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → set → (set → ((set → set → set → (set → set → set → prop ∀X3 : (set → set → set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ ) X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) X3 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : ((set → set → set → set ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set X10 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set ∅ ) False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : (set → (set → set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set Inj0 X8 ) X1 (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (setsum X8 ∅ (Inj1 (Inj1 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ X5 ) (setsum ∅ (X7 (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) (Inj1 (Inj1 (setsum ∅ ∅ ∈ X7 (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set , (Inj0 (Inj1 ∅ ∈ X7 → X0 (λX8 : set → set → set → set X6 X7 (Inj1 (setsum ∅ (setsum ∅ ∅ (setsum (Inj1 X7 (Inj0 (Inj0 ∅ ) (X6 (setsum ∅ (Inj0 (setsum ∅ ∅ (X6 X4 (X6 ∅ (setsum ∅ ∅ (setsum ∅ ∅ X5 X4 (Inj1 X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : set → set → set → set setsum (Inj1 ∅ ∅ ) ∅ (setsum X4 (Inj0 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKHufQoXDvyhqtiuyWi4xqZNAYtD5UhEx5 )
∀X0 : (set → set → set → ((((set → set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → (set → set → set → prop ∀X2 : (set → set → set → (set → set → set → prop ∀X3 : (set → (set → (set → set → set → set → set → set → (set → set → set → set → (set → set → prop (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set , (X7 ∈ setsum (setsum (setsum (Inj1 ∅ X7 (Inj0 (Inj1 ∅ (X4 (X6 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X5 ∅ (Inj1 (Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set setsum (Inj0 (X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) ∅ ) (Inj0 X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) (Inj1 X5 (λX8 : set ⇒ Inj1 (Inj1 (Inj1 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → ((set → set → set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (X7 (λX10 : set ⇒ λX11 : set → set X11 X10 ) (λX10 : set → set λX11 : set ⇒ setsum (X10 ∅ (setsum ∅ ∅ ) (λX10 : set ⇒ X8 ) (Inj0 (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ X5 ∅ (setsum ∅ (Inj1 (X5 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) (setsum (X7 (λX9 : set ⇒ λX10 : set → set setsum ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ ) ∅ X6 ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ Inj1 (setsum (Inj0 X5 (Inj1 (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : set → ((set → set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X5 (λX9 : (set → set → set → set Inj0 (Inj0 (setsum ∅ ∅ ) (λX9 : set → set ∅ ) (X5 (λX9 : (set → set → set → set ∅ ) (λX9 : set → set ∅ ) X6 X7 X6 ) (setsum (Inj0 (setsum ∅ (setsum ∅ ∅ X7 (λX8 : set ⇒ λX9 : set ⇒ setsum X7 (setsum (setsum (setsum ∅ ∅ X7 (setsum X9 ∅ ) (X6 ∈ X7 ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X8 ) X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (X6 (λX10 : (set → set → set → set λX11 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (Inj0 (Inj1 X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X7 ∈ Inj1 (X6 (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set (setsum ∅ (setsum (Inj0 ∅ (X6 (setsum ∅ ∅ ∅ ∈ Inj1 (setsum (setsum X5 (setsum ∅ ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (X7 (setsum ∅ ∅ (Inj1 (Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set → set setsum ∅ (X7 (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ ∅ X9 ) (λX8 : ((set → set → set → set → set → set → set X7 ) (Inj0 X4 ∈ setsum (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMY5zFpjScVVqCfzBemCaWToGKzaMFqJ4jn )
∀X0 : (set → set → (set → set → set → set → set → ((set → set → set → (set → set → set → set → set → prop ∀X1 : (set → (set → set → set → ((((set → set → set → set → set → set → (set → set → set → set → prop ∀X2 : ((set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set , (Inj1 (setsum (X5 ∅ (setsum (X5 ∅ ∅ ∈ Inj0 (setsum X4 (Inj1 (Inj1 ∅ → X3 (λX8 : set ⇒ X6 ∅ ∅ ) (X5 ∅ X3 (λX8 : set ⇒ X6 (Inj0 (setsum (X5 ∅ ∅ (Inj1 (setsum (X6 ∅ ∅ (Inj0 ∅ ) X4 ) → (∀X4 : set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → ((set → set → set → set → set → set X3 (λX8 : set ⇒ Inj1 ∅ ) ∅ (Inj1 (X5 (Inj0 (Inj1 ∅ ∈ Inj1 X6 ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → set → set → (set → set → set → (set → set → set ∀X7 : set , (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ (setsum ∅ ∅ ∅ ) ∈ X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum X7 (setsum (Inj0 ∅ ∅ ) → X2 (λX8 : set → set λX9 : set ⇒ Inj0 (Inj0 ∅ ) (Inj1 (setsum ∅ (Inj1 X7 X2 (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum (setsum (Inj0 (Inj0 ∅ ∅ (X4 (λX8 : (set → set → set → set λX9 : set → set Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ Inj0 (X8 ∅ ) ∅ (Inj0 (Inj0 (Inj0 (X7 (λX8 : (set → set → set λX9 : set → set ∅ ) ∅ ∈ setsum (X7 (λX8 : (set → set → set λX9 : set → set Inj1 X6 ) (setsum ∅ (Inj0 ∅ X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → (set → set → set (setsum (setsum X6 (Inj1 (setsum ∅ ∅ X4 ∈ X7 (Inj1 (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 X8 ) (λX8 : set ⇒ Inj1 (Inj0 (Inj0 ∅ ) → X1 (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set setsum (setsum (Inj0 (Inj1 ∅ ∅ X6 ) ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set X8 (λX10 : set → set λX11 : set ⇒ setsum (X8 (λX12 : set → set λX13 : set ⇒ Inj1 ∅ ) ∅ ∅ ) (Inj0 (setsum ∅ (Inj0 ∅ ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : ((set → set → set → set → ((set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set Inj1 X8 ) (setsum (X4 (setsum ∅ ∅ (setsum X5 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj0 X5 ) → (∀X4 : (set → (set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set Inj1 (Inj0 ∅ ) X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWdsY187NBSH7jMZ1fRbXeubSA7RVhp8fH )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → set → set → (set → set → prop (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set ⇒ X6 X5 ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) (λX8 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ ∅ ) (Inj0 (X6 (λX8 : (set → set → set → set Inj1 (setsum ∅ ∅ ) ∈ Inj1 (setsum ∅ ∅ ) → (∀X4 : (set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → (set → set → set ∀X7 : (((set → set → set → (set → set → set → set → set (Inj1 ∅ ∈ Inj0 (setsum (Inj0 (setsum ∅ ∅ X5 → X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) X5 (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ Inj1 (setsum (X7 (λX11 : (set → set → set λX12 : set → set λX13 : set ⇒ ∅ ) (X8 (λX11 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) (Inj0 X7 ∅ (λX8 : set → set λX9 : set ⇒ X6 ∅ ) (setsum ∅ X4 ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (setsum (setsum ∅ ∅ (Inj0 (Inj1 ∅ (Inj0 (Inj0 (Inj1 ∅ ∈ Inj0 ∅ → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ (Inj0 X6 ) X1 (λX8 : set ⇒ setsum X5 (setsum ∅ X8 ) (Inj0 (setsum X5 (setsum (Inj0 ∅ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ setsum (Inj0 (Inj1 (Inj0 ∅ ∅ ) ∅ False ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set → set (X6 (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ ∈ X5 → X0 (λX8 : set ⇒ Inj1 X8 ) (setsum (Inj0 ∅ (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : (set → (set → set → set → set → set X0 (λX8 : set ⇒ Inj0 ∅ ) (setsum (setsum ∅ (Inj0 (setsum ∅ ∅ (Inj1 (Inj1 ∅ (X4 ∈ X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRyTNcXuAyD3fbQbhNMGYed1353zYM8pSA )
∀X0 : (((((set → set → set → set → (set → set → set → set → set → (set → set → set → (set → set → set → set → (set → set → set → set → set → set → set → prop ∀X1 : (set → set → (set → set → ((set → set → set → (set → set → set → set → set → (set → set → prop ∀X2 : (set → (set → set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (Inj0 (setsum X7 X7 (X4 (X4 (Inj0 (setsum ∅ ∅ X5 ∅ X3 (λX8 : (set → (set → set → set → set → set ∅ ) (Inj0 (Inj0 (X6 (setsum ∅ ∅ (Inj0 (X4 ∅ (setsum (X4 (Inj0 (setsum ∅ ∅ (setsum (X6 X7 (X4 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 (λX12 : set ⇒ λX13 : set → set λX14 : set ⇒ Inj0 (setsum ∅ ∅ ) ) ) ∅ ∅ (setsum (setsum (Inj1 ∅ ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set (Inj0 ∅ ∈ X5 → X2 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (Inj1 (Inj1 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum ∅ X5 (setsum ∅ ∅ ∈ Inj0 (setsum (setsum (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum X5 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ X4 → X2 (λX8 : set ⇒ λX9 : set → set ∅ ) X4 ∅ X1 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ setsum ∅ X7 ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (setsum (Inj1 ∅ (setsum (Inj0 X6 (setsum (Inj1 ∅ X7 (λX8 : set ⇒ setsum ∅ X7 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X1 (λX8 : set ⇒ Inj0 X5 ) (λX8 : set ⇒ setsum (Inj0 (setsum X8 X5 (setsum X6 X5 ) (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (X7 (setsum (Inj0 (Inj0 ∅ (Inj0 (X4 ∅ X5 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 X6 ) (setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) ∈ setsum (Inj1 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : set , (setsum ∅ (setsum (setsum ∅ X7 X5 ∈ X7 → X0 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X11 X12 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (Inj1 (Inj0 ∅ X8 ) (Inj0 ∅ X7 ∅ (X6 (setsum X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X0 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X9 X10 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (setsum X9 (Inj0 ∅ ∅ ) X7 (setsum (Inj1 X7 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ X7 ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set ∀X7 : set → set X0 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum X9 ∅ ) (X6 (Inj1 X4 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (Inj1 X5 (setsum (setsum (X7 (Inj0 ∅ ∅ (Inj1 (setsum ∅ (Inj1 ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYq5ycg5R3CXz86hR5g2EvgJXQHeKq2pLW )
∀X0 : (((((set → set → set → set → set → set → set → (set → set → set → set → set → prop ∀X1 : ((set → set → set → set → set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → set → set → set → prop ∀X3 : (set → (set → set → ((set → set → set → set → set → set → (set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , (X4 (setsum (X5 X7 (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) ∅ ∈ setsum (setsum (setsum (X4 ∅ (setsum ∅ ∅ X6 (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : ((set → set → set → set → set (setsum ∅ (Inj0 ∅ ∈ setsum (X6 (setsum (X6 ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ (setsum (Inj0 (setsum ∅ ∅ (Inj0 (Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 (setsum (X6 ∅ (Inj0 ∅ X8 ) X0 (λX8 : (((set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (Inj0 (setsum (X7 (λX8 : set → set → set ∅ ) (setsum (X7 (λX8 : set → set → set ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : (set → (set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj1 (setsum (Inj1 ∅ (Inj0 (Inj0 ∅ ∈ Inj1 (setsum (setsum (X7 (λX8 : (set → set → set ∅ ) ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set Inj0 X8 ) (X7 (λX8 : (set → set → set Inj0 (X8 (λX9 : set ⇒ setsum ∅ ∅ ) ) X6 (setsum (X5 (λX8 : set ⇒ λX9 : set → set Inj0 (setsum ∅ ∅ ) (Inj1 (Inj0 ∅ (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) ∅ ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set ∅ ) ∅ (X6 (λX8 : (set → set → set Inj0 X7 ) (Inj0 (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ∈ Inj1 (Inj0 (setsum (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (X4 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set → set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set Inj1 (X7 (Inj0 X8 ∅ (λX10 : set ⇒ X10 ) (Inj0 (X9 ∅ (λX10 : set ⇒ ∅ ) ∅ ) (X7 (Inj1 (Inj1 (Inj1 ∅ (X6 (Inj0 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (X4 (λX8 : set → set → set setsum (Inj0 ∅ (Inj0 ∅ ) (setsum ∅ (setsum ∅ ∅ X1 (λX8 : set → set setsum (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ) ∅ (X7 (setsum (X6 ∅ (X5 (X4 (λX8 : set → set → set ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (X6 ∅ (X6 ∅ (λX8 : set ⇒ setsum (X5 (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ X9 ) ∅ (setsum (setsum ∅ ∅ (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ ) ∅ (X6 (X5 ∅ (λX8 : set → set X6 ∅ ) (λX8 : set ⇒ X8 ) ∅ (λX8 : set ⇒ X7 ∅ (Inj1 (Inj0 (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ Inj0 (X7 (setsum ∅ ∅ (setsum ∅ ∅ (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (Inj1 (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X1 (λX8 : set → set X5 ) X6 ∅ ∅ (λX8 : set ⇒ X7 (λX9 : set ⇒ ∅ ) ) X0 (λX8 : (((set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ Inj1 (setsum (X8 (λX11 : (set → set → set ∅ ) (Inj0 ∅ ∅ (Inj0 ∅ ) (Inj0 (X4 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ (Inj1 ∅ ) ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set → set → set ∀X7 : set , (X6 (X4 ∅ (λX8 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (X4 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ setsum ∅ (Inj0 ∅ ) (Inj0 (setsum (Inj1 ∅ X5 ∈ X4 (Inj1 (setsum ∅ (Inj0 ∅ (λX8 : set ⇒ Inj0 (setsum X7 (Inj1 ∅ ) → X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 (X9 X12 ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum (Inj1 (X9 (λX10 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ∅ ) X0 (λX8 : (((set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) X7 ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set → ((set → set → set → set (Inj0 (X6 (X7 (setsum ∅ ∅ (λX8 : set → set X6 ∅ ) ∈ X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) → X0 (λX8 : (((set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ X9 (X9 X10 ) ∅ X0 (λX8 : (((set → set → set → set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 (Inj0 (setsum X10 (X7 ∅ (λX11 : set → set ∅ ) ) (setsum (setsum (X7 (X6 ∅ (λX8 : set → set ∅ ) (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 ∅ (λX11 : set → set ∅ ) ) (X7 X4 (λX8 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZhJeSKLZDmBmXQhEdppcAT1JLTR7UACuJ )
∀X0 : ((set → (set → set → set → set → set → (set → set → set → set → ((((set → set → set → (set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → ((set → set → set → (set → set → set → set → set → set → ((set → set → set → (set → set → set → prop (∀X4 : set → set → set ∀X5 : ((set → set → set → (set → set → set → set → (set → set → set → set ∀X6 : ((set → set → (set → set → set → set → (set → set → set ∀X7 : ((set → set → set → set → set X3 (λX8 : (((set → set → set → set → ((set → set → set → (set → set → set → set X8 (λX9 : (set → set → set ∅ ) (λX9 : set → set setsum ∅ (setsum ∅ (X7 (λX10 : set → set → set ∅ ) ) (λX9 : set ⇒ X7 (λX10 : set → set → set X9 ) ) (setsum (X7 (λX9 : set → set → set ∅ ) (Inj1 ∅ ) (setsum ∅ (setsum ∅ (Inj0 ∅ (λX8 : set → set → set λX9 : set → set Inj1 (X8 (X7 (λX10 : set → set → set X10 ∅ ∅ ) (Inj1 (X7 (λX10 : set → set → set ∅ ) ) ) → (∀X4 : set → (set → set → set ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : set , ∀X7 : set → set → set → set X3 (λX8 : (((set → set → set → set → ((set → set → set → (set → set → set → set Inj1 (setsum ∅ (setsum (setsum ∅ ∅ ∅ ) (setsum ∅ (X5 (Inj1 (setsum ∅ ∅ (λX8 : set → set Inj0 (Inj0 ∅ ) (λX8 : set ⇒ Inj1 (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set → set λX9 : set → set Inj0 ∅ ) X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set ∅ ) (λX8 : ((set → set → set → (set → set → set → set setsum (setsum (X7 (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (Inj1 ∅ (setsum (Inj0 ∅ (X5 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (X8 (λX9 : set → set setsum (setsum ∅ ∅ ∅ ) (λX9 : set ⇒ X6 ) (Inj1 (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : (((set → set → set → set → ((set → set → set → (set → set → set → set X5 ) (X4 (λX8 : (set → set → set λX9 : set ⇒ X7 (Inj1 (setsum ∅ ∅ ) (λX8 : set → set → set λX9 : set → set ∅ ) X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → ((set → set → set → set X2 (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ) False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X1 (λX8 : set ⇒ setsum ∅ (Inj1 (setsum (Inj1 ∅ X8 ) (setsum (setsum (Inj0 X6 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ ∅ ) ∅ X3 (λX8 : (((set → set → set → set → ((set → set → set → (set → set → set → set setsum (X8 (λX9 : (set → set → set X6 ) (λX9 : set → set X9 (X7 ∅ ) (λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (setsum X5 (setsum ∅ ∅ (setsum (X7 (Inj0 ∅ (Inj0 (X8 (λX9 : (set → set → set ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (setsum (Inj0 X4 ∅ (λX8 : set → set → set λX9 : set → set X9 (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set → set X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set X10 (X8 (X10 ∅ (Inj0 ∅ (λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 ∅ (Inj0 ∅ ) (setsum (Inj0 X9 ∅ ) (λX8 : ((set → set → set → (set → set → set → set setsum (Inj0 (Inj1 (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : (set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X0 (λX8 : set → (set → set → set → set λX9 : set ⇒ λX10 : set → set → set Inj0 (setsum ∅ (Inj0 (X8 ∅ (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → (set → set → set → set ∅ ) (Inj0 (Inj0 (setsum ∅ (setsum ∅ ∅ ∈ Inj1 (setsum ∅ (setsum (X4 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcpYAEnkH2ThFjqPcN2vmvZE5ovXfVKTkt )
∀X0 : (((set → set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : ((set → set → set → set → set → ((set → set → (set → set → set → set → prop ∀X3 : (set → set → set → ((set → set → set → set → set → (set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set → set setsum (Inj1 (Inj1 (setsum ∅ ∅ (Inj1 (Inj1 (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj0 X8 ) (Inj1 (Inj1 ∅ X3 (λX8 : set ⇒ ∅ ) X7 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ setsum (setsum (setsum ∅ ∅ (Inj1 X8 (X6 (setsum (setsum ∅ ∅ ∅ ) (Inj1 (setsum (Inj1 ∅ (Inj1 (Inj1 ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 (X6 ∅ ) X1 (λX8 : set ⇒ X5 (setsum (setsum X7 (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set (Inj1 (Inj1 (Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∈ Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) → X3 (λX8 : set ⇒ Inj0 (Inj0 (setsum (setsum ∅ ∅ (X6 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 X9 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X2 (λX8 : set → set λX9 : set ⇒ setsum (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ (Inj1 ∅ ) (Inj0 ∅ (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → set λX9 : set ⇒ setsum ∅ (X8 (setsum (Inj1 ∅ ∅ ) X4 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set → set X3 (λX8 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 X4 ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ ∅ ) (X6 X4 (Inj1 (Inj1 ∅ (λX8 : set ⇒ X7 (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → (set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ setsum X5 (setsum (Inj0 (Inj1 ∅ ∅ ) (setsum ∅ (Inj1 ∅ X1 (λX8 : set ⇒ X8 ) (X7 X5 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : (set → set → set → set → set ∀X7 : set , X0 (λX8 : (set → set → set → set setsum ∅ (X8 (λX9 : set ⇒ λX10 : set ⇒ X10 ) ) (λX8 : set ⇒ setsum ∅ (X5 (λX9 : (set → set → set → set setsum (setsum ∅ ∅ (X9 (λX10 : set ⇒ ∅ ) ∅ ) ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set → set ∅ ) (λX8 : set ⇒ Inj1 (Inj1 X7 ) X7 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWGN5piGECkuKd1tNqB7ia613VAqAc1x2D )
∀X0 : (set → set → set → set → prop ∀X1 : (((set → set → ((set → set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : ((set → set → set → set → ((set → set → set → set → set Inj1 (setsum (Inj0 X7 (setsum (X6 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum X7 (Inj0 (setsum X8 X8 ) (λX8 : set ⇒ Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : ((set → set → set → set → ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set X7 (setsum ∅ (X7 ∅ ) (λX8 : set ⇒ X8 ) X5 False ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → ((set → set → set → set → set → set λX9 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (Inj1 ∅ (Inj0 X9 ) (λX8 : set → set → set ∅ ) X2 (λX8 : ((set → set → set → set Inj1 (Inj0 (setsum X7 (Inj0 ∅ ) (setsum (Inj0 (setsum (Inj0 ∅ X7 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set X2 (λX8 : ((set → set → set → set ∅ ) ∅ False ) → (∀X4 : (set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → ((set → set → set → set → set (setsum (Inj1 (X7 (λX8 : set → set → set Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ ∈ setsum (Inj0 (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ∅ (X5 ∅ → X3 (λX8 : ((set → set → set → set → ((set → set → set → set → set setsum (Inj0 ∅ (Inj0 (X6 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (Inj1 (Inj1 ∅ ) ∅ X1 (λX8 : (set → set → ((set → set → set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set → set → set Inj1 (X5 (X7 (λX9 : set → set → set setsum ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → (set → set → set → set → set ∀X7 : set , (setsum (setsum ∅ X7 (X5 (Inj1 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ∅ ∈ setsum (Inj1 (X5 (X5 ∅ (setsum (Inj1 X4 X7 → X1 (λX8 : (set → set → ((set → set → set → set → set → set λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set → set Inj0 X7 ) X3 (λX8 : ((set → set → set → set → ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ Inj1 (setsum (X5 (Inj1 ∅ X7 ) (setsum X7 ∅ ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (X6 (λX8 : set → set X6 (λX9 : set → set Inj0 (Inj1 ∅ ) ) (X4 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X6 (λX10 : set → set X8 (X10 ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : ((set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ setsum (X5 (Inj0 (X5 ∅ (Inj0 (setsum X8 ∅ ) (X7 (setsum (setsum (Inj1 ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ X4 (setsum (setsum (X6 (λX8 : set → set setsum ∅ ∅ ) X4 ∅ X0 (λX8 : set ⇒ Inj1 (X7 (setsum (Inj1 ∅ (Inj0 ∅ ) (X6 (λX8 : set → set Inj0 (setsum (Inj1 ∅ (X5 ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQaPomGbLFJksCmNpiAECz4xhhtKXuJF4Y )
∀X0 : (set → set → (((set → set → set → (set → set → set → set → set → set → prop ∀X1 : (set → set → (set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → (set → set → set → set → set → set → (set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set → (set → set → set ∀X6 : set , ∀X7 : set , (X5 (X5 ∅ ∅ (λX8 : set ⇒ setsum ∅ (Inj1 ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∈ X7 → X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set ∅ ) ∅ X3 (λX8 : (((set → set → set → set → (set → set → set → set → set Inj0 X7 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum X11 (setsum ∅ (setsum ∅ ∅ ) X0 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ X7 ) ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set setsum (setsum ∅ (Inj1 (X8 ∅ ∅ ∅ ) ∅ (Inj1 X4 ∈ Inj1 (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set (setsum (Inj0 (X7 (λX8 : (set → set → set ∅ ) (setsum (X7 (λX8 : (set → set → set setsum ∅ ∅ ) ∅ ∈ X5 → X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 ) X1 (λX8 : set ⇒ Inj0 (setsum (setsum (X7 (λX9 : (set → set → set ∅ ) ∅ ∅ ) (λX8 : set ⇒ setsum X6 X8 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ setsum ∅ (X5 (λX9 : (set → set → set λX10 : set ⇒ Inj0 (setsum ∅ ∅ ) ∅ (X5 (λX9 : (set → set → set λX10 : set ⇒ X7 ) ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum (Inj1 ∅ (setsum (Inj0 (X5 (λX9 : (set → set → set λX10 : set ⇒ ∅ ) ∅ ∅ (Inj0 ∅ ) X3 (λX8 : (((set → set → set → set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) ) → (∀X4 : ((set → set → set → (set → set → set → set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → set X0 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ ∅ ) X3 (λX8 : (((set → set → set → set → (set → set → set → set → set Inj1 (setsum ∅ (X8 (λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTjWvD6yvABncQHTPomyimZ8rUxANTfu4o )
∀X0 : ((set → ((set → set → set → set → set → set → set → (((set → set → set → set → prop ∀X1 : ((set → (set → set → set → set → set → (((set → set → set → set → prop ∀X2 : (set → set → set → (set → set → prop ∀X3 : ((set → set → (set → set → set → ((set → set → set → set → set → set → (set → (set → set → set → set → set → (((set → set → set → set → ((set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → (set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set → set → (set → set → set λX9 : (set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum (setsum ∅ (setsum ∅ ∅ X7 ∅ ) (λX8 : set ⇒ X6 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ ∅ (Inj0 (setsum ∅ ∅ ) (λX9 : set ⇒ X8 ) (Inj1 (setsum ∅ (X6 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (Inj0 (X6 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) (setsum (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set → (set → set → set λX9 : (set → set → set → set → set X7 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set setsum (setsum X7 (X5 (setsum ∅ ∅ (Inj1 (X8 (λX9 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) (Inj0 ∅ (X7 ∈ Inj1 X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set (X4 ∈ X5 (λX8 : (set → set → set → set setsum ∅ ∅ ) → X3 (λX8 : set → set → (set → set → set λX9 : (set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set setsum (Inj0 (Inj0 (Inj1 ∅ (setsum (X7 (λX9 : set → set → set Inj0 ∅ ) (Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj1 (Inj0 (setsum (X5 (λX9 : (set → set → set → set ∅ ) (Inj0 ∅ ) (X7 (λX8 : set → set → set setsum (Inj1 ∅ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X1 (λX8 : set → (set → set → set X5 (setsum (setsum X7 (X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (Inj1 (Inj0 (Inj0 X7 (λX8 : (set → set → set Inj0 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : set → set (Inj1 ∅ ∈ Inj1 X4 → X1 (λX8 : set → (set → set → set setsum ∅ (X7 (Inj0 (setsum ∅ ∅ ) (Inj0 (X7 (setsum (Inj1 ∅ ∅ (λX8 : (set → set → set setsum (Inj0 (Inj0 (X7 ∅ (X7 (Inj0 (X8 (λX9 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : set → (set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → set → (set → set → set → set ∀X7 : ((set → set → set → (set → set → set → set X1 (λX8 : set → (set → set → set X5 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X8 (setsum ∅ ∅ (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj1 X9 ) (setsum ∅ (Inj1 (X8 ∅ (λX9 : set ⇒ ∅ ) ) (setsum (setsum X4 (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) X4 ∅ (λX8 : (set → set → set ∅ ) X1 (λX8 : set → (set → set → set Inj1 ∅ ) (Inj0 ∅ (λX8 : (set → set → set X5 ∅ (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (Inj1 ∅ ∅ ) ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → ((set → set → set → set → set → set X5 ) (λX8 : (set → set → set Inj1 X7 ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → ((set → set → set → set → set → set X7 ) (λX8 : (set → set → set Inj0 (X8 (λX9 : set ⇒ Inj0 ∅ ) ) (Inj0 ∅ ∈ Inj0 (setsum (X5 (Inj0 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZCHMPWBRVDfk41jyc1NgaEyKPpa5P5nDU )
∀X0 : (set → set → ((((set → set → set → set → set → (set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → set → set → (set → set → prop ∀X3 : (set → set → set → (set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : (set → (set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (X6 ∅ (setsum (Inj1 ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 X8 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : (set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (Inj0 X7 ) X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (Inj0 (Inj1 ∅ ∅ ∅ ) (λX8 : set ⇒ X5 (λX9 : set → set → set λX10 : set → set ∅ ) ) ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → (set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ X6 ) (λX8 : set ⇒ X5 ) X2 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : (set → set → set → set X9 ) ∅ (λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj0 (Inj0 (Inj0 X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 X8 ) (λX8 : set ⇒ Inj1 (Inj1 (setsum (X6 ∅ (λX9 : set → set ∅ ) ∅ X7 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 ∈ Inj0 (setsum (setsum X7 (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ Inj0 X6 ) (setsum (setsum X5 (setsum (Inj1 ∅ (Inj1 ∅ (setsum X6 X6 ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ Inj0 (Inj1 (setsum ∅ (Inj1 ∅ ) (setsum (setsum (Inj1 X7 (setsum ∅ (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (X6 (λX8 : set → set Inj1 (setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ ∅ ∈ Inj1 (setsum ∅ (setsum ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ setsum X5 (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ ∅ ) (Inj0 (Inj0 ∅ X0 (λX8 : set ⇒ Inj1 (Inj0 (Inj1 (Inj0 ∅ ) (λX8 : ((set → set → set → set → set λX9 : set → set → set λX10 : set → set λX11 : set ⇒ Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set → set X0 (λX8 : set ⇒ X5 ) (λX8 : ((set → set → set → set → set λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ∈ Inj0 (X4 (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUHHcDXbMvkpAZQMTUdPnGsdUNQqqE2gt7 )
∀X0 : (set → set → set → prop ∀X1 : ((set → ((set → set → set → (set → set → set → set → (set → set → prop ∀X2 : ((set → set → (set → set → set → set → ((set → set → set → set → (set → (set → set → set → set → set → set → prop ∀X3 : (set → set → set → set → set → prop (∀X4 : (((set → set → set → (set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (X6 (setsum (Inj1 (X6 ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (setsum (Inj1 (Inj0 (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → set ∀X6 : (set → set → set ∀X7 : (set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ X6 ∈ Inj1 X7 → X2 (λX8 : set → set → (set → set → set → set λX9 : (set → set → set setsum ∅ (setsum ∅ X7 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : set → set → (set → set → set → set λX9 : (set → set → set setsum (X7 (λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X9 (X9 (Inj0 (Inj0 ∅ (Inj1 (setsum ∅ ∅ (setsum (setsum X8 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (Inj0 (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ ∅ X5 ∈ X6 → X1 (λX8 : set → ((set → set → set → (set → set → set Inj0 (Inj1 (X8 (Inj0 ∅ (λX9 : set → set X7 ) (λX9 : set ⇒ X9 ) ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → ((set → set → set → (set → set → set Inj0 ∅ ) (λX8 : set ⇒ ∅ ) X1 (λX8 : set → ((set → set → set → (set → set → set setsum (X8 (Inj1 (X8 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ X5 ) ) → (∀X4 : set → set → set ∀X5 : set → (set → set → set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (setsum (Inj0 (Inj0 (Inj1 ∅ (setsum (X6 (λX8 : (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (X5 X7 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (setsum ∅ ∅ X0 (λX8 : set ⇒ X5 (Inj1 (X6 (λX9 : (set → set → set → set X8 ) (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (setsum (setsum ∅ ∅ (X5 ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ ) (setsum (X6 (λX8 : (set → set → set → set Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set X0 (λX8 : set ⇒ X5 (X5 X6 (λX9 : set → set ∅ ) (λX9 : set → set X6 ) ) (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ (Inj1 (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ ∈ X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRRrLB6YaVQsuYBMXyxus8cePd7Who1d5D )
∀X0 : (((set → set → set → set → ((((set → set → set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → (set → (set → set → set → (((set → set → set → set → (set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → (set → set → set → set → set → ((set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → set → set → set → (set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (X6 ∈ Inj0 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum X7 (Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X10 ) (λX8 : set ⇒ setsum (setsum (setsum (Inj0 ∅ ∅ (setsum (X5 (λX9 : (set → set → set → set λX10 : set → set ∅ ) (Inj1 ∅ ∅ ) ) → (∀X4 : (set → (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → ((set → set → set → set (Inj0 X4 ∈ setsum (Inj1 ∅ (Inj0 (setsum (setsum ∅ ∅ X5 → X2 (λX8 : (((set → set → set → set → set λX9 : set → set → set λX10 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : set → set setsum ∅ (Inj0 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set , (Inj0 (setsum (setsum X7 ∅ (Inj0 (setsum ∅ ∅ ∈ setsum (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj1 X4 (X6 (setsum X4 ∅ (λX8 : set → set λX9 : set ⇒ setsum (setsum ∅ ∅ (X8 ∅ ) → X2 (λX8 : (((set → set → set → set → set λX9 : set → set → set λX10 : set ⇒ setsum (Inj1 (Inj0 (Inj1 ∅ (X9 (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ) (λX8 : set → set setsum ∅ (Inj0 ∅ ) X3 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 (setsum X11 (Inj0 ∅ ) (λX8 : set ⇒ X5 ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , (setsum ∅ (X5 (Inj0 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ∈ Inj1 (X5 (Inj1 (Inj1 ∅ (X6 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) → X0 (λX8 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ X10 ) (Inj1 X7 (setsum (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) X7 (Inj0 ∅ ∅ ) X1 (λX8 : set → set → set setsum (X6 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (X8 ∅ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) ∅ ) False ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set (Inj1 (Inj1 (Inj1 (Inj0 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : ((set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X12 ) (λX8 : set ⇒ Inj1 (setsum (setsum ∅ (Inj0 ∅ X8 ) X0 (λX8 : (set → set → set X6 ) (λX8 : ((set → set → set → set → set → set → set ∅ ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : (set → set → (set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set → set → set Inj1 (X6 (Inj0 ∅ ) X0 (λX8 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set → set → set Inj1 X7 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRq7nRfYkm6ofb65NKUkwkSjT6vFEtJaNU )
∀X0 : ((set → set → set → set → set → set → prop ∀X1 : (set → (((set → set → set → (set → set → set → set → ((set → set → set → set → (set → set → (set → set → set → set → prop ∀X2 : ((((set → set → set → set → ((set → set → set → set → set → set → prop ∀X3 : (((set → set → set → (set → set → set → set → ((((set → set → set → set → (set → set → (set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → set → (set → set → set Inj1 (X8 (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (Inj0 ∅ (X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X6 ) ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum (X10 (X8 (λX12 : set → set Inj0 ∅ ) X11 ) (λX8 : set → set Inj0 X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set → set X3 (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (X10 (Inj1 (Inj0 ∅ ) (λX8 : set → set ∅ ) (X6 ∈ setsum (Inj0 (setsum (X7 (λX8 : (set → set → set → set ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → (set → set → set → set → set (Inj0 X5 ∈ X6 → X2 (λX8 : ((set → set → set → set → ((set → set → set → set X8 (λX9 : set → set → set ∅ ) (λX9 : set → set Inj1 (Inj0 ∅ ) ) ∅ ) → (∀X4 : (set → set → set → set → set → set ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set → set → set → set ∀X7 : ((set → set → set → set X2 (λX8 : ((set → set → set → set → ((set → set → set → set setsum (setsum ∅ (Inj0 (X8 (λX9 : set → set → set ∅ ) (λX9 : set → set ∅ ) (setsum (X5 (λX9 : set → set λX10 : set → set setsum ∅ ∅ ) (X5 (λX9 : set → set λX10 : set → set ∅ ) ∅ (setsum (Inj0 ∅ (X7 (λX9 : set → set ∅ ) ) (Inj1 ∅ False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (setsum ∅ (X5 (λX8 : (set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ ∅ ) ∅ ) ∈ Inj0 X7 → X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : (set → set → set setsum (setsum (Inj1 (Inj1 ∅ ∅ ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (X5 (λX9 : (set → set → set → set λX10 : set → set ∅ ) (setsum (Inj1 ∅ (Inj1 ∅ (setsum (Inj1 (setsum ∅ ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj1 X7 ) ) → (∀X4 : set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set → set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : (set → set → set ∅ ) (λX8 : set ⇒ X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ setsum X11 (Inj1 (Inj1 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X9 (Inj0 X8 ) X1 (λX8 : set ⇒ λX9 : ((set → set → set → (set → set → set → set λX10 : (set → set → set X8 ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set → set X2 (λX8 : ((set → set → set → set → ((set → set → set → set X7 (setsum (Inj0 ∅ ∅ ∅ (Inj1 (setsum X6 (X7 ∅ ∅ ∅ ) (Inj0 ∅ X0 (λX8 : set → set λX9 : set ⇒ X7 (Inj1 X6 ∅ ∅ ) (setsum ∅ (setsum ∅ (X7 (X7 ∅ ∅ ∅ (setsum ∅ ∅ ∅ (setsum (Inj0 (setsum (setsum ∅ ∅ (X7 ∅ ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , (setsum ∅ (Inj0 (Inj0 ∅ ∈ Inj0 (setsum ∅ X5 → X0 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (setsum (Inj0 (setsum (setsum ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum ∅ ∅ ∅ X0 (λX8 : set → set λX9 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj1 (Inj1 ∅ ) X7 X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWCXAwQjkM9pkUdErr6pLAsm2aHYqdntuv )
∀X0 : ((((set → set → set → set → set → set → set → prop ∀X1 : (set → (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → ((set → set → set → ((set → set → set → set → ((set → set → set → set → prop ∀X2 : (((((set → set → set → (set → set → set → set → set → (set → set → set → set → prop ∀X3 : ((set → ((set → set → set → set → set → set → set → ((set → set → set → prop (∀X4 : set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → set (Inj1 (setsum (setsum (X7 ∅ (X6 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∈ Inj0 (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set → set → set λX9 : (set → set → set setsum ∅ (X8 (setsum (setsum ∅ ∅ (Inj1 ∅ ∅ ) (λX8 : set → set → set ∅ ) X3 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ Inj1 ∅ ) (λX8 : set → set Inj1 (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set → set setsum X6 ∅ ) (X7 ∈ Inj0 X6 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , (setsum (Inj1 (Inj1 ∅ ∅ ∈ Inj0 X4 → X2 (λX8 : (((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set Inj1 (X8 (λX11 : (set → set → set λX12 : set → set Inj0 (Inj0 ∅ ) ) X6 ) → (∀X4 : (((set → set → set → (set → set → set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set , X2 (λX8 : (((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) ∅ (Inj1 ∅ ∈ setsum (X6 (setsum X5 (Inj0 ∅ (Inj0 (Inj0 ∅ (Inj0 (setsum ∅ ∅ X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → (set → set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set → set → set λX9 : (set → set → set setsum ∅ ∅ ) (λX8 : set → set → set ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : ((set → set → set → ((set → set → set → (set → set → set ∀X7 : set → set → set → set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set X8 ) (λX8 : set → set → set λX9 : (set → set → set Inj0 (Inj1 ∅ ) (λX8 : set → set → set X7 (setsum (Inj1 (Inj0 ∅ (setsum (Inj1 ∅ (X7 ∅ ∅ ∅ ∅ ∅ (X8 (setsum ∅ (X6 (λX9 : set → set ∅ ) (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (setsum (setsum (X7 ∅ ∅ ∅ ∅ (X7 ∅ ∅ ∅ ∅ (X5 (λX9 : set ⇒ X7 ∅ ∅ ∅ ∅ ) ) False ) → (∀X4 : (set → (set → set → set → ((set → set → set → set → (set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : ((set → set → set → set λX9 : set ⇒ X8 (λX10 : set → set setsum (Inj1 (Inj0 ∅ X9 ) ) (X4 (λX8 : set ⇒ λX9 : set → set setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X8 ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → (set → set → set → set ∀X7 : set , (X5 ∈ Inj0 (Inj1 (X6 (λX8 : set → set → set λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) → X0 (λX8 : ((set → set → set → set λX9 : set ⇒ Inj1 (setsum ∅ (X8 (λX10 : set → set setsum ∅ ∅ ) ) (setsum X4 (setsum (Inj0 ∅ ∅ X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → (set → set → set → set λX10 : (set → set → set → set X10 (λX11 : set ⇒ setsum X8 (setsum ∅ X11 ) X7 ) (λX8 : set → set → set λX9 : (set → set → set ∅ ) (λX8 : set → set → set Inj1 (Inj0 (setsum X5 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVTKFLMLT8HT4eGEyVGU8RKWoF32BKSf1F )
∀X0 : (((set → set → set → (set → set → set → set → set → set → set → set → set → ((set → set → (set → set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : ((set → set → set → (set → set → prop ∀X3 : (((((set → set → set → set → set → set → (((set → set → set → set → set → set → set → prop (∀X4 : ((set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : (((set → set → set → set → set ∅ ) (λX8 : (set → set → set → set setsum ∅ (setsum (setsum ∅ (Inj1 ∅ (X7 ∅ ) ∅ X6 ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X3 (λX8 : (((set → set → set → set → set Inj0 ∅ ) (λX8 : (set → set → set → set Inj0 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj0 (setsum ∅ ∅ ) (setsum ∅ ∅ ∅ False ) → (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : set → set X6 ) (λX8 : set ⇒ Inj0 (Inj1 X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set → set X8 (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X6 ) False ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (set → set → set → set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ X9 ) ∅ (Inj0 (setsum (Inj0 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X5 (setsum X6 (X5 (Inj0 ∅ (setsum ∅ ∅ X6 ∅ (X5 (Inj0 (setsum ∅ ∅ ∅ ∅ ∅ False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → set Inj1 X5 ) (λX8 : (set → set → set → set Inj1 X5 ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ X5 (setsum (setsum ∅ ∅ ∅ (Inj1 X5 X0 (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum X10 (setsum (X8 ∅ (setsum (X9 ∅ ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : (set → set → set ∀X6 : (((set → set → set → set → set → set → set → (set → set → set ∀X7 : set → set X0 (λX8 : (set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X9 ∅ ) (Inj1 (setsum ∅ (X5 (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum (X7 (setsum ∅ ∅ (setsum ∅ (X7 ∅ (setsum X10 (X8 ∅ ) (X4 (λX8 : (set → set → set ∅ ) (X7 (setsum (setsum (setsum ∅ ∅ (X4 (λX8 : (set → set → set ∅ ) (setsum (Inj1 ∅ ∅ ∈ setsum (setsum (X4 (λX8 : (set → set → set X8 (λX9 : set ⇒ ∅ ) ) (Inj0 (X6 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ (Inj1 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJtLMyeoBzKGnEggTBmyrT9n26SHgV2rwB )
∀X0 : ((set → set → set → (((set → set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj1 X8 ) (Inj0 ∅ X3 (λX8 : set ⇒ Inj1 (setsum (Inj0 X8 (Inj0 (setsum ∅ ∅ ) X4 ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ setsum ∅ (Inj0 (setsum X8 (Inj0 ∅ ) (setsum (X6 (λX8 : set → set λX9 : set → set setsum (X9 ∅ (Inj0 ∅ ) (setsum X7 (setsum ∅ (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) ∅ X2 (λX8 : set ⇒ X6 ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 (setsum ∅ X6 ) ∅ X3 (λX8 : set ⇒ setsum ∅ (setsum (setsum (Inj1 ∅ (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → set ∀X7 : set , (Inj0 (X5 (setsum (Inj0 ∅ ∅ ∈ Inj1 (X6 (λX8 : set ⇒ setsum X8 (setsum ∅ ∅ ) ∅ (Inj0 (setsum ∅ ∅ → X2 (λX8 : set ⇒ X7 ) (X6 (λX8 : set ⇒ Inj0 X8 ) X4 (setsum (setsum X4 X7 X4 X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ (setsum (X6 (λX8 : set ⇒ ∅ ) X4 (setsum (Inj0 ∅ (X5 ∅ X7 ) → (∀X4 : set → set ∀X5 : (set → set → set → set ∀X6 : (set → set → ((set → set → set → (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X4 (X5 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) ∅ (Inj0 (setsum (setsum ∅ (setsum ∅ ∅ X7 ∈ setsum (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ X7 (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set (setsum (setsum X6 (setsum X4 (Inj1 ∅ ∅ ∈ Inj0 (setsum (setsum (Inj0 ∅ ∅ ∅ → X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set setsum (Inj1 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum X6 (setsum ∅ ∅ ) (λX8 : set → set X5 (X5 ∅ ) (Inj0 (Inj1 (Inj1 ∅ ) → (∀X4 : (set → set → ((set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → (set → set → (set → set → set → set ∀X7 : set → set → set → set X0 (λX8 : set → set → set λX9 : ((set → set → set → set → set ∅ ) (λX8 : set → set X6 (λX9 : set → set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (setsum (Inj1 ∅ (Inj1 (setsum ∅ ∅ ) ∅ X3 (λX8 : set ⇒ setsum (X7 (Inj0 ∅ (setsum (Inj0 ∅ X8 (setsum (Inj1 ∅ (Inj0 ∅ ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYg8GK7WWnZozK3iERsUWU1QAPCfseUvWY )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → (set → set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → set → set → set → prop ∀X3 : (set → set → (set → (set → set → set → (set → set → set → set → (set → (set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → (set → set → set → set → set (Inj1 ∅ ∈ X4 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 (X10 (λX13 : set ⇒ Inj1 (Inj1 ∅ ) ∅ ) ∅ X3 (λX8 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X5 ∅ ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X10 (X10 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 (λX11 : set → set → set λX12 : set → set λX13 : set ⇒ Inj0 (setsum ∅ (setsum ∅ ∅ ) ) ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ Inj0 X6 ) (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ X10 ) (Inj0 ∅ (λX8 : set ⇒ X8 ) False ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set (setsum (Inj0 ∅ (Inj0 ∅ ∈ X4 (λX8 : set ⇒ X8 ) (Inj0 (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 X8 (Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ X8 ) (Inj1 (Inj1 (Inj0 (setsum ∅ ∅ X5 ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj0 (X4 (λX8 : set ⇒ X7 (Inj0 ∅ (λX9 : set ⇒ Inj1 ∅ ) ) X6 ) → (∀X4 : (((set → set → set → set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (X5 (Inj1 (setsum (X4 (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ X7 (Inj1 (setsum (Inj0 ∅ (X6 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) X7 ∈ setsum (setsum X7 (X4 (λX8 : (set → set → set → set λX9 : set ⇒ Inj1 ∅ ) (X6 (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (Inj0 ∅ (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum X9 X9 ) (λX8 : set ⇒ Inj0 ∅ ) (setsum (Inj1 ∅ ∅ (setsum (Inj1 X6 ∅ (Inj1 (Inj1 (X5 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 ∅ ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 (setsum X5 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum X8 ∅ ) (setsum ∅ ∅ (Inj0 ∅ ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (setsum X6 ∅ ∅ (setsum X7 (setsum (Inj1 (Inj0 ∅ X5 (X4 (Inj1 (Inj1 X6 (setsum (Inj1 (Inj1 ∅ ∅ (Inj0 ∅ X6 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set → ((set → set → set → set → set → set X0 (λX8 : set ⇒ setsum ∅ (setsum (X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (λX9 : set → set Inj0 ∅ ) (setsum ∅ ∅ (setsum ∅ ∅ (X5 (setsum ∅ ∅ ) (Inj0 X4 X0 (λX8 : set ⇒ setsum ∅ (Inj0 (Inj1 (Inj1 ∅ ) X6 ) → (∀X4 : ((set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ setsum (Inj1 X7 X6 ) (setsum (X5 (λX8 : (set → set → set → set λX9 : set → set X7 ) (Inj0 (setsum ∅ ∅ (X4 (λX8 : set → set λX9 : set ⇒ X6 ) X0 (λX8 : set ⇒ X8 ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMFuqcGLgxqthvXpWSbJeDA6HWgQaDeHPeE )
∀X0 : (set → set → (set → (set → set → set → set → set → prop ∀X1 : (set → set → set → set → ((set → set → set → set → set → set → (set → set → (set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : ((set → set → (set → (set → set → set → ((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set (setsum X5 X5 ∈ Inj1 (Inj1 (X7 (λX8 : set ⇒ setsum ∅ ∅ ) → X3 (λX8 : set → set λX9 : set → (set → set → set λX10 : (set → set → set → set λX11 : set ⇒ setsum ∅ (setsum (X10 (λX12 : set ⇒ X11 ) (X9 ∅ (λX12 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) X6 (Inj0 X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → set X3 (λX8 : set → set λX9 : set → (set → set → set λX10 : (set → set → set → set λX11 : set ⇒ Inj0 (setsum (setsum (X8 ∅ (X9 ∅ (λX12 : set ⇒ ∅ ) ∅ ) X5 (Inj0 ∅ False ) → (∀X4 : set → (set → set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X7 ) X7 X2 (λX8 : set ⇒ Inj0 (X5 (λX9 : (set → set → set → set X6 (λX10 : set ⇒ X8 ) ) ) (Inj1 (Inj1 (setsum (setsum ∅ ∅ (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : (set → set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : set → set X2 (λX8 : set ⇒ Inj0 X8 ) (setsum (Inj0 (X4 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) ∅ ) (setsum (Inj0 (setsum ∅ ∅ (X7 (Inj1 ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set → set → set Inj1 (Inj1 (setsum ∅ (setsum ∅ ∅ ) (X6 (Inj1 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (Inj1 ∅ X8 (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ∅ ∅ (X7 (Inj1 ∅ (setsum ∅ (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ∅ ∅ ∅ ) (X7 (setsum ∅ (setsum (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set → set → set Inj0 (setsum (Inj0 ∅ (X8 X6 X7 (Inj1 ∅ ) (Inj1 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set → ((set → set → set → set → set ∀X7 : (((set → set → set → (set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj0 (Inj0 ∅ (Inj1 (setsum ∅ ∅ (X7 (λX11 : (set → set → set λX12 : set → set setsum (Inj1 ∅ (Inj1 ∅ ) ) (λX8 : set → set → set → set ∅ ) (X5 ∅ (λX8 : set ⇒ X7 (λX9 : (set → set → set λX10 : set → set Inj1 (X9 (λX11 : set ⇒ Inj1 ∅ ) ) ) (λX8 : set ⇒ setsum (Inj1 X8 (Inj0 X8 ) (setsum X4 X4 X0 (λX8 : set ⇒ setsum (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set (Inj1 ∅ ∈ X5 → X0 (λX8 : set ⇒ setsum ∅ X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ setsum (Inj1 X10 (setsum ∅ (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 (Inj0 ∅ ) (Inj1 (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWiSw8Hg274twYeAL5Y58H1Nkz3xjXh47P )
∀X0 : (set → (set → set → set → set → set → set → prop ∀X1 : (((set → set → set → set → set → set → set → (set → set → set → ((((set → set → set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → (((set → set → set → set → set → set → (set → set → set → (set → set → set → prop ∀X3 : ((set → set → ((set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set (Inj0 (setsum ∅ (setsum (Inj0 ∅ (X4 ∅ ∈ Inj1 X5 → X3 (λX8 : set → set λX9 : (set → set → set → set Inj0 (setsum (X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (Inj0 (Inj1 ∅ X3 (λX8 : set → set λX9 : (set → set → set → set setsum (X7 (λX10 : set → set X8 (Inj0 ∅ ) ∅ ) (X4 X5 ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set (X4 (X7 (Inj0 ∅ (X4 (setsum ∅ ∅ (X7 ∅ ∅ (setsum ∅ ∅ (Inj0 ∅ X6 (setsum (Inj0 (Inj1 ∅ (setsum (Inj0 ∅ (Inj0 ∅ (X4 (Inj0 (setsum ∅ ∅ X6 X6 ∅ ∈ setsum X5 (X4 ∅ ∅ (X7 (setsum ∅ ∅ X5 (X7 (Inj1 ∅ ∅ → X3 (λX8 : set → set λX9 : (set → set → set → set setsum (Inj1 (X7 (setsum ∅ ∅ (setsum ∅ ∅ (X9 (λX10 : set ⇒ λX11 : set ⇒ Inj1 (setsum ∅ ∅ ) ) ∅ X3 (λX8 : set → set λX9 : (set → set → set → set X6 ) (setsum (Inj1 (setsum X5 (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum ∅ ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) ) X7 ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set → (set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → set X2 (λX8 : set ⇒ X6 (Inj1 (Inj0 (Inj0 ∅ (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ Inj0 (X6 (Inj1 ∅ (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ) (setsum (setsum (Inj0 ∅ (X7 (λX9 : (set → set → set ∅ ) ∅ ) (λX8 : set → set ∅ ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 (X8 (λX11 : set ⇒ Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : (set → set → set ∅ ) ) (λX8 : set ⇒ X6 (Inj1 (Inj0 ∅ (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (λX9 : set ⇒ X9 ) (setsum ∅ (Inj0 (Inj1 ∅ ) X4 False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set → set λX9 : (set → set → set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X7 (Inj0 ∅ ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ X4 (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (X8 ∅ ) X1 (λX8 : (set → set → set → set → set → set → set λX9 : set → set ∅ ) (λX8 : ((set → set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set → set → set → set → set λX9 : set → set ∅ ) (λX8 : ((set → set → set → set → set ∅ ) X1 (λX8 : (set → set → set → set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ X7 ) (λX8 : ((set → set → set → set → set setsum (setsum (X8 (λX9 : set → set Inj0 ∅ ) X7 (setsum X7 X7 (setsum (X6 (Inj1 ∅ (λX9 : set → set Inj1 ∅ ) (setsum X5 (Inj1 ∅ ) ) → (∀X4 : set → (set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → (set → set → set → set ∀X7 : (set → set → set → set (X6 (setsum (Inj0 (X5 ∅ (Inj0 ∅ (λX8 : set → set X5 (Inj1 ∅ ) (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 X8 ) ∈ setsum (Inj1 ∅ (X6 (Inj0 (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (λX8 : set → set Inj1 ∅ ) (λX8 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) (setsum (X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ∅ → X0 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ (Inj0 (X9 (setsum ∅ ∅ ) ∅ ∅ ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set , (setsum (Inj1 (Inj0 (setsum ∅ ∅ (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ∈ Inj0 X5 → X0 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (setsum (Inj1 (Inj0 ∅ X8 ) ∅ ∅ X3 (λX8 : set → set λX9 : (set → set → set → set setsum (setsum (X9 (λX10 : set ⇒ λX11 : set ⇒ X10 ) (Inj0 ∅ (Inj0 (Inj0 (X8 ∅ ) (setsum (setsum (Inj0 X5 ∅ (setsum ∅ (Inj1 X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRzvTcwxhHB3DcLM6CpazDFuxHQGPtTQZS )
∀X0 : (set → set → set → (set → set → prop ∀X1 : (((set → set → set → ((set → set → set → set → set → set → ((((set → set → set → (set → set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → set → (set → ((set → set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → set → ((set → set → set → set → set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set λX10 : (set → set → set λX11 : set ⇒ setsum (X9 (λX12 : set → set Inj0 (X9 (λX13 : set → set ∅ ) ∅ ∅ ) (setsum (Inj0 ∅ (Inj0 ∅ ∅ (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ X8 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set λX10 : (set → set → set λX11 : set ⇒ Inj1 (setsum (X10 (λX12 : set ⇒ Inj0 ∅ ) ∅ ) (λX8 : set → set λX9 : set ⇒ X7 X6 ) (Inj0 (Inj1 ∅ ∈ setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , (setsum (Inj1 (Inj1 ∅ (Inj1 ∅ ∈ setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ (setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (Inj1 (Inj0 (Inj1 ∅ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , (Inj0 X5 ∈ X7 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 ∅ X9 ) (λX8 : set ⇒ λX9 : (set → set → set setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ∅ ) X1 (λX8 : (set → set → set → ((set → set → set → set → set X5 ) (λX8 : ((set → set → set → (set → set → set → set X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ Inj0 (X8 (λX10 : set → set setsum ∅ ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (X8 (λX9 : set → set setsum (setsum ∅ ∅ X7 ) (λX9 : set ⇒ X8 (λX10 : set → set ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) (Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → (set → set → set ∀X7 : set → set → set X1 (λX8 : (set → set → set → ((set → set → set → set → set Inj0 (Inj0 (setsum ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → (set → set → set → set setsum (Inj0 (setsum ∅ (Inj1 ∅ (X7 ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → (set → set → set → (set → set → set → set ∀X7 : ((set → set → (set → set → set → set → set X1 (λX8 : (set → set → set → ((set → set → set → set → set ∅ ) (λX8 : ((set → set → set → (set → set → set → set X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : set → set λX12 : set → set λX13 : set ⇒ ∅ ) ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 (setsum (Inj0 ∅ (Inj0 ∅ (setsum ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set X6 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X12 ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ ) ) → (∀X4 : ((set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ Inj1 ∅ ) (Inj1 ∅ (λX8 : set ⇒ ∅ ) X0 (λX8 : set ⇒ ∅ ) (setsum (X7 (Inj1 X6 (setsum (Inj1 (X7 ∅ (X5 (λX8 : (set → set → set setsum ∅ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (setsum (Inj0 (setsum (setsum ∅ ∅ ∅ X7 (λX8 : set ⇒ Inj0 (Inj1 (X5 (setsum ∅ ∅ (λX9 : set → set Inj1 ∅ ) ) (setsum (Inj1 (setsum ∅ (setsum ∅ ∅ (Inj0 (Inj1 (Inj0 ∅ ∈ Inj0 X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMY2MfiUmeGKvN8wGGTVysErKUGQnToVD4j )
∀X0 : ((set → set → set → set → set → set → prop ∀X1 : ((set → (set → set → set → set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj1 X4 ∈ Inj1 (Inj1 ∅ → X3 (λX8 : set ⇒ ∅ ) (Inj1 (setsum (X6 (λX8 : set ⇒ λX9 : set → set X8 ) (setsum (Inj1 ∅ X7 X3 (λX8 : set ⇒ Inj0 ∅ ) (setsum X7 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (Inj0 ∅ X8 ) ∅ (setsum ∅ ∅ ∈ Inj1 (Inj1 (Inj1 X6 → X3 (λX8 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ X3 (λX8 : set ⇒ X8 ) (Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 ∅ ) (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → (set → set → set ∀X7 : set → set (Inj0 (Inj0 ∅ ∈ setsum (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 (X7 (setsum ∅ ∅ → X1 (λX8 : set → (set → set → set → set ∅ ) (Inj1 (Inj0 (Inj0 (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) X5 X2 (λX8 : set ⇒ Inj1 X5 ) X5 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set ∀X7 : set → (set → set → set → set (Inj0 ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ ∅ ) (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ X3 (λX8 : set ⇒ Inj1 (setsum ∅ (X6 X5 (λX9 : set → set Inj0 ∅ ) (λX9 : set ⇒ ∅ ) ) (setsum ∅ (setsum ∅ (Inj0 (setsum ∅ ∅ ) → (∀X4 : (set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → ((set → set → set → set → set → set ∀X7 : set → (set → set → set → set X3 (λX8 : set ⇒ Inj0 ∅ ) (Inj1 (Inj1 (Inj1 ∅ X1 (λX8 : set → (set → set → set → set ∅ ) (X6 (setsum (setsum ∅ ∅ (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) ∅ (setsum (setsum (setsum ∅ (Inj0 ∅ (Inj0 (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → (set → set → set X1 (λX8 : set → (set → set → set → set Inj1 (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ ∅ ) (Inj1 (Inj0 (X7 (λX8 : (set → set → set ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) ∅ X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum X9 (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) (Inj0 (X4 (X4 (X4 ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj1 X7 ) (Inj1 ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → (set → set → set ∀X7 : (set → set → set X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ (Inj0 ∅ (Inj0 ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMa7U6FxmunecpSsNVdf1ThwNWuWxVjBonK )
∀X0 : ((((set → set → (set → set → set → set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → (set → ((set → set → set → (set → set → set → prop ∀X2 : (((set → set → set → set → set → (((set → set → set → set → ((set → set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → (set → set → set → (set → set → set → ((set → set → (set → set → (set → set → set → set → (set → (set → set → set → set → (set → set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → set (setsum ∅ (X4 (X6 ∅ (λX8 : set → set Inj1 ∅ ) ∈ X7 ∅ → X3 (λX8 : ((set → set → set → set λX9 : set → set → set λX10 : set → set Inj1 ∅ ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (setsum (setsum (setsum ∅ ∅ (X9 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (Inj1 (Inj1 (X9 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj0 (Inj1 (Inj1 (setsum ∅ ∅ ) (setsum ∅ (setsum ∅ ∅ X3 (λX8 : ((set → set → set → set λX9 : set → set → set λX10 : set → set ∅ ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ X8 (Inj0 (setsum (Inj0 ∅ (X9 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X10 ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set λX9 : set → set → set λX10 : set → set X7 ) (λX8 : set → set λX9 : set → set λX10 : set → set λX11 : set ⇒ X9 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ ∅ ) (setsum (Inj1 ∅ X4 (setsum (setsum X7 (Inj1 X4 ∅ ∈ setsum X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (setsum ∅ X4 ∈ X4 → X2 (λX8 : (set → set → set X5 ) (setsum ∅ (Inj1 (setsum ∅ (setsum ∅ ∅ (λX8 : (set → set → set Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ X7 ) (setsum ∅ (setsum (Inj1 (Inj0 ∅ ∅ (Inj0 ∅ ) → (∀X4 : (set → set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : (set → set → set ∅ ) ∅ (λX8 : (set → set → set Inj0 (X8 (λX9 : set ⇒ ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ setsum (setsum (Inj1 ∅ (Inj0 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ∅ X2 (λX8 : (set → set → set ∅ ) (setsum X7 (Inj1 (setsum X7 (setsum ∅ ∅ (λX8 : (set → set → set Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 (Inj1 (setsum ∅ ∅ (X6 X9 ) (Inj0 (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 (setsum ∅ ∅ (X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set setsum ∅ (setsum (X7 ∅ (X10 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 X9 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set ∅ ) (X7 (λX8 : set → set → set ∅ ) ∈ X4 (setsum (X4 (Inj1 ∅ (setsum ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X0 (λX8 : ((set → set → (set → set → set → set setsum (Inj1 (Inj0 (X8 (λX9 : set → set λX10 : set → set ∅ ) ∅ ) (X6 (λX8 : set ⇒ ∅ ) X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X8 (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj1 (Inj0 ∅ ) X0 (λX8 : ((set → set → (set → set → set → set Inj0 (setsum (setsum (Inj1 ∅ (Inj0 ∅ ∅ ) (Inj0 (X6 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (((set → set → set → (set → set → set → set ∀X7 : (set → set → (set → set → set X0 (λX8 : ((set → set → (set → set → set → set ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set X10 (Inj0 (Inj0 (Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKeLJSriySMRaZUpcAFT5rgFYJimV43rX3 )
∀X0 : ((set → ((set → set → set → set → ((set → set → set → set → set → (set → set → set → (set → set → set → set → set → (set → set → set → prop ∀X1 : (((set → set → set → set → set → set → set → (set → set → prop ∀X2 : (set → (set → (set → set → set → set → ((set → set → set → set → (set → set → set → set → (set → (set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum X8 (Inj1 (setsum ∅ ∅ ) X3 (λX8 : set ⇒ setsum (setsum X7 (setsum (Inj1 ∅ (setsum ∅ ∅ X6 ) ∅ ) → (∀X4 : set → set → set ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set X3 (λX8 : set ⇒ Inj0 ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 X6 X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (Inj1 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj0 X5 ∈ X7 → X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set λX11 : set → set X8 ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj1 X8 (Inj1 (setsum ∅ (Inj0 ∅ ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set → (set → set → (set → set → set → set ∀X7 : ((set → set → set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set λX11 : set → set X9 ∅ (λX12 : set ⇒ ∅ ) (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) X3 (λX8 : set ⇒ ∅ ) (X7 (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → ((set → set → set → (set → set → set X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ setsum (Inj0 ∅ X9 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 X6 ∈ X6 → X1 (λX8 : (set → set → set → set → set λX9 : set ⇒ setsum (setsum (Inj1 X9 (Inj1 (X8 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ setsum X6 (setsum (Inj0 X6 (Inj1 (Inj0 ∅ ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set → set λX10 : (set → set → set → set λX11 : set → set X8 ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum X7 (Inj1 (Inj1 ∅ X8 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (X4 ∈ X6 → X3 (λX8 : set ⇒ Inj0 X8 ) X6 X0 (λX8 : set → ((set → set → set → set λX9 : (set → set → set → set → set λX10 : set → set → set λX11 : set → set λX12 : set ⇒ Inj1 (Inj0 X12 ) (setsum (setsum (setsum (X7 ∅ (X5 ∅ X4 (Inj1 (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : set → ((set → set → set → set λX9 : (set → set → set → set → set λX10 : set → set → set λX11 : set → set λX12 : set ⇒ setsum ∅ (X10 (setsum (X10 ∅ ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) (X4 (Inj1 ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (Inj0 X8 (Inj1 (X7 ∅ ∅ (setsum (setsum (setsum ∅ ∅ (X7 ∅ ∅ X9 ) (Inj0 (setsum (Inj1 (Inj0 ∅ ∅ ∈ Inj1 (X5 (λX8 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZtsGvJGBZ1WrDwGxdiYoH3DN5e3b6JQbp )
∀X0 : (set → set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → ((set → set → set → set → (set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → (((set → set → set → set → set → prop ∀X3 : (set → set → (set → set → prop (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) (setsum (X7 X5 (Inj0 (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ X3 (λX8 : set ⇒ Inj0 (setsum X8 (Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (Inj0 (X7 (Inj1 ∅ ) ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → set → set (X4 ∈ Inj1 ∅ → X2 (λX8 : set → set ∅ ) (λX8 : (set → set → set → set X8 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set X2 (λX8 : set → set ∅ ) (λX8 : (set → set → set → set ∅ ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X6 ∈ X7 ∅ → X2 (λX8 : set → set ∅ ) (λX8 : (set → set → set → set Inj0 (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ setsum (X9 (λX13 : set → set λX14 : set ⇒ Inj1 ∅ ) (Inj1 (setsum (X11 ∅ ∅ ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set → set ∀X5 : (set → set → (set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set (Inj0 (setsum (X4 (X4 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj1 (Inj1 (setsum ∅ (setsum ∅ ∅ → X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ setsum ∅ (X9 (λX13 : set → set λX14 : set ⇒ setsum (Inj0 ∅ ∅ ) ) (λX8 : set ⇒ X7 (λX9 : (set → set → set Inj0 (Inj0 (X7 (λX10 : (set → set → set ∅ ) ∅ ∅ ) (setsum X8 (setsum (setsum ∅ ∅ (Inj1 ∅ (X7 (λX9 : (set → set → set Inj1 X8 ) (Inj1 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X0 (λX8 : set ⇒ Inj0 ∅ ) (Inj0 ∅ (Inj1 (Inj0 (Inj1 ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : (set → set → (set → set → set → (set → set → set → set ∀X7 : set → set (setsum (setsum (Inj1 ∅ ∅ ∅ ∈ setsum (X4 (X4 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X7 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (X4 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X7 (Inj0 ∅ ) → X3 (λX8 : set ⇒ setsum (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj0 (setsum (setsum ∅ ∅ (X5 ∅ ) (λX8 : set ⇒ setsum (X5 (X5 (Inj1 ∅ ∅ ) X0 (λX8 : set ⇒ Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ) (Inj1 ∅ (X4 (X7 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj1 (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : (set → set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum (Inj1 X8 (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (setsum ∅ (setsum (Inj0 (X6 ∅ (setsum (setsum ∅ ∅ ∅ X7 X0 (λX8 : set ⇒ Inj0 (X6 (setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ ) (Inj0 (setsum (Inj0 (X6 ∅ (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZomy9Lt9YoWYQXXYxLzgc456PBXda1sMK )
∀X0 : (((set → (set → set → set → set → set → (set → set → set → (set → set → (set → set → prop ∀X1 : (((set → (set → set → set → set → set → set → set → set → set → ((set → set → set → prop ∀X2 : ((set → set → set → set → set → (set → set → set → prop ∀X3 : (set → (set → set → set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set → set → set Inj1 (setsum (setsum (setsum ∅ ∅ (X9 ∅ ∅ ∅ X7 ) (X4 ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : set → set → set → set Inj1 ∅ ) (X4 ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) False ) → (∀X4 : ((set → set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : (set → (set → set → set → set → set → set → set → set X7 (Inj0 (setsum ∅ (Inj0 ∅ ) (λX8 : set → set X5 (Inj1 (Inj0 ∅ ) X2 (λX8 : set → set → set X8 (Inj0 (setsum (Inj1 ∅ ∅ (X5 (Inj1 (Inj1 ∅ ) X6 (λX8 : set ⇒ X7 (setsum (setsum ∅ (X5 ∅ (Inj1 (setsum ∅ ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ ∅ (X5 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 (X5 (setsum (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ X8 (X7 ∅ ) ∈ Inj0 X4 → X2 (λX8 : set → set → set setsum (Inj0 (X7 (Inj1 ∅ (Inj0 ∅ ) ∅ (λX8 : set ⇒ Inj0 (X5 X6 (λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ) (X7 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ X6 X1 (λX8 : (set → (set → set → set → set → set → set → set → set X5 (Inj0 (Inj1 (setsum ∅ ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ) (λX8 : set → set X5 (Inj0 ∅ (λX9 : set → set λX10 : set ⇒ Inj0 (X8 ∅ ) ) ) → (∀X4 : (((set → set → set → set → set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set → set X1 (λX8 : (set → (set → set → set → set → set → set → set → set ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set X1 (λX8 : (set → (set → set → set → set → set → set → set → set Inj0 (Inj0 (X7 (λX9 : (set → set → set Inj1 ∅ ) (setsum ∅ ∅ ) (λX8 : set → set setsum (X8 (Inj1 (setsum ∅ ∅ ∅ ) X1 (λX8 : (set → (set → set → set → set → set → set → set → set ∅ ) (λX8 : set → set Inj1 (X7 (λX9 : (set → set → set Inj1 (setsum ∅ ∅ ) (setsum ∅ ∅ ) ) → (∀X4 : set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set → set Inj1 ∅ ) (Inj0 (X5 (setsum (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) X0 (λX8 : (set → (set → set → set → set setsum (X5 (X5 ∅ (Inj1 (Inj0 X6 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (setsum (Inj1 ∅ (X5 (Inj0 ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : (set → (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X7 ) (λX8 : set ⇒ X6 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGXJKdABmtqT9Hi21LmWeCPBWqxuxNNVBf )
∀X0 : ((set → set → set → (set → set → set → set → set → set → prop ∀X1 : (set → (set → set → ((set → set → set → (set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → prop ∀X3 : (set → set → set → (set → set → ((set → set → set → prop (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (Inj1 (Inj0 ∅ ∈ setsum (Inj1 (setsum (setsum ∅ ∅ X6 (Inj0 ∅ → X3 (λX8 : set ⇒ Inj1 (Inj1 (Inj0 (setsum ∅ ∅ ) (Inj0 (setsum (setsum ∅ X7 X7 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum (Inj0 (setsum ∅ ∅ ∅ ) X3 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ X5 ) (λX8 : set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → ((set → set → set → set ∀X7 : (set → (set → set → set → set → (set → set → set (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (setsum X8 (Inj0 ∅ ) (λX8 : set → set X7 (λX9 : set ⇒ λX10 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) ∈ Inj1 X4 → X3 (λX8 : set ⇒ ∅ ) (setsum X4 (setsum X5 (X7 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (Inj0 ∅ (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set setsum (X8 (setsum (X8 ∅ (setsum ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set Inj0 ∅ ) ) X2 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (X7 (λX9 : set ⇒ λX10 : set → set ∅ ) X5 (λX9 : set ⇒ Inj1 (Inj1 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set setsum (X6 (X8 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 X7 X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj0 (Inj0 ∅ ∅ (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 X7 ) False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set → set (X5 (λX8 : (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) ∈ setsum X4 (setsum ∅ (setsum (X7 ∅ ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set setsum (setsum ∅ (setsum (Inj0 ∅ (X9 ∅ (Inj0 (setsum (X10 (λX12 : set ⇒ ∅ ) (setsum ∅ ∅ ) (setsum (X7 (setsum ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (setsum (Inj0 (setsum ∅ ∅ X5 X0 (λX8 : set → set Inj0 (X8 X5 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → set → (set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (Inj0 ∅ ∈ setsum ∅ X7 → X0 (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj1 (Inj1 (Inj1 ∅ ) (Inj0 (setsum X7 (Inj0 X7 ) → (∀X4 : (set → set → set ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set → set Inj0 X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (setsum X8 (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum X8 ∅ ) (Inj0 ∅ (X6 ∈ X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGnvo5BJciRE7S6gfwxYJ8MBfpeirja9Cq )
∀X0 : (set → set → set → set → (((set → set → set → set → set → set → prop ∀X1 : (((set → set → set → set → ((set → set → set → (set → set → set → (set → set → set → ((set → set → set → set → (set → set → set → set → (set → set → set → prop ∀X2 : (set → set → (((set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → ((set → set → set → set → set → (((set → set → set → set → set → set → set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set → set → set X3 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set X8 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 X10 ) (λX9 : set → set ∅ ) ) (λX8 : (set → set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) (Inj0 (X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (Inj0 (setsum ∅ X4 (X6 (X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ X8 (λX11 : set ⇒ ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set Inj1 (Inj0 (setsum (Inj0 ∅ ∅ ) (λX8 : (set → set → set → set → set → set setsum (setsum ∅ (setsum (Inj0 ∅ X7 (setsum X6 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ (Inj1 (setsum (Inj1 ∅ X6 (setsum (setsum (Inj1 X6 (Inj1 X6 ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ setsum (setsum (Inj1 (Inj0 ∅ X7 ∅ → X2 (λX8 : set ⇒ X5 ) (λX8 : (set → set → set → set Inj1 ∅ ) X3 (λX8 : (((set → set → set → set → set → set → ((set → set → set → set setsum ∅ ∅ ) (λX8 : (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 ) (Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X5 (setsum X6 (Inj1 X4 ) → (∀X4 : ((set → set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → set → set → ((set → set → set → (set → set → set λX9 : set → set setsum (setsum ∅ (Inj1 (Inj1 ∅ ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : (set → set → set → set → ((set → set → set → (set → set → set λX9 : set → set Inj0 (Inj1 (setsum (Inj1 ∅ (X7 ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set setsum (setsum (X8 (X7 ∅ (Inj1 ∅ ∅ (X10 (setsum ∅ (setsum ∅ ∅ ) (setsum (Inj0 X4 (Inj0 (Inj1 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 ) False ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ X8 ) (λX8 : (set → set → set → set Inj1 (Inj1 (X8 (λX9 : set ⇒ λX10 : set ⇒ X9 ) ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj0 X10 ) (λX8 : (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ ∅ ) (Inj1 (Inj0 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum (Inj1 ∅ (X6 (λX10 : set ⇒ λX11 : set → set ∅ ) ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcoJ75GgbBZ6ieyiM2EVvpFctw3sPQ6f8o )
∀X0 : (set → (set → set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → (set → set → set → (set → set → (((set → set → set → set → set → set → prop ∀X2 : ((set → set → (set → set → set → (set → set → set → set → prop ∀X3 : (set → set → (set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (setsum X6 ∅ ∈ setsum (setsum (X4 (X4 ∅ (setsum (setsum ∅ ∅ (X5 ∅ ∅ (X4 X7 → X3 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : set → set setsum ∅ (Inj1 ∅ ) (Inj1 (setsum (setsum X6 ∅ (Inj1 (X5 ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → (set → set → set → ((set → set → set → set X3 (λX8 : set ⇒ X7 (λX9 : set → set → set λX10 : set → set setsum (setsum (Inj1 ∅ (Inj1 ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set ⇒ λX9 : set → set ∅ ) (setsum (setsum ∅ X5 (Inj1 (setsum (Inj0 ∅ (Inj0 ∅ (Inj0 (Inj1 (setsum ∅ (X4 ∅ ∈ Inj0 (setsum X5 (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set , (Inj0 X5 ∈ Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X9 ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set X5 ) (X6 (setsum (setsum ∅ (X6 ∅ ∅ (λX8 : set ⇒ ∅ ) X5 ∅ (λX8 : set ⇒ Inj0 ∅ ) X2 (λX8 : set → set → (set → set → set λX9 : set → set ∅ ) (Inj1 (setsum (Inj0 (Inj0 ∅ (Inj1 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → set → (set → set → set λX9 : set → set setsum (Inj1 (X8 ∅ (X9 ∅ (λX10 : set ⇒ Inj1 ∅ ) (X7 (setsum ∅ (Inj1 ∅ ∅ ) (setsum X4 (X5 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ X7 (setsum ∅ ∅ (Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (Inj1 X8 ) (λX8 : set ⇒ X7 ∅ ) (λX8 : (set → set → set → set ∅ ) (X6 (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 (setsum X6 ∅ ∈ X5 (X7 (Inj0 (Inj1 ∅ (Inj1 (X7 (X5 ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X10 ) (λX8 : set ⇒ X8 ) (λX8 : (set → set → set → set Inj1 ∅ ) (Inj1 (Inj1 (Inj1 (setsum ∅ ∅ X2 (λX8 : set → set → (set → set → set λX9 : set → set ∅ ) (Inj1 (setsum ∅ (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : set → set → set → set → set (X7 (Inj1 ∅ ∅ (Inj0 (setsum (X5 ∅ (λX8 : set ⇒ ∅ ) (Inj0 ∅ (Inj0 (X7 (Inj1 ∅ (X4 ∅ ∅ X6 ∈ Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ (X7 (X7 ∅ ∅ ∅ ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ (X5 (setsum (Inj0 ∅ (X7 ∅ ∅ ∅ ∅ (λX8 : set ⇒ X6 ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (X5 (Inj1 (setsum X6 (Inj0 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYceSHmzyEX1kk31SPyAmJmhfFr6xi9z6p )
∀X0 : (set → set → (set → set → set → ((set → set → set → (set → set → set → prop ∀X1 : ((set → set → set → (set → set → (set → set → set → set → (set → set → prop ∀X2 : (set → set → set → set → (set → set → prop ∀X3 : (set → ((set → set → (set → set → set → set → set → set → set → (set → set → prop (∀X4 : (set → (set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set → set → (set → set → set → set (Inj1 ∅ ∈ Inj0 (Inj0 (setsum X5 (Inj0 ∅ → X2 (λX8 : set ⇒ setsum X5 (X6 (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) (setsum ∅ (setsum ∅ (setsum ∅ (setsum ∅ ∅ ∅ (λX8 : set ⇒ setsum (X7 (Inj0 (setsum ∅ ∅ ∅ (λX9 : set ⇒ X7 X8 (setsum ∅ ∅ (λX10 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ ) (Inj1 (Inj0 ∅ (setsum ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ ∅ ) X5 (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ Inj0 (X9 (λX11 : set ⇒ setsum (Inj0 ∅ X11 ) (λX11 : set ⇒ Inj1 X8 ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (Inj0 (X6 (λX8 : (set → set → set setsum (Inj0 ∅ (Inj1 ∅ ) (Inj1 (Inj0 ∅ (λX8 : set ⇒ ∅ ) (setsum (setsum (setsum ∅ (Inj0 ∅ ∅ (Inj0 (Inj0 ∅ ∈ Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ ∅ ) (setsum (Inj1 (setsum (Inj1 ∅ X6 (Inj1 (setsum (Inj0 ∅ ∅ (setsum X6 ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set X2 (λX8 : set ⇒ setsum ∅ ∅ ) (X4 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) X6 (λX8 : set ⇒ X8 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set X1 (λX8 : set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set X10 ∅ ) (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ setsum X5 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set Inj1 (setsum (Inj1 (X11 ∅ (X8 (setsum ∅ ∅ ) X7 (λX8 : set ⇒ Inj0 X6 ) False ) → (∀X4 : (set → set → set ∀X5 : (set → set → set → set ∀X6 : set → set ∀X7 : set , (X4 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) ∈ setsum ∅ (setsum (Inj0 (Inj0 ∅ ∅ → X0 (λX8 : set ⇒ setsum (Inj1 (Inj0 (X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 (Inj1 ∅ (Inj0 ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ X7 ) (Inj1 (X6 (setsum (X4 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (λX8 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (setsum (X7 (λX9 : set ⇒ setsum ∅ ∅ ) ∅ ) (X7 (λX8 : set ⇒ Inj0 X8 ) X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ setsum (X9 (λX11 : set ⇒ setsum X10 X10 ) (λX11 : set ⇒ X8 ) (Inj0 X10 (X7 (λX11 : set ⇒ X8 ) ) (X4 (λX8 : (set → set → set ∅ ) (λX8 : set ⇒ Inj1 (setsum X6 (Inj1 (Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXvEFMDDF5zHym6MS3DE4fcuPbaATUtdvM )
∀X0 : (set → (set → set → (set → set → set → set → set → prop ∀X1 : ((set → set → (((set → set → set → set → set → ((set → set → set → set → set → ((set → set → (set → set → set → set → (((set → set → set → set → (set → set → set → prop ∀X2 : (set → set → set → set → set → (set → set → prop ∀X3 : (set → (set → set → (set → set → set → set → (set → ((set → set → set → set → (set → set → (set → set → set → (set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X4 ∅ ∈ setsum (Inj1 (setsum (X4 ∅ (Inj1 ∅ X5 → X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (Inj0 ∅ (λX8 : set ⇒ Inj0 (setsum (Inj1 (Inj1 ∅ (Inj1 ∅ ) X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set setsum ∅ (setsum ∅ (X9 X8 ) (λX8 : set ⇒ λX9 : (set → set → set Inj0 (setsum (setsum (setsum ∅ ∅ (X7 ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (setsum ∅ (Inj1 (Inj1 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : (set → (set → set → set → set ∀X6 : (set → set → (set → set → set ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set Inj1 (X9 (λX10 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ) (λX8 : set ⇒ Inj1 (X6 (λX9 : set ⇒ X8 ) (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ X10 ) (λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (Inj0 ∅ ∈ X4 (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ (Inj0 (setsum (Inj0 ∅ ∅ (λX8 : set ⇒ Inj0 (setsum (Inj0 ∅ X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → (set → set → set → set ∀X7 : set → set (setsum (Inj1 X4 (Inj0 ∅ ∈ setsum (Inj0 (Inj0 X5 X5 → X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj0 X9 ) (X6 (λX8 : set → set λX9 : set → set setsum (X7 (setsum ∅ ∅ (X8 (setsum ∅ ∅ ) X4 (λX8 : set ⇒ X5 ) X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set X8 ) (λX8 : set ⇒ λX9 : (set → set → set X8 ) (λX8 : set ⇒ Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum (Inj1 (Inj1 ∅ (Inj1 (Inj1 X5 ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set , (X4 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∈ Inj1 (X6 (setsum X7 X5 (λX8 : set ⇒ λX9 : set ⇒ X7 ) → X3 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (setsum (Inj0 ∅ X7 (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ ∅ ) X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set X7 ) (λX8 : set → set λX9 : set → set → set Inj0 (Inj1 (setsum (X6 ∅ (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (X8 (λX10 : set ⇒ ∅ ) (Inj1 X7 (setsum (Inj1 ∅ (Inj0 (Inj0 ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → (set → set → set → set → ((set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set setsum (Inj0 (Inj1 (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ ∅ X7 ) (λX8 : set → set λX9 : set → set → set ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (X8 (λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ∅ (Inj1 (setsum ∅ X7 ) X1 (λX8 : set → set λX9 : ((set → set → set → set → set λX10 : (set → set → set → set setsum (setsum (X10 (λX11 : set ⇒ ∅ ) (X9 (λX11 : set → set λX12 : set ⇒ ∅ ) ∅ (Inj0 (X8 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set → set → set setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set → set Inj1 ∅ ) ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → set → set ∀X6 : set → set ∀X7 : set → set (X7 ∅ ∈ Inj1 (X5 (λX8 : set ⇒ ∅ ) → X0 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (X7 (X7 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set setsum (Inj0 X7 X8 ) ∅ (Inj1 (setsum (setsum ∅ (X4 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X7 ∈ X6 (setsum (Inj0 (setsum ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMX8H4LDgeXLDxrTanpugJKwqxwGjUvEYhL )
∀X0 : (set → ((set → set → (set → set → set → set → (set → set → prop ∀X1 : (set → set → ((((set → set → set → (set → set → set → set → prop ∀X2 : (set → set → ((((set → set → set → set → set → set → set → (set → set → prop ∀X3 : (set → (set → set → set → (set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : (set → (set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum X8 ∅ ) (λX8 : ((set → set → set → (set → set → set Inj1 (Inj1 ∅ ) X3 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj0 ∅ ) (X6 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ (X6 X7 (X4 (Inj1 ∅ (X6 (Inj0 X7 ∅ ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (X5 (λX8 : set → set λX9 : set ⇒ ∅ ) (X5 (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (setsum (X5 (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) X6 ∈ Inj1 (setsum (Inj0 (Inj0 ∅ (setsum ∅ X6 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → set X1 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → (set → set → set X8 (λX9 : set → set setsum ∅ (Inj0 (X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX9 : set ⇒ setsum (setsum (X8 (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) (X8 (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) (setsum (Inj1 ∅ (Inj1 ∅ ) ) X2 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set Inj0 (X8 (λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (setsum X6 ∅ ) (λX8 : set ⇒ Inj1 (setsum ∅ (Inj1 (Inj0 ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set , (setsum ∅ (setsum X5 ∅ ∈ setsum (setsum ∅ ∅ (Inj1 ∅ → X2 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → set → set → set ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ (Inj0 ∅ ) X2 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : ((set → set → set → set → set → set setsum (X8 (λX9 : set → set λX10 : set ⇒ X9 (X9 ∅ ) X6 ∅ ) (λX8 : set ⇒ X8 ) X1 (λX8 : set ⇒ setsum X7 ∅ ) (λX8 : ((set → set → set → (set → set → set setsum (Inj1 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → (set → set → set Inj0 X7 ) X3 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (setsum (Inj0 X5 (Inj0 X4 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum ∅ ∅ ∈ X4 → X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set X7 ) (λX8 : set ⇒ setsum X8 (setsum (Inj0 ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : (((set → set → set → (set → set → set → ((set → set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set ∅ ) (λX8 : set ⇒ X7 ∅ ) (Inj0 X4 ∈ Inj1 (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWjByXu1FtwSbtYz7iwPJjvvBzHcx9nUtM )
∀X0 : ((set → set → (set → set → set → set → set → set → (set → set → prop ∀X1 : (set → (set → set → set → (set → set → (set → set → set → set → set → ((set → set → (set → set → set → set → set → prop ∀X2 : (set → set → ((set → set → set → (set → set → set → set → set → set → set → prop ∀X3 : ((set → ((set → set → set → set → set → set → (set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ Inj1 (X4 ∅ → X2 (λX8 : set ⇒ X7 ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (Inj0 (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ X3 (λX8 : set → ((set → set → set → set → set Inj0 (X8 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → ((set → set → set → set → set setsum (Inj0 ∅ (X8 X6 (λX9 : set → set λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 X11 ∅ ) False ) → (∀X4 : (set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (setsum (setsum (Inj1 ∅ (Inj0 ∅ ∅ ∈ Inj0 (setsum ∅ (Inj1 ∅ → X2 (λX8 : set ⇒ Inj0 (setsum (Inj1 X6 (Inj0 ∅ ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 (setsum X7 (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → ((set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj1 (setsum (setsum (Inj0 ∅ (Inj1 ∅ (setsum X6 (Inj0 ∅ (Inj0 ∅ ∈ X6 ) → (∀X4 : set → ((set → set → set → set ∀X5 : set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ X10 ) (setsum (Inj0 (Inj1 (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 (setsum X7 (setsum ∅ ∅ X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set → set λX12 : set ⇒ setsum (setsum ∅ (Inj0 (setsum ∅ ∅ (Inj0 ∅ ) (X4 ∅ (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum X10 X10 (Inj1 ∅ ) ∅ ) → (∀X4 : (set → set → set → ((set → set → set → set → set → set → set ∀X5 : set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : (set → set → set → (set → set → set → set (setsum ∅ (setsum (Inj1 (setsum ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∈ setsum (setsum (Inj1 (setsum ∅ ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) → X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set → set λX12 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (X8 (Inj1 (Inj1 ∅ (X7 (λX11 : set ⇒ λX12 : set ⇒ setsum X11 (Inj1 ∅ ) (λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 ∅ ) ) ∅ X2 (λX8 : set ⇒ setsum (setsum (Inj1 (Inj0 ∅ ∅ (setsum ∅ (Inj0 (Inj0 ∅ ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (Inj0 (X8 (Inj1 ∅ (Inj1 ∅ ∅ ) (setsum (X6 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 X9 ) (Inj0 ∅ ) → (∀X4 : (((set → set → set → (set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → (set → set → set → set X0 (λX8 : set → set → (set → set → set → set setsum (setsum ∅ (Inj0 (setsum ∅ ∅ (X5 ∅ ) (setsum ∅ (X6 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum (X5 ∅ (setsum (Inj1 (X7 ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X5 (setsum ∅ ∅ ) X0 (λX8 : set → set → (set → set → set → set Inj0 (Inj1 (Inj1 (setsum ∅ ∅ ) (Inj1 ∅ (λX8 : set ⇒ X8 ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X0 (λX8 : set → set → (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ Inj0 (X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X11 X9 ) ) X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set → set λX11 : set → set λX12 : set ⇒ X9 X12 ∅ ) ∅ (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (X4 (setsum (Inj1 (Inj0 ∅ (X4 (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set ⇒ Inj0 ∅ ) ∅ (Inj0 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum (setsum (Inj1 ∅ X5 (Inj0 (setsum ∅ ∅ ) (Inj0 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPQ16vbqRJK8Wr14L5YMUYRhrTURTyhXe9 )
∀X0 : ((set → set → set → ((set → set → set → set → set → set → prop ∀X1 : ((set → set → set → ((set → set → set → set → (set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → prop ∀X3 : (((((set → set → set → set → (set → set → set → set → (set → set → set → set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X7 ∈ X4 (λX8 : set ⇒ Inj0 (Inj0 X8 ) ∅ → X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj0 ∅ ) ∅ X3 (λX8 : (((set → set → set → set → (set → set → set → set → (set → set → set X7 ) (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : (((set → set → set → set → (set → set → set → set → (set → set → set X5 ) (X7 (setsum ∅ ∅ (setsum ∅ (X6 (Inj1 ∅ (Inj0 ∅ ∈ setsum ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : (set → set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set ∅ ) X6 ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set (Inj1 (Inj1 (Inj0 ∅ ∈ Inj1 (X7 (λX8 : set → set X5 (setsum ∅ ∅ ) (X6 (X6 ∅ ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set X10 (λX11 : set ⇒ ∅ ) ) (Inj0 (X4 (λX8 : (set → set → set → set λX9 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ setsum ∅ (Inj0 ∅ ) (Inj1 (Inj1 (setsum (Inj1 ∅ ∅ ) → (∀X4 : ((set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum (Inj0 ∅ X10 ) ∅ X1 (λX8 : set → set X8 ∅ ) (λX8 : set → set λX9 : set ⇒ X6 ) (λX8 : set ⇒ Inj0 (setsum ∅ (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set → set → (set → set → set ∀X6 : set → (set → set → set ∀X7 : set , (setsum (setsum ∅ (Inj1 (Inj1 ∅ ∅ ∈ Inj1 ∅ → X1 (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ X6 (Inj0 (setsum ∅ (Inj1 ∅ (λX10 : set ⇒ X8 X9 ) ) (λX8 : set ⇒ setsum (Inj1 (Inj1 X7 (setsum (Inj0 (Inj1 ∅ (Inj0 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X3 (λX8 : (((set → set → set → set → (set → set → set → set → (set → set → set Inj0 (Inj0 (setsum (X8 (λX9 : (set → set → set → set λX10 : set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) (Inj1 ∅ ) (setsum (setsum (Inj0 ∅ (Inj1 (X5 ∅ (Inj1 (Inj1 ∅ ∅ X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (Inj1 X10 ) ∅ ) → (∀X4 : (((set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set (X6 ∈ X6 → X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ X10 ) (Inj0 ∅ X0 (λX8 : set → set → set λX9 : (set → set → set λX10 : set ⇒ setsum (X8 X10 (X8 (X9 (λX11 : set ⇒ ∅ ) ∅ X10 ) (X4 (λX8 : (set → set → set λX9 : set → set X7 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHyHGRMf6hnGCuSydW9tP1aWkYDtDJuGYx )
∀X0 : (set → set → set → set → prop ∀X1 : (((set → (set → set → set → set → (set → (set → set → set → set → set → ((set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum (Inj1 (Inj1 (Inj1 ∅ (setsum (setsum (setsum ∅ ∅ ∅ ∅ ∈ setsum X7 X7 → X3 (λX8 : set ⇒ setsum (setsum ∅ ∅ (X5 (λX9 : set → set → set Inj1 ∅ ) (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) X8 X7 ) X6 X7 (Inj1 ∅ (Inj1 (setsum ∅ (setsum (setsum ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → set → set → set → set ∀X6 : set → set ∀X7 : set → set X3 (λX8 : set ⇒ setsum ∅ (X6 (X7 ∅ ) ∅ (setsum (Inj1 ∅ (Inj0 (X7 (Inj1 ∅ (setsum (setsum (Inj0 (Inj1 ∅ (Inj1 (setsum ∅ ∅ (X4 (Inj1 (X7 ∅ (X7 (Inj0 (setsum (X7 ∅ ∅ X0 (λX8 : set ⇒ setsum ∅ (setsum (X5 (setsum ∅ ∅ ∅ ∅ (X5 ∅ ∅ ∅ ∅ ∅ ) (Inj0 (setsum (X7 (setsum ∅ ∅ ∅ (X4 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set → set → (set → set → set → set ∀X7 : set → (set → set → set X0 (λX8 : set ⇒ X8 ) X4 (X5 ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (X6 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (setsum (Inj1 ∅ (Inj0 ∅ (λX10 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ∅ ) (setsum (Inj1 ∅ X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (setsum (setsum ∅ ∅ (Inj1 (Inj0 (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set → set (Inj0 ∅ ∈ Inj0 (setsum (Inj1 X4 (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) X5 → X1 (λX8 : (set → (set → set → set → set λX9 : set → (set → set → set → set ∅ ) (λX8 : set → set → set → set λX9 : (set → set → set → set X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → set → (set → set → set → set → set ∀X7 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set → set X1 (λX8 : (set → (set → set → set → set λX9 : set → (set → set → set → set X7 (λX10 : (set → set → set λX11 : set ⇒ Inj1 (X10 (λX12 : set ⇒ X9 ∅ (λX13 : set ⇒ ∅ ) ∅ ) ) (λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) (Inj1 (Inj1 (Inj0 ∅ ) (λX8 : set → set → set → set λX9 : (set → set → set → set Inj0 (setsum (setsum (Inj0 ∅ ∅ (setsum (setsum ∅ ∅ (X9 (λX10 : set ⇒ ∅ ) ∅ ) (Inj1 X4 ∈ X5 (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 (Inj0 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set → set (setsum ∅ (X7 ∅ ∈ Inj1 (X5 (Inj0 ∅ ∅ → X3 (λX8 : set ⇒ ∅ ) (Inj0 ∅ (setsum X4 (Inj0 ∅ (Inj1 ∅ ∅ X0 (λX8 : set ⇒ ∅ ) (X5 ∅ (Inj1 (Inj0 (Inj1 ∅ (setsum (setsum X6 (X7 (setsum ∅ ∅ ∅ ) → (∀X4 : (set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : (((set → set → set → set → set → (set → set → set ∀X7 : set → set → set → set → set X0 (λX8 : set ⇒ Inj0 (setsum (Inj1 ∅ X8 ) (setsum (setsum (X6 (λX8 : (set → set → set → set ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMU4FJVtKTVkTxfqZTVsmtTMTUZfAXdeAf9 )
∀X0 : (set → ((set → set → set → set → set → prop ∀X1 : (set → set → (set → set → (set → set → set → prop ∀X2 : (set → set → (set → set → prop ∀X3 : ((((set → set → set → set → set → set → ((set → (set → set → set → set → ((set → set → set → (set → set → set → set → prop (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : (set → set → ((set → set → set → set → set X1 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X10 (Inj0 (Inj1 (setsum ∅ ∅ ) X3 (λX8 : ((set → set → set → set λX9 : set ⇒ X8 (λX10 : set → set Inj0 ∅ ) ) (λX8 : set → (set → set → set → set λX9 : (set → set → set λX10 : set → set X9 (λX11 : set ⇒ X11 ) ) (X6 (setsum (setsum ∅ (Inj1 ∅ (X4 (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ X6 ∅ ∅ ) (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : ((set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set λX10 : set → set X9 (λX11 : set ⇒ setsum (setsum ∅ (X8 ∅ (λX12 : set ⇒ ∅ ) ∅ (Inj1 (X9 (λX12 : set ⇒ ∅ ) ) ) (setsum (Inj0 (X6 ∅ X4 (Inj1 X4 ∈ Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ setsum (X5 ∅ X6 ) (λX8 : set ⇒ Inj0 ∅ ) X1 (λX8 : set ⇒ setsum X6 (setsum (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (setsum X8 ∅ (setsum (X10 X9 (Inj0 ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X8 ) False ) → (∀X4 : (set → set → set → set → set ∀X5 : set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → set ∅ ) (Inj0 (Inj0 X6 ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → set Inj1 (X9 (λX10 : set ⇒ setsum X8 (Inj1 ∅ ) ) (X6 (X6 X5 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMLZjfk5hKFBHYDA3qqPMbb8hkELYFjGNBP )
∀X0 : ((((set → set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → set → (set → set → set → (set → set → prop ∀X2 : (((set → set → set → set → set → set → (set → ((set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → ((set → set → set → (set → set → set → set → set → set → (set → set → prop (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → (set → set → set → set (Inj0 ∅ ∈ Inj1 X5 → X3 (λX8 : (set → (set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (X9 ∅ ∅ ) (λX8 : set ⇒ Inj1 (setsum (X7 (Inj0 ∅ (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) X5 X8 ) X3 (λX8 : (set → (set → set → set → set → set setsum X5 (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (setsum (X8 (setsum ∅ ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ setsum X8 (setsum (X7 X5 (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (setsum (X6 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set setsum ∅ (X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 X9 ) ) (λX8 : set → set → set λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum X10 ∅ ∅ ) (λX8 : set ⇒ Inj0 X7 ) X0 (λX8 : ((set → set → set → set → set ∅ ) (λX8 : set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ X6 ∈ Inj1 (Inj0 (setsum (Inj0 ∅ X4 → X2 (λX8 : (set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : (set → set → set Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set Inj1 (Inj1 (setsum ∅ (Inj1 ∅ ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set (X7 (setsum (setsum (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ (setsum (setsum (Inj1 ∅ ∅ X6 (λX8 : set ⇒ Inj1 (setsum ∅ (Inj0 ∅ ) ∈ Inj0 (X7 (setsum (Inj0 ∅ (Inj1 ∅ (setsum ∅ (X7 ∅ ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 X9 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set (X6 ∅ ∈ Inj0 (setsum (X4 ∅ (setsum X5 (X7 (λX8 : set ⇒ ∅ ) → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (Inj0 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ setsum X8 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X10 ) (λX8 : set ⇒ Inj0 (setsum (X7 (λX9 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 ∈ setsum (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 ∅ (setsum (Inj1 (X6 ∅ (X4 (Inj0 ∅ X0 (λX8 : ((set → set → set → set → set Inj0 X7 ) (λX8 : set → set → set setsum X7 (Inj0 X7 ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set → set X0 (λX8 : ((set → set → set → set → set setsum (Inj1 (X8 (λX9 : set → set → set ∅ ) X6 ) (λX8 : set → set → set ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJLg9Y7BegzMWCuLtPsYJaZHfVcng1SoSi )
∀X0 : ((set → (set → set → set → set → set → set → ((set → set → set → set → set → ((set → set → set → (set → set → (set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → (set → set → set → set → set → ((set → set → set → set → set → (((set → set → set → set → set → set → prop ∀X2 : (set → (((set → set → set → set → set → set → ((((set → set → set → (set → set → set → set → set → prop ∀X3 : (((set → set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → ((set → set → set → set ∀X7 : set , (X6 (λX8 : (set → set → set setsum (Inj0 (X8 (λX9 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) (λX8 : set → set ∅ ) ∈ Inj1 ∅ → X3 (λX8 : (set → set → set → set → set ∅ ) X7 ) → (∀X4 : ((set → set → set → set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set (Inj1 ∅ ∈ setsum ∅ ∅ → X3 (λX8 : (set → set → set → set → set setsum (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ X6 ) ∅ X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set ∅ ) (Inj1 (X7 ∅ ∅ (λX8 : (set → set → set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : ((set → set → set → set → set X7 ∅ ) (λX8 : ((set → set → set → (set → set → set → set setsum (setsum ∅ ∅ (setsum (X8 (λX9 : set → set ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) X6 (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : ((set → set → set → set → set X8 ) (λX8 : ((set → set → set → (set → set → set → set X8 (λX9 : set → set Inj0 (Inj0 (Inj0 ∅ ) (λX9 : set ⇒ X9 ) X6 ) False ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 (Inj1 (X4 ∅ ∅ ∈ X7 → X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set Inj0 (setsum (Inj0 (setsum ∅ ∅ (X10 (λX11 : set ⇒ setsum ∅ ∅ ) ) ∅ (λX8 : (set → set → set → set setsum (X8 (λX9 : set ⇒ ∅ ) X5 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) X6 ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set → (set → set → set ∀X7 : set , (setsum (Inj0 (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ X7 ) ∅ ∈ Inj1 X5 → X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set X7 ) (Inj1 (Inj0 (Inj1 (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ ) X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : (set → set → set ∅ ) (Inj0 (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : (set → set → set → set Inj0 (setsum ∅ ∅ ) (setsum (Inj1 (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : (set → set → ((set → set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : ((set → set → set → set → set X0 (λX8 : set → (set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set setsum (Inj0 (setsum ∅ (Inj0 ∅ (Inj1 X9 ) (λX8 : set → set → set λX9 : set → set λX10 : set → set X10 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → (set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set X10 (λX11 : set ⇒ ∅ ) ∅ ) (λX8 : set → set → set λX9 : set → set λX10 : set → set X10 (setsum (X8 (Inj0 ∅ (Inj1 ∅ (setsum (Inj0 ∅ (X10 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcjVhZHntQSiQLLmcWFkXZsntm4WWUtbkV )
∀X0 : (set → set → set → (set → set → set → set → prop ∀X1 : (((set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : ((set → set → set → set → set → ((set → set → (set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X3 (λX8 : set → set → set λX9 : set ⇒ X8 (setsum (X8 X9 ∅ (setsum X6 (X8 ∅ ∅ X6 ) (λX8 : set → set λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) X6 (Inj1 (Inj0 (setsum ∅ ∅ (Inj1 (X7 (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set → set (setsum ∅ (setsum ∅ (setsum X4 X5 ∈ X5 → X3 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X9 (X9 (Inj0 ∅ (Inj0 (X10 ∅ (setsum (X10 (X9 ∅ ∅ ∅ ) (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj0 (X7 (λX11 : set ⇒ λX12 : set → set λX13 : set ⇒ ∅ ) ∅ ∅ ) ∅ (Inj1 (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) X6 X4 X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X9 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X8 ) X4 X2 (λX8 : set ⇒ ∅ ) X6 ) → (∀X4 : set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → (set → set → set → set → set X2 (λX8 : set ⇒ ∅ ) ∅ False ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set X6 (X8 (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) (Inj1 ∅ (setsum ∅ (X8 (λX9 : set ⇒ setsum ∅ ∅ ) ) ∅ (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → (set → set → (set → set → set ∀X7 : set , X1 (λX8 : (set → set → set X8 (λX9 : set ⇒ Inj1 (setsum ∅ (setsum ∅ ∅ ) ) ∅ (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (Inj0 ∅ X10 ) X3 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X11 ) X5 X5 (Inj1 (setsum (setsum (Inj0 ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → ((set → set → set → set → set ∀X6 : set → set ∀X7 ∈ Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 X8 ) (Inj1 (X6 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → ((set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (Inj1 ∅ X1 (λX8 : (set → set → set Inj1 (setsum ∅ (Inj1 (Inj1 ∅ ) (setsum (Inj0 (Inj1 (setsum ∅ ∅ (X6 (Inj0 (setsum ∅ ∅ (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMaQFrxCoGzxe1t4LH1VG7r6t3PsSLoFZz4 )
∀X0 : (set → (((set → set → set → set → set → (set → set → set → set → set → (set → ((set → set → set → set → set → prop ∀X1 : ((set → set → set → (((set → set → set → set → set → set → (set → set → set → set → ((set → (set → set → set → set → (set → set → prop ∀X2 : ((((set → set → (set → set → set → set → set → set → set → ((((set → set → set → set → (set → set → set → set → set → prop ∀X3 : (set → (set → set → ((set → set → set → set → (set → set → set → set → set → (set → set → set → prop (∀X4 : set → set → set ∀X5 : (set → set → set → set ∀X6 : set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ setsum (Inj0 (Inj1 (setsum ∅ ∅ (setsum (setsum (Inj0 ∅ ∅ (Inj1 (X11 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 X6 ∅ ) (setsum ∅ (Inj1 X6 ∈ Inj0 X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ setsum (Inj1 (Inj1 (Inj0 ∅ X4 → X2 (λX8 : ((set → set → (set → set → set → set → set → set X5 ) (λX8 : ((set → set → set → set → (set → set → set → set Inj1 X5 ) X2 (λX8 : ((set → set → (set → set → set → set → set → set Inj0 (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → (set → set → set → set → set → set setsum X7 (setsum ∅ (Inj1 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ X8 (λX11 : set → set λX12 : set ⇒ setsum ∅ (X11 ∅ ) (λX11 : set ⇒ setsum (X9 ∅ (Inj1 ∅ ) ∅ ) (λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ X9 ) (Inj0 (Inj0 ∅ ) False ) → (∀X4 : set → set ∀X5 : ((set → set → (set → set → set → set ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ Inj1 (setsum (X10 (λX13 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj1 (Inj1 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) X1 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (X11 (setsum ∅ ∅ ∅ ) (λX8 : set → (set → set → set setsum X7 (X8 (X8 (setsum ∅ ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ X7 ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → set → set λX9 : ((set → set → set → set → set λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ ∅ ) (λX8 : set → (set → set → set ∅ ) (λX8 : set ⇒ X7 ) False ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set , (X4 ∅ ∈ Inj1 X7 → X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set → set → set λX11 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set → set → set λX11 : set ⇒ setsum ∅ (setsum (setsum (X10 ∅ ∅ X11 (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTEX1bQJmDHZVjWy2PU6yDYG8w9CsnNxDw )
∀X0 : (((((set → set → set → set → set → ((set → set → set → set → set → (set → set → set → set → set → (set → (set → set → (set → set → set → set → set → ((set → set → set → set → set → set → prop ∀X1 : (set → (set → set → set → (set → set → prop ∀X2 : (set → set → set → (set → ((set → set → set → set → (set → set → set → prop ∀X3 : (set → set → (set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ X7 ∈ Inj0 (setsum (setsum (Inj1 ∅ ∅ (Inj1 (Inj1 ∅ → X3 (λX8 : set ⇒ setsum X8 ∅ ) (λX8 : set ⇒ X7 ) ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : set → set (X4 ∈ setsum (Inj0 (X7 X6 (setsum ∅ ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X7 X6 ) (setsum ∅ (setsum ∅ (X7 (Inj0 ∅ X1 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ setsum (X5 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX9 : set ⇒ X7 X9 ) (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set (Inj1 (Inj1 (X7 (λX8 : set → set → set Inj1 ∅ ) ∈ Inj0 (setsum ∅ ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (Inj0 (X5 (λX9 : (set → set → set ∅ ) (setsum ∅ ∅ ) (setsum (Inj0 X6 (setsum X4 (Inj0 X4 X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set X10 ∅ ) ) → (∀X4 : ((set → set → set → set → set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum X8 (Inj0 ∅ (Inj1 X9 ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set setsum (Inj0 (X9 (λX11 : set ⇒ ∅ ) (X10 ∅ (setsum X8 (Inj1 ∅ ) False ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set (setsum ∅ (setsum (X7 X5 X5 ∈ Inj0 (setsum (X4 (λX8 : set ⇒ X8 ) ∅ (setsum (setsum ∅ ∅ X5 → X1 (λX8 : set ⇒ λX9 : set → set X9 (X9 X8 ) (λX8 : set ⇒ X6 (Inj1 X8 ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X1 (λX8 : set ⇒ λX9 : set → set setsum X8 ∅ ) (λX8 : set ⇒ Inj0 X8 ) X1 (λX8 : set ⇒ λX9 : set → set setsum X8 (setsum X6 (X7 (λX10 : set ⇒ Inj0 ∅ ) ) (λX8 : set ⇒ Inj0 (setsum (Inj1 X5 (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (Inj0 X7 ∈ Inj1 X4 → X0 (λX8 : (((set → set → set → set → set → ((set → set → set → set → set λX9 : set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ setsum X7 (Inj0 (setsum (Inj0 ∅ X7 ) (setsum (Inj0 ∅ (Inj0 X7 (setsum (X6 X4 (setsum (setsum ∅ ∅ X5 (setsum ∅ (Inj0 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : (((set → set → set → set → set → ((set → set → set → set → set λX9 : set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (setsum ∅ (X9 (Inj1 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum X4 (Inj0 (setsum ∅ (Inj1 ∅ (Inj1 (Inj1 (setsum ∅ (Inj1 ∅ X1 (λX8 : set ⇒ λX9 : set → set Inj0 (Inj0 (setsum (setsum ∅ ∅ X8 ) (λX8 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRj8Me9ReibpM6xCHMYhnfzA5L4uUkv9GD )
∀X0 : ((set → set → ((set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → ((((set → set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → (set → set → ((set → set → set → (set → set → prop ∀X3 : ((set → set → set → set → prop (∀X4 : set → set → set → set → set ∀X5 : set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set ∅ ) (setsum (Inj0 (Inj1 (Inj0 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X3 (λX8 : set → set X8 (X8 (Inj1 (Inj0 ∅ ) X4 False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → (set → set → set → (set → set → set ∀X7 : set , (Inj1 (Inj0 (Inj1 (setsum ∅ ∅ ∈ setsum (Inj0 (Inj1 (X4 ∅ (setsum (X6 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ ∅ ) ∅ → X1 (λX8 : set ⇒ X7 ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : set ⇒ Inj0 (X8 (λX10 : set → set λX11 : set ⇒ setsum (setsum ∅ ∅ X11 ) (λX10 : set ⇒ X8 (λX11 : set → set λX12 : set ⇒ X10 ) (λX11 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ) X7 ) X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 X5 ) (λX8 : set ⇒ setsum (Inj1 (X6 (λX9 : set ⇒ X8 ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) X7 ) (λX8 : set → set X8 (Inj1 (Inj1 (X8 ∅ ) (λX8 : set ⇒ Inj1 (setsum (Inj0 ∅ (setsum ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (X5 (setsum ∅ (Inj1 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ setsum ∅ X8 ) ) (λX8 : set ⇒ Inj0 X6 ) (λX8 : set → set ∅ ) (λX8 : set ⇒ Inj1 (setsum (Inj0 (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) X3 (λX8 : set → set setsum ∅ (setsum (setsum ∅ (Inj0 ∅ (X7 (λX9 : set ⇒ setsum ∅ ∅ ) ∅ ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set (setsum (Inj0 (X7 (Inj0 ∅ ∅ ∈ X4 → X3 (λX8 : set → set setsum (Inj0 (X7 (setsum ∅ ∅ ∅ ) X4 X1 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : set ⇒ Inj0 (setsum ∅ (Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : (((set → set → set → set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum (setsum (X5 (λX9 : (set → set → set → set Inj1 ∅ ) (setsum ∅ (Inj1 ∅ ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : set ⇒ Inj0 ∅ ) X3 (λX8 : set → set setsum (X6 (λX9 : (set → set → set → set setsum (setsum ∅ ∅ (X9 (λX10 : set ⇒ ∅ ) ∅ ) ∅ (λX9 : set ⇒ ∅ ) (Inj1 (Inj0 ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ ∅ ) (λX8 : set → set X8 ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (Inj0 (Inj0 ∅ (setsum X5 (Inj0 ∅ ) X0 (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ ∅ ) (λX8 : set → set X8 ∅ ) (setsum ∅ (setsum X4 (setsum X4 (setsum ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set → set λX9 : (set → set → set λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set → set X6 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X8 (Inj1 (setsum ∅ ∅ ) ∅ ) (setsum ∅ (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ X5 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMF8aSSwxaVFj72yJuASPADtEtFE3qQbwcP )
∀X0 : (set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → (set → set → set → set → (set → set → prop ∀X2 : (set → set → (set → set → set → set → (set → set → (set → set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set ⇒ Inj0 ∅ ) (setsum X7 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set ⇒ X10 ) (setsum (setsum (setsum (setsum ∅ ∅ X7 (setsum (setsum ∅ ∅ (setsum ∅ ∅ X6 (setsum (Inj1 (setsum X4 X6 ∅ ∈ X4 ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X9 ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set (setsum (setsum ∅ X5 X5 ∈ Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : set ⇒ Inj0 (setsum (Inj1 (setsum ∅ ∅ (Inj1 ∅ ) (Inj1 (setsum (setsum X4 (Inj0 ∅ (Inj1 (Inj0 ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 ) (Inj1 X4 (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set → set → set ∀X6 : (set → (set → set → set → set → set → (set → set → set ∀X7 : set → set (Inj1 (setsum (X7 (Inj1 ∅ (Inj0 (setsum ∅ ∅ ∈ setsum (Inj0 ∅ (Inj1 (Inj1 (Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ X7 ∅ ) (setsum (Inj1 ∅ (X7 (X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ X7 ∅ ) (λX8 : set ⇒ Inj0 (setsum ∅ (X5 (setsum ∅ ∅ (Inj0 ∅ (Inj1 ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X8 (setsum X9 (Inj1 ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) ∅ (Inj1 (X7 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set X9 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (X10 (Inj0 ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 (Inj0 (X7 (setsum ∅ ∅ (X7 ∅ ) → (∀X4 : ((set → set → set → (set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X4 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X9 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (Inj0 ∅ ∅ ) (setsum X5 (setsum ∅ (setsum (setsum ∅ ∅ (X6 ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQwAyf7tgenWdnx62yCm2GxbP8gSvRZo1M )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → set → ((set → (set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → ((set → set → set → set → set → (set → set → set → prop ∀X3 : (((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : (set → set → set ∀X6 : (set → set → set → set → set ∀X7 : (((set → set → set → set → set (setsum (X4 ∅ (setsum ∅ ∅ ∈ Inj1 (X4 (X5 (λX8 : set ⇒ ∅ ) → X3 (λX8 : (set → set → set Inj1 (X7 (λX9 : (set → set → set Inj1 (Inj1 ∅ ) ) (X6 (λX8 : set ⇒ λX9 : set ⇒ setsum X9 (Inj1 ∅ ) (X5 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → set ∅ ) ∅ X3 (λX8 : (set → set → set X6 (λX9 : (set → set → set ∅ ) ) (Inj1 (Inj0 (Inj0 ∅ ) → (∀X4 : set → (set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set → set (Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ∈ X4 ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ Inj1 (Inj0 (X5 ∅ ) (setsum (Inj1 (X5 ∅ (setsum (X5 ∅ ∅ → X2 (λX8 : (((set → set → set → set → set → ((set → set → set → set setsum ∅ (X8 (λX9 : (set → set → set λX10 : set ⇒ X10 ) (λX9 : set → set X9 (X7 ∅ ∅ ) ) (λX8 : set ⇒ setsum X8 X6 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → ((set → set → set → set Inj1 ∅ ) (λX8 : set ⇒ X7 ) (setsum (setsum ∅ ∅ X6 False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set → (set → set → set → set ∅ ) X1 (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj0 X8 ) (λX8 : set → (set → set → set → set X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → (set → set → set → set ∀X7 : (set → (set → set → set → set → set X1 (λX8 : set ⇒ X6 (Inj0 (setsum (Inj0 ∅ ∅ (λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum ∅ (Inj1 ∅ ) ) (λX8 : set → (set → set → set → set X8 (Inj0 (X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ X6 (Inj0 ∅ (λX10 : set ⇒ λX11 : set ⇒ Inj1 (X8 ∅ (λX12 : set ⇒ ∅ ) ∅ ) ) (Inj0 (setsum ∅ (Inj0 ∅ ) X3 (λX8 : (set → set → set X6 ∅ (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ) (Inj0 (Inj1 (Inj0 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X6 ∈ X5 → X2 (λX8 : (((set → set → set → set → set → ((set → set → set → set X8 (λX9 : (set → set → set λX10 : set ⇒ X9 (λX11 : set ⇒ setsum (setsum ∅ ∅ (X8 (λX12 : (set → set → set λX13 : set ⇒ ∅ ) (λX12 : set → set ∅ ) ) ) (λX9 : set → set setsum (setsum (setsum ∅ ∅ ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) (λX8 : set ⇒ Inj0 X5 ) (Inj1 (setsum ∅ (X4 X5 X0 (λX8 : set ⇒ X6 ) ∅ X6 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ ∅ ) ∅ X4 (setsum X6 ∅ X3 (λX8 : (set → set → set Inj0 ∅ ) (setsum X6 (setsum ∅ (Inj1 (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdG9KuVXpBXYFxpja8aPNor3gYAvqYJpgk )
∀X0 : (set → set → ((((set → set → set → set → set → set → prop ∀X1 : (set → set → (set → ((set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : ((set → set → (set → set → set → (((set → set → set → set → set → (set → set → set → set → ((set → set → set → set → set → prop (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set X3 (λX8 : set → set λX9 : set → set X8 (setsum (X6 ∅ (X8 (setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 (λX12 : set ⇒ λX13 : set ⇒ setsum (Inj0 ∅ (setsum ∅ (setsum ∅ ∅ ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum ∅ (setsum (Inj0 ∅ (X7 (λX11 : set ⇒ ∅ ) ) ) → (∀X4 : (set → set → set → set → set ∀X5 : (set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set → set Inj1 (setsum ∅ ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj0 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ ∅ ) (X7 ∈ Inj1 (setsum ∅ (setsum X7 (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : (set → set → set → set ∀X7 : (set → (set → set → set → set X3 (λX8 : set → set λX9 : set → set Inj1 (X6 (λX10 : set ⇒ λX11 : set ⇒ setsum X10 X11 ) ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (Inj0 (X8 (λX12 : set ⇒ λX13 : set ⇒ X13 ) X11 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) X2 (λX8 : set ⇒ Inj1 ∅ ) (Inj0 (setsum (setsum (Inj0 ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) (Inj0 X6 X0 (λX8 : set ⇒ Inj1 (Inj1 X5 ) (λX8 : ((set → set → set → set → set X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set → set → set (setsum (Inj1 (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ ∈ setsum ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ X6 (Inj1 (X5 (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX9 : set → set X8 ) ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : ((set → set → (set → set → set → set ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum X8 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) X0 (λX8 : set ⇒ X7 ) (λX8 : ((set → set → set → set → set ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ setsum (setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set → set ∅ ) (Inj1 (setsum X5 ∅ ∈ Inj0 (Inj1 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMM1A8SBcfLYtdUYck9CmRi9HULJxpqtyzo )
∀X0 : (set → set → set → prop ∀X1 : ((set → ((set → set → set → set → (set → set → set → set → ((((set → set → set → set → set → set → prop ∀X2 : (((set → set → set → set → set → (((set → set → set → set → set → set → (set → ((set → set → set → (set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → (set → set → set → set → set → set → set → ((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → (set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 X7 ∈ setsum X6 (setsum ∅ (setsum (Inj1 ∅ (Inj0 ∅ → X3 (λX8 : (set → (set → set → set → set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set X3 (λX8 : (set → (set → set → set → set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ X11 ) (Inj0 (X5 (X7 (λX8 : (set → set → set → set ∅ ) X2 (λX8 : (set → set → set → set → set λX9 : ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : (set → (set → set → set → set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ Inj1 ∅ ) ∅ X2 (λX8 : (set → set → set → set → set λX9 : ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → (set → set → set → (set → set → set → set X2 (λX8 : (set → set → set → set → set λX9 : ((set → set → set → set → set Inj0 (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj1 (Inj1 (Inj1 ∅ (Inj1 (Inj0 (Inj0 ∅ ) X0 (λX8 : set ⇒ ∅ ) (Inj1 (X7 (X4 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ X10 ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set → ((set → set → set → set → (set → set → set ∅ ) (λX8 : ((set → set → set → set X8 (λX9 : set → set Inj0 (setsum ∅ (Inj1 ∅ ) ) X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set → ((set → set → set → set → (set → set → set Inj1 (X8 (X8 (Inj1 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X7 ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X8 (X7 ∅ (λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ ∅ ) ) ) (λX8 : ((set → set → set → set ∅ ) (X7 ∅ False ) → (∀X4 : set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set → set (Inj0 (setsum (setsum ∅ ∅ X5 ∈ X7 ∅ → X0 (λX8 : set ⇒ ∅ ) (X6 (λX8 : (set → set → set Inj1 (X6 (λX9 : (set → set → set ∅ ) (setsum ∅ ∅ (Inj1 ∅ ) (X7 (Inj0 ∅ ∅ ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) X6 (setsum (X4 (λX8 : set ⇒ X6 ) (X5 (X5 ∅ ∈ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYZf8TLwyAHYRUmBWio1RPU2WA3ywGTJrn )
∀X0 : (((set → set → set → set → set → set → (set → set → set → set → prop ∀X1 : (((set → set → set → set → ((set → set → set → set → set → set → set → set → (set → set → ((set → set → set → set → (set → set → set → prop ∀X2 : (((set → set → set → set → set → set → (set → set → set → ((set → set → set → set → set → (((set → set → set → set → set → prop ∀X3 : (set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : ((set → set → (set → set → set → set → ((set → set → set → set ∀X7 : set → set → (set → set → set (Inj0 (Inj0 ∅ ∈ Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set → set → set → set Inj0 (X6 (λX10 : set → set λX11 : set → set λX12 : set ⇒ ∅ ) (λX10 : set → set X7 (Inj0 ∅ ∅ (λX11 : set ⇒ setsum ∅ ∅ ) ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set → set ∅ ) ∅ False ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set (Inj0 (setsum (Inj1 (Inj1 ∅ X4 ∈ setsum (Inj0 ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set → set → set → set setsum X6 (setsum (setsum ∅ ∅ (X7 (λX10 : set ⇒ Inj0 ∅ ) ) X4 X2 (λX8 : (set → set → set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set → set → set ∅ ) (λX8 : (set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (set → set → set → (set → set → set → set X2 (λX8 : (set → set → set → set → set → set λX9 : set → set Inj1 (setsum (X7 (λX10 : set ⇒ X9 ∅ ) (X8 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) (λX8 : set → set → set → set X7 (λX9 : set ⇒ X9 ) (Inj1 (Inj1 (Inj0 ∅ (λX9 : set ⇒ ∅ ) (Inj0 (X7 (λX9 : set ⇒ X7 (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ ) (X7 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ X9 ) ∅ ) (λX8 : (set → set → set λX9 : set ⇒ Inj0 (Inj1 (setsum (Inj0 ∅ ∅ ) (Inj1 (X7 (λX8 : set ⇒ X5 (λX9 : set ⇒ X8 ) ) (setsum ∅ X6 (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) (setsum (setsum ∅ ∅ X6 ∈ X7 (λX8 : set ⇒ setsum (X5 (λX9 : set ⇒ setsum ∅ ∅ ) ∅ ) (Inj0 X6 (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (λX9 : set ⇒ setsum ∅ ∅ ) X8 ∅ ) (setsum (X7 (λX8 : set ⇒ X6 ) (Inj0 ∅ (λX8 : set ⇒ Inj0 ∅ ) ∅ (setsum X4 ∅ ) → (∀X4 : (set → (set → set → set → set → (set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 (setsum (setsum ∅ ∅ (Inj0 ∅ ∈ Inj0 (X4 (λX8 : set ⇒ λX9 : set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) (setsum (Inj0 ∅ ∅ (λX8 : set ⇒ Inj0 ∅ ) → X1 (λX8 : (set → set → set → set λX9 : (set → set → set → set → set λX10 : set ⇒ X10 ) (Inj0 (Inj0 (Inj0 (Inj1 ∅ (λX8 : set ⇒ setsum (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (X5 X8 (λX9 : set → set λX10 : set ⇒ X8 ) X7 ) (setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set → set X7 ) (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set → set ∀X7 : set → (set → set → set X1 (λX8 : (set → set → set → set λX9 : (set → set → set → set → set λX10 : set ⇒ ∅ ) (setsum (setsum (X5 (Inj1 ∅ (setsum ∅ ∅ ∅ (X7 ∅ (λX8 : set ⇒ X6 (X7 ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ setsum (X6 ∅ (setsum ∅ (Inj0 X8 ) (λX8 : set → set λX9 : set ⇒ setsum (X7 (setsum (setsum ∅ ∅ (X7 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ Inj1 (setsum ∅ ∅ ) (setsum ∅ (X6 (X8 ∅ ) (λX8 : set ⇒ setsum (setsum (X5 (Inj1 ∅ ∅ (setsum ∅ (Inj0 ∅ (X6 (Inj0 (Inj1 ∅ ) (setsum X4 X4 (Inj1 (Inj1 (Inj1 (Inj0 ∅ ∈ setsum (Inj0 (Inj1 (Inj1 ∅ (X7 (X7 (setsum ∅ ∅ (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set setsum (Inj0 (setsum (Inj0 ∅ X7 ∅ ) (Inj1 X6 (setsum ∅ X7 (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum X6 (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ ) (setsum (setsum (Inj1 (setsum ∅ ∅ ∅ (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : ((set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set (Inj0 ∅ ∈ setsum ∅ (setsum ∅ ∅ → X0 (λX8 : (set → set → set setsum (Inj1 (Inj1 (setsum ∅ ∅ X6 ) (setsum (Inj0 (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (setsum (Inj0 (setsum ∅ ∅ ∅ (setsum ∅ (setsum (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X8 ∅ ) (Inj1 ∅ (λX8 : set ⇒ Inj0 (Inj0 X8 ) (Inj1 (Inj0 (X7 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ (setsum (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ X3 (λX8 : set ⇒ λX9 : set → set → set → set setsum X6 X6 ) (Inj0 (Inj1 (setsum ∅ (X5 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHfGju8LMrtVjZ3Ryb8Pi11Pe4JQdgizME )
∀X0 : (set → set → set → set → ((set → set → set → prop ∀X1 : (set → set → set → set → ((set → set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → (set → set → set → set → set → set → set → ((set → set → set → set → prop ∀X3 : (set → (((set → set → set → set → set → set → set → ((set → set → set → (set → set → set → (set → set → prop (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set Inj0 (Inj0 ∅ ) (λX8 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (setsum X7 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set ∅ ) (λX8 : set → set setsum (Inj0 (Inj1 (setsum ∅ ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum X6 X8 ) (λX8 : set ⇒ Inj0 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ X8 ) False ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → ((set → set → set → set → set (Inj1 ∅ ∈ setsum (X4 X5 (λX8 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ → X1 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) (setsum (setsum ∅ (setsum (setsum ∅ ∅ ∅ ∅ (Inj1 (Inj0 (setsum (Inj1 ∅ X6 (λX8 : set → set λX9 : set ⇒ ∅ ) X2 (λX8 : (set → (set → set → set → set → set → (set → set → set → set λX9 : set ⇒ X7 (λX10 : set → set → set Inj1 (Inj1 (Inj1 ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) ) (X4 X6 (λX8 : set → set X7 (λX9 : set → set → set ∅ ) (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ) (λX8 : set → set ∅ ) (setsum (setsum ∅ (Inj1 (setsum ∅ ∅ (X7 (λX8 : set → set → set Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X8 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X2 (λX8 : (set → (set → set → set → set → set → (set → set → set → set λX9 : set ⇒ setsum X9 (setsum (setsum (Inj0 ∅ ∅ ∅ ) (X7 (setsum (Inj0 (Inj0 ∅ (Inj0 ∅ (λX8 : set → set setsum (Inj0 (setsum (setsum ∅ ∅ ∅ (setsum ∅ (Inj1 (Inj0 ∅ ) (Inj0 (Inj0 (X7 ∅ X1 (λX8 : set ⇒ ∅ ) (setsum (X7 (Inj1 (setsum ∅ ∅ X4 (setsum (setsum (setsum (Inj1 ∅ (Inj0 ∅ (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ (X6 (setsum (X8 ∅ (Inj1 ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → (set → set → set → set X1 (λX8 : set ⇒ Inj1 (Inj0 (Inj1 (Inj0 ∅ ) (setsum (Inj0 ∅ (X7 (λX8 : (set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ X9 ∅ ) ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj0 X8 ) (Inj1 ∅ (setsum (setsum ∅ (Inj0 (Inj1 ∅ (setsum (Inj1 (Inj0 ∅ (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ X6 ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → ((set → set → set → set ∀X6 : set → ((set → set → set → (set → set → set ∀X7 : set , (Inj0 (Inj1 (Inj1 (Inj1 ∅ ∈ Inj0 (X4 ∅ → X1 (λX8 : set ⇒ ∅ ) ∅ (Inj1 (setsum (X6 (setsum ∅ ∅ (λX8 : set → set X5 (λX9 : set → set → set ∅ ) (λX9 : set → set ∅ ) ) (λX8 : set ⇒ Inj0 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ ∅ ) (setsum (X6 ∅ (λX8 : set → set X7 ) (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : (set → set → set → ((set → set → set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set (setsum ∅ (setsum ∅ (setsum (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∈ Inj1 (setsum ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ → X2 (λX8 : (set → (set → set → set → set → set → (set → set → set → set λX9 : set ⇒ setsum (setsum ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) ∅ (λX8 : set → set Inj0 (X7 (λX9 : (set → set → set ∅ ) (λX9 : set ⇒ ∅ ) ) ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : set → set ∀X6 : set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj1 (setsum X7 ∅ ) (λX8 : set → set X8 (X8 (Inj1 (Inj1 ∅ ) X2 (λX8 : (set → (set → set → set → set → set → (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) X9 (λX10 : set ⇒ setsum ∅ ∅ ) (setsum (X8 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj1 ∅ ) X7 (λX10 : set ⇒ ∅ ) (Inj0 ∅ (Inj1 ∅ ) (setsum (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ (λX8 : set → set setsum (Inj1 (X5 (X6 ∅ (λX9 : set ⇒ ∅ ) ∅ ∅ (setsum X7 ∅ ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZ95AdJoFUu7qzhgbt4YbNSfNufs8NSeRN )
∀X0 : ((set → set → set → set → set → (set → set → (set → set → set → prop ∀X1 : ((set → set → set → (set → (set → set → set → set → set → set → set → set → (set → set → set → (((set → set → set → (set → set → set → set → ((set → set → set → set → prop ∀X2 : (set → ((set → set → set → set → set → ((set → (set → set → set → set → ((set → set → set → set → prop ∀X3 : ((((set → set → (set → set → set → ((set → set → set → set → set → ((((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set (X6 ∈ setsum (Inj1 ∅ (Inj0 (setsum (setsum ∅ ∅ ∅ → X3 (λX8 : ((set → set → (set → set → set → ((set → set → set → set setsum (setsum ∅ X5 (Inj0 ∅ ) (λX8 : ((set → set → set → set Inj0 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set → set → set ∀X6 : set → set ∀X7 : set → set → set (setsum (setsum (X7 (X6 ∅ ∅ ∅ (Inj0 (Inj0 ∅ ∈ setsum (Inj0 (Inj0 (X6 ∅ ∅ → X3 (λX8 : ((set → set → (set → set → set → ((set → set → set → set ∅ ) (λX8 : ((set → set → set → set X7 (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ (setsum (Inj0 (Inj0 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (X7 ∅ (Inj1 X10 (setsum ∅ (setsum (Inj1 ∅ X10 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum (Inj0 (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : ((set → set → (set → set → set → ((set → set → set → set X6 (X6 (setsum ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set setsum (Inj0 (X8 (λX9 : set → set Inj1 ∅ ) (Inj1 ∅ ) X2 (λX8 : set ⇒ λX9 : (set → set → set → set ∅ ) (λX8 : set → (set → set → set → set λX9 : (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (setsum (X6 (setsum X7 (Inj0 ∅ ∅ ∅ ∈ Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : (set → set → set → set Inj1 X8 ) (λX8 : set → (set → set → set → set λX9 : (set → set → set Inj0 ∅ ) X3 (λX8 : ((set → set → (set → set → set → ((set → set → set → set X5 ) (λX8 : ((set → set → set → set Inj1 X5 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → ((set → set → set → set → (set → set → set ∀X6 : set → (set → set → set ∀X7 : set → (set → set → set → (set → set → set (Inj0 ∅ ∈ X7 (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (setsum ∅ ∅ (λX10 : set ⇒ X8 ) ) (λX8 : set ⇒ X6 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (λX9 : set ⇒ Inj0 X9 ) ) → X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X10 X8 ) X1 (λX8 : set → set → set λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum X12 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum ∅ (Inj1 ∅ ) (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ X9 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (setsum X9 (setsum ∅ (X8 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → (set → set → (set → set → set → set X1 (λX8 : set → set → set λX9 : set → (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ (setsum (Inj0 ∅ (Inj1 ∅ (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ X9 (setsum (Inj0 (setsum ∅ ∅ (setsum (Inj1 ∅ (X9 ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) (Inj0 X4 ∈ Inj0 (Inj1 (Inj1 (X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 X7 ) X0 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum X8 (Inj0 (Inj0 X9 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXrtEoPKiXJzAHrzMmPuWfGpRV2F1GqbaK )
∀X0 : (set → set → set → (set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → set → prop ∀X2 : (set → set → set → (set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ setsum X8 (Inj0 (setsum ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 (Inj0 ∅ ) X3 (λX8 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (Inj1 (X10 ∅ (X8 (λX12 : set → set λX13 : set ⇒ X13 ) (Inj0 (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → ((set → set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : set → set → (set → set → set → set X3 (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set → set ∅ ) ) (λX8 : ((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) X0 (λX8 : set ⇒ X5 (λX9 : (set → set → set λX10 : set ⇒ X7 (setsum (Inj0 ∅ ∅ (Inj0 ∅ (λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) ∅ ) (λX9 : set → set setsum (setsum (Inj0 ∅ (Inj1 ∅ X8 ) ) (setsum (Inj0 (Inj0 ∅ (setsum (Inj0 (Inj0 ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → (set → set → set → ((set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X11 ) X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 (Inj1 (Inj0 ∅ (setsum ∅ (setsum (setsum ∅ ∅ (X6 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 X7 ∈ Inj1 (setsum (Inj1 ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → ((set → set → set → set X1 (λX8 : ((set → set → set → set → set Inj0 (setsum (Inj0 (setsum ∅ ∅ (X8 (λX9 : set → set λX10 : set ⇒ X8 (λX11 : set → set λX12 : set ⇒ ∅ ) ) ) X6 ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → ((set → set → set → set → (set → set → set ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : ((set → set → set → (set → set → set → set → set X1 (λX8 : ((set → set → set → set → set X5 (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ X8 (λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ) ) (X4 (setsum (Inj1 ∅ ∅ False ) → (∀X4 : set → set → (set → set → set ∀X5 : ((set → set → set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ X5 (λX9 : set → set → set setsum (setsum (X9 ∅ ∅ ∅ (X9 (X9 ∅ ∅ (setsum ∅ ∅ ) X8 ) (λX8 : ((set → set → set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) X0 (λX8 : set ⇒ Inj1 (X6 ∅ (λX9 : set → set setsum (setsum ∅ ∅ (Inj0 ∅ ) ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 ∅ ) ∅ ) → (∀X4 : (set → set → set ∀X5 : (set → set → set → set → (set → set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set X0 (λX8 : set ⇒ X7 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj1 X10 ) ) (setsum (Inj0 (setsum ∅ (Inj0 ∅ (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (X4 (λX8 : set ⇒ ∅ ) ∈ X6 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYkn28TYQKTAvsZmtLfDsyJyCVQRjaUfJ5 )
∀X0 : ((set → set → (set → set → set → set → (set → set → set → set → set → set → ((set → set → set → set → (set → set → prop ∀X1 : (set → set → (set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → set → prop ∀X3 : (set → set → set → (((set → set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : set → (set → set → set ∀X7 : set , (Inj1 (Inj1 ∅ ∈ Inj1 (Inj0 (X5 (λX8 : (set → set → set λX9 : set → set Inj0 ∅ ) → X3 (λX8 : set ⇒ Inj1 (Inj0 (X6 ∅ (λX9 : set ⇒ ∅ ) ) (Inj0 ∅ (λX8 : (set → set → set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set X3 (λX8 : set ⇒ setsum ∅ ∅ ) (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set → set setsum (Inj1 ∅ ∅ ) (Inj1 (setsum ∅ ∅ ∈ setsum (Inj1 (X7 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ Inj1 ∅ → X2 (λX8 : set ⇒ Inj1 (Inj1 X7 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ setsum (Inj0 (setsum ∅ (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 (setsum ∅ ∅ X7 ) X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ (setsum (Inj1 ∅ ∅ ) ∅ (X4 ∅ (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum X8 (X5 (λX9 : set → set λX10 : set ⇒ setsum (Inj1 ∅ ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ X6 (setsum X8 (Inj0 (X6 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (Inj0 X8 ) (Inj1 ∅ ∈ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → (set → set → set (X6 ∈ Inj0 X5 → X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 (setsum (Inj1 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) (setsum ∅ (setsum ∅ ∅ (Inj0 (X7 (λX8 : (set → set → set → set setsum ∅ X5 ) ∅ (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set → set → (set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 X11 (Inj0 (Inj1 (setsum ∅ ∅ (λX12 : set ⇒ ∅ ) ) X7 (setsum X7 (setsum (Inj0 (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ X7 ) (λX8 : set ⇒ ∅ ) (X4 ∈ X6 (setsum (X6 (Inj1 ∅ X4 (setsum X7 (X5 ∅ (setsum (Inj0 (setsum ∅ ∅ (Inj1 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKWZnaPZj8YpQghxvrDu6gPh4ZCtJrgZAE )
∀X0 : ((((set → set → (set → set → set → set → set → set → set → (((set → set → set → set → prop ∀X1 : ((set → set → set → set → set → ((set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → set → set → (((set → set → set → set → prop ∀X3 : (set → set → set → (((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : (((set → set → set → set → set → set → (set → set → set → set ∀X7 : ((set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum (X7 (λX11 : set → set → set ∅ ) (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : (set → set → set Inj1 (X8 (λX9 : set ⇒ Inj0 (X8 (λX10 : set ⇒ ∅ ) ) ) X3 (λX8 : set ⇒ setsum (X6 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum X11 (Inj0 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (setsum ∅ (X5 (X7 (λX9 : set → set → set ∅ ) X8 (λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ) (setsum (setsum ∅ (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set Inj0 ∅ ) ∅ (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (X7 (λX11 : set → set → set Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (X10 (λX13 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (Inj0 (X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (X8 (λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → (set → set → set ∀X7 : set → set X3 (λX8 : set ⇒ X7 X8 ) X4 (λX8 : (set → set → set → set ∅ ) (Inj1 ∅ ∅ (X5 (Inj0 (X5 (setsum ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , (X4 ∈ X7 → X3 (λX8 : set ⇒ setsum (setsum (Inj1 ∅ (setsum (Inj1 ∅ ∅ (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) (setsum (Inj1 (setsum (Inj0 ∅ ∅ (Inj1 (setsum (X6 ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set ∅ ) (setsum X4 X7 ∅ (setsum ∅ ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X4 (λX8 : (set → set → set Inj1 X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ X9 ) ∅ (λX8 : (set → set → set ∅ ) (setsum (Inj1 X4 ∅ ∈ X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set → set → set (X5 ∈ Inj0 X4 → X1 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ (Inj1 ∅ (setsum X9 (Inj1 (Inj1 ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum (X8 (Inj1 ∅ ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) X1 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (setsum ∅ (setsum ∅ X11 ) ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set → ((set → set → set → set → (set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 (X8 (Inj1 (Inj0 ∅ (X10 (Inj0 ∅ ) (Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj1 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : ((set → set → (set → set → set → set → set X5 (λX9 : (set → set → set setsum ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ ) ) ∅ (λX8 : (set → set → set Inj1 (setsum ∅ (X5 (λX9 : (set → set → set Inj0 ∅ ) ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set , (Inj0 (X4 ∅ ∈ X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X0 (λX8 : ((set → set → (set → set → set → set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ (Inj0 (Inj0 ∅ ) (λX8 : (set → set → set Inj0 (setsum (setsum X7 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) X3 (λX8 : set ⇒ Inj1 (setsum (X6 (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (Inj0 X8 ) (setsum (Inj1 ∅ (X4 (Inj1 ∅ (λX8 : (set → set → set → set ∅ ) ∅ (X4 (setsum ∅ (setsum X7 (X5 (λX8 : (set → set → set → set ∅ ) (setsum (setsum (setsum (setsum ∅ ∅ (X5 (λX8 : (set → set → set → set ∅ ) (setsum (setsum ∅ ∅ X7 (setsum (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUy4rjSqaXJr7WjqRtNB9GTJvZzNYX5vb8 )
∀X0 : (set → set → set → set → prop ∀X1 : ((set → set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → set → set → (set → set → prop ∀X3 : (set → ((set → set → set → (set → set → set → set → set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set (X7 (λX8 : set → set λX9 : set ⇒ ∅ ) (X7 (λX8 : set → set λX9 : set ⇒ ∅ ) X4 ∈ Inj0 (X5 ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum X6 X8 ∅ ) (Inj1 ∅ X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set setsum (X7 (λX10 : set → set λX11 : set ⇒ Inj1 X8 ) (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : (((set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set Inj1 X6 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) False ) → (∀X4 : set , ∀X5 : set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ X6 → X2 (λX8 : set ⇒ setsum X8 X6 ) (setsum ∅ X6 (Inj1 ∅ X6 (λX8 : set ⇒ X6 ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set → (set → set → set → set ∀X6 : (set → set → set → (set → set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ setsum ∅ (Inj1 ∅ → X2 (λX8 : set ⇒ ∅ ) ∅ (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) ∅ (X5 X7 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (setsum (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ (Inj1 ∅ (Inj0 (Inj1 ∅ (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ X9 ) ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) X1 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (setsum X8 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 X9 ) ∅ (setsum (Inj0 (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ (λX8 : set → set setsum ∅ (Inj0 ∅ ) (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set → set λX9 : set ⇒ X8 (setsum X9 (Inj0 X7 (X8 (Inj1 ∅ ∅ ) ∅ (Inj1 (setsum (Inj0 (setsum ∅ ∅ X7 (λX8 : set → set ∅ ) (Inj0 (Inj0 (Inj0 ∅ (X5 (setsum X4 (X6 (Inj1 ∅ X4 (Inj1 ∅ ∅ X7 X7 (X5 ∅ (Inj0 X7 ∅ (setsum (setsum ∅ ∅ (X5 ∅ ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → ((set → set → set → set → (set → set → set → set ∀X7 : set → set X1 (λX8 : set → set → set λX9 : set ⇒ ∅ ) (X7 ∅ (Inj0 (X7 (X7 ∅ (λX8 : set → set setsum ∅ ∅ ) (setsum (Inj0 ∅ (Inj0 (setsum ∅ (setsum ∅ ∅ (setsum ∅ (setsum (setsum ∅ (X5 ∅ (Inj1 (X5 ∅ False ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : ((set → set → set → (set → set → set ∀X7 : (set → set → set (Inj0 X4 ∈ Inj0 (X5 (λX8 : (set → set → set setsum (X8 (λX9 : set ⇒ ∅ ) (X6 (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ) → X0 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 (Inj1 (Inj0 ∅ ) (setsum (X6 (λX8 : set → set X5 (λX9 : (set → set → set X7 (λX10 : set ⇒ ∅ ) ) ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (setsum (setsum ∅ ∅ X9 X10 ) ) (setsum (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (Inj0 (Inj1 ∅ (Inj0 (Inj1 ∅ (Inj0 (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (X5 ∅ ∈ Inj1 (setsum ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZ3xBCnirjXm8e6Z3dfMYy6nBTkAQGnZKg )
∀X0 : (set → set → ((set → set → (set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → set → (set → set → set → set → set → set → set → prop ∀X2 : (((set → set → set → set → set → set → (set → (set → set → set → set → prop ∀X3 : (set → set → ((set → set → set → set → set → (set → set → ((set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : (set → (set → set → set → set → set (setsum (Inj0 ∅ (Inj0 X5 ∈ setsum (setsum X5 (setsum (Inj1 ∅ X5 (Inj1 (Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ X6 X8 (λX9 : set ⇒ λX10 : set ⇒ X8 ) ) (λX8 : set → set Inj0 ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 ∅ ∈ setsum ∅ (X7 (Inj1 (Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (setsum (setsum ∅ ∅ (X5 (λX9 : set → set ∅ ) ) (λX8 : set → set ∅ ) X1 (λX8 : ((set → set → set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ ∅ ) (X5 (λX8 : set → set ∅ ) ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → ((set → set → set → set → set ∀X7 : set , (setsum (X4 (Inj0 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (X4 ∅ (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (Inj0 ∅ (Inj0 X7 ∈ Inj0 (X6 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 (X6 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) ) → X0 (λX8 : set ⇒ setsum ∅ (X6 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set → set λX10 : set ⇒ X9 (Inj0 ∅ ) ) (λX8 : set → set λX9 : set → set → set setsum ∅ (Inj1 ∅ ) X2 (λX8 : (set → set → set → set X7 ) (setsum (Inj1 (Inj1 (Inj1 ∅ (setsum (Inj1 (X6 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (Inj1 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X9 X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : (set → set → set → set setsum (Inj1 (Inj1 ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (X9 (setsum ∅ X10 ) False ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ Inj0 (X8 (λX11 : set → set → set λX12 : set ⇒ setsum X12 (Inj0 ∅ ) ∅ ) (Inj1 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set → set ∀X7 : (((set → set → set → set → set → set → set X1 (λX8 : ((set → set → set → set → set → set → set λX9 : set → set → set → set λX10 : set ⇒ setsum ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) ∅ False ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → set → set ∀X6 : (set → set → ((set → set → set → (set → set → set → set ∀X7 : set , (X7 ∈ Inj1 (Inj1 (setsum X7 ∅ → X0 (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : set → set → set Inj1 (setsum (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set ∅ ) (λX10 : set ⇒ X7 ) (X6 (λX10 : set ⇒ ∅ ) (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (setsum (setsum ∅ ∅ (X8 ∅ ) ) → (∀X4 : (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj1 (setsum X7 (setsum X6 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set → set → set Inj0 (Inj0 X6 ) (X4 (λX8 : set ⇒ Inj0 (setsum X5 ∅ ) (X4 (λX8 : set ⇒ ∅ ) (Inj1 (X4 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (Inj1 (Inj0 (setsum ∅ ∅ ∈ X7 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVWitktgpTKmc9Pj9UVxWHHURbR92HFtXR )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → set → set → set → (set → ((set → set → set → set → set → prop ∀X2 : (set → (((set → set → set → set → set → set → prop ∀X3 : ((set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set → set (X5 ∈ X4 → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : (set → set → set → set ∅ ) X3 (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (Inj1 ∅ ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set → set X3 (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ ∅ ) (Inj0 (setsum (X4 (λX8 : set ⇒ Inj1 ∅ ) (X4 (λX8 : set ⇒ ∅ ) False ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → (set → set → set → (set → set → set → set (X4 (λX8 : set → set setsum X5 (Inj0 (Inj1 ∅ ) ∈ X6 (setsum (setsum ∅ ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : ((set → set → set → set X9 (λX10 : set → set setsum ∅ (Inj1 (setsum ∅ ∅ ) ) (X6 ∅ ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 (Inj1 (setsum ∅ ∅ ∈ setsum ∅ (Inj1 (setsum ∅ (X4 (λX8 : set ⇒ ∅ ) → X2 (λX8 : set ⇒ λX9 : ((set → set → set → set Inj0 X6 ) (setsum X6 ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 X7 ) ) → (∀X4 : set → set ∀X5 : (set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → ((set → set → set → set → set → set (setsum (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ X6 ∈ setsum (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X9 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 ∅ (setsum (setsum (Inj1 ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj0 X10 X11 ) (λX8 : set ⇒ λX9 : (set → set → set → set X9 (λX10 : set ⇒ Inj0 (setsum (X7 (λX11 : set → set λX12 : set → set λX13 : set ⇒ ∅ ) (λX11 : set → set λX12 : set ⇒ ∅ ) ∅ (X9 (λX11 : set ⇒ ∅ ) ∅ ) (Inj0 (Inj0 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj1 X8 ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X7 ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set → (set → set → set ∀X7 : (set → set → set → set → set X0 (λX8 : set ⇒ Inj0 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → (set → set → set → set ∀X7 : set → set → set → set → set X0 (λX8 : set ⇒ Inj1 (Inj0 (setsum ∅ (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) (setsum (X6 (λX8 : set → set λX9 : set → set Inj0 (X9 ∅ ) (Inj1 (Inj1 (setsum ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMHgE1ejGAaSedERoeYm4PH2bdcpFt6btwS )
∀X0 : ((set → set → set → set → set → (set → set → prop ∀X1 : ((set → (set → set → set → set → (set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → set → (set → set → set → set → set → prop ∀X3 : (((set → set → set → set → (set → set → set → set → set → set → ((set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set ∀X7 : set , (Inj0 (Inj0 (setsum (setsum ∅ ∅ ∅ ∈ setsum (Inj0 (Inj1 (Inj1 ∅ ∅ → X3 (λX8 : (set → set → set → set λX9 : set → set → set X7 ) ∅ (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ X7 ) ) → (∀X4 : ((set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set X3 (λX8 : (set → set → set → set λX9 : set → set → set setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (X6 ∈ X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 (setsum ∅ ∅ ) (Inj1 (X7 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 ) (X4 (λX8 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → ((set → set → set → (set → set → set ∀X7 : set , (setsum (setsum X7 (Inj0 (Inj1 ∅ (Inj0 ∅ ∈ Inj0 (Inj0 (Inj0 (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) → X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ (X6 (λX8 : set ⇒ λX9 : set → set X9 (Inj0 ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum X7 (setsum ∅ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ X9 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 ) X5 ) → (∀X4 : ((set → set → set → set → (set → set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 X6 ) X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (Inj0 ∅ False ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : (set → set → set (Inj0 ∅ ∈ X4 (Inj1 (setsum (Inj1 ∅ X5 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ ∅ (Inj0 (X6 ∅ ∅ ∅ ∅ ) → X2 (λX8 : set ⇒ λX9 : set ⇒ X6 X8 (setsum (Inj1 ∅ (Inj0 X8 (Inj1 (Inj0 (setsum ∅ ∅ (Inj0 X8 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 ∅ X1 (λX8 : set → (set → set → set → set λX9 : set → set λX10 : (set → set → set X8 (X8 ∅ (λX11 : set ⇒ λX12 : set ⇒ setsum X11 (setsum ∅ ∅ ) (λX11 : set ⇒ λX12 : set ⇒ X10 (λX13 : set ⇒ ∅ ) ) ) (setsum (Inj0 (Inj0 ∅ (Inj1 (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → ((set → set → set → set → set X1 (λX8 : set → (set → set → set → set λX9 : set → set λX10 : (set → set → set ∅ ) (Inj1 (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : (set → set → ((set → set → set → (set → set → set (Inj0 X4 ∈ Inj1 X4 → X3 (λX8 : (set → set → set → set λX9 : set → set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 (X8 ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum X5 ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ ) X0 (λX8 : set → set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 X4 → X0 (λX8 : set → set → set → set ∅ ) (λX8 : set ⇒ X8 ) X0 (λX8 : set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ X7 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQSmG5r8i9Z9LB749bpQHBiJRQ9fBj2sHJ )
∀X0 : (((((set → set → set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → set → (set → set → set → set → set → set → (set → set → set → (set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → (set → set → (set → set → set → set (Inj1 ∅ ∈ Inj1 (setsum (X7 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (X7 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ (setsum (Inj0 ∅ (X7 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) ∅ → X3 (λX8 : (((set → set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 X8 (Inj0 ∅ ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set → (set → set → (set → set → set ∀X7 : ((set → set → (set → set → set → set → set (X4 ∅ ∅ (λX8 : set ⇒ Inj0 ∅ ) ∅ ∈ Inj0 (setsum (X6 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (X7 (λX8 : set → set λX9 : set → set ∅ ) ∅ (setsum ∅ ∅ → X3 (λX8 : (((set → set → set → set → set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum X10 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X1 (λX8 : set ⇒ X5 ) (setsum ∅ (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (Inj1 ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ ∈ X7 → X1 (λX8 : set ⇒ Inj1 (setsum X5 (setsum X7 ∅ ) (setsum (setsum ∅ (Inj1 ∅ (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ X2 (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ X8 (Inj0 X7 (Inj0 (setsum (setsum ∅ ∅ X5 ) X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X6 (Inj0 (Inj1 (Inj0 ∅ (λX9 : set → set X6 X8 (λX10 : set → set X7 ) ) ) (X6 (X6 (Inj0 (setsum ∅ ∅ (λX8 : set → set Inj0 X7 ) (λX8 : set → set Inj0 (X6 (setsum ∅ ∅ (λX9 : set → set X7 ) ) X1 (λX8 : set ⇒ setsum (Inj0 (setsum (setsum ∅ ∅ ∅ X7 ) ∅ (setsum (X6 (setsum (setsum ∅ ∅ X4 (λX8 : set → set setsum (Inj0 ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set → (set → set → set → (set → set → set → set X1 (λX8 : set ⇒ setsum X5 (X6 (λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj0 ∅ ) ) (Inj0 (Inj1 (Inj0 (Inj0 ∅ (Inj0 (X7 (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) ) (λX8 : set ⇒ X8 ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set → set → set → set X1 (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum ∅ (setsum ∅ ∅ (Inj0 (Inj0 (setsum (setsum ∅ ∅ X4 (setsum X5 ∅ ∈ Inj0 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set (Inj1 ∅ ∈ Inj1 (X7 (λX8 : (set → set → set → set Inj1 (X8 (λX9 : set ⇒ ∅ ) ∅ ) → X0 (λX8 : (((set → set → set → set → set → set ∅ ) (setsum (setsum ∅ (Inj0 (X7 (λX8 : (set → set → set → set ∅ ) (Inj0 (setsum ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set → (set → set → set → set (X4 ∈ Inj1 (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ → X0 (λX8 : (((set → set → set → set → set → set Inj0 (Inj1 ∅ ) ∅ X1 (λX8 : set ⇒ X5 (X5 (Inj1 (Inj1 ∅ ) (X6 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ (setsum (Inj1 (Inj1 ∅ (Inj0 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcDSicyK8qhEj9KgSAH4qVJbdK5nLj4wBp )
∀X0 : ((set → set → set → ((set → set → set → set → set → set → prop ∀X1 : (set → set → ((set → (set → set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → set → (set → (set → set → set → set → ((set → set → set → set → set → (set → set → (set → (set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , (X6 (X6 X7 ∅ (Inj1 (X6 ∅ ∅ ∅ ∅ (X6 X5 X7 ∅ ∅ ∅ ∅ (Inj0 (Inj0 ∅ ∈ X6 (X6 (Inj1 (Inj0 ∅ ∅ X7 ∅ X7 ∅ (X6 (setsum X7 (setsum ∅ ∅ ∅ ∅ (Inj0 ∅ → X3 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ (setsum (setsum X7 ∅ (Inj0 ∅ ) (setsum ∅ X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X3 (λX8 : set → set Inj1 (Inj0 ∅ ) (λX8 : set ⇒ setsum X6 X6 ) (setsum ∅ (Inj0 (Inj1 (setsum ∅ ∅ False ) → (∀X4 : set → ((set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → set → set → set → set → set λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ setsum X7 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set X9 (setsum ∅ (Inj0 X7 ) (λX8 : set → set λX9 : set ⇒ X6 ) X2 (λX8 : ((set → set → set → set → set → set → set λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ setsum ∅ (Inj0 (Inj1 X6 ) (λX8 : set ⇒ λX9 : set → set setsum (X9 (setsum X8 (Inj1 ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X8 (Inj1 X6 ) ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → set → set → set → set → set λX9 : set → (set → set → set → set λX10 : (set → set → set → set setsum (Inj1 (X9 (Inj1 ∅ (λX11 : set ⇒ Inj1 ∅ ) (X8 (λX11 : set → set ∅ ) ∅ ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ X7 ) X0 (λX8 : set → set Inj0 (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set → set ∀X6 : set → (set → set → set → (set → set → set ∀X7 : ((set → set → (set → set → set → set (setsum (X7 (λX8 : set → set λX9 : set → set setsum ∅ (X9 ∅ ) (setsum ∅ (setsum (Inj1 ∅ ∅ ∈ setsum (Inj1 ∅ (setsum (X7 (λX8 : set → set λX9 : set → set Inj1 ∅ ) ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set Inj0 (Inj1 (X8 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (Inj1 ∅ ) X1 (λX8 : set ⇒ ∅ ) (λX8 : set → (set → set → set → set setsum (Inj0 ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → ((set → set → set → set ∀X6 : set → set → set → set ∀X7 : set , (Inj1 (setsum (Inj1 (Inj1 ∅ (Inj0 (setsum ∅ ∅ ∈ X4 → X1 (λX8 : set ⇒ Inj1 (setsum (setsum (Inj1 ∅ (Inj0 ∅ ∅ ) (λX8 : set → (set → set → set → set X7 ) X2 (λX8 : ((set → set → set → set → set → set → set λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ (Inj0 ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set → (set → set → set ∀X7 : (set → set → (set → set → set → set → set (setsum (setsum ∅ X4 (X6 (λX8 : (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum (X6 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (Inj0 ∅ ) ∈ setsum (Inj1 ∅ ∅ → X3 (λX8 : set → set setsum (Inj1 (X8 (X6 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (setsum (Inj0 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ setsum (Inj0 (setsum ∅ ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ ) ∅ X0 (λX8 : set → set X8 X5 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) ) → (∀X4 : ((set → set → (set → set → set → set → (set → set → set → set → set → set ∀X5 : set → set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) X2 (λX8 : ((set → set → set → set → set → set → set λX9 : set → (set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set Inj0 (setsum (X6 (λX10 : set ⇒ X8 ) (X6 (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKd5sxpzwyWiWkj4mhVWzAbBpYc4BaP2Px )
∀X0 : (set → set → ((set → set → set → set → ((set → set → set → prop ∀X1 : (((set → set → set → set → set → set → ((set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → set → set → set → set → prop ∀X3 : (((set → set → set → set → set → set → (((set → set → set → (set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X5 ∈ Inj1 X7 → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj1 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set X5 ) X3 (λX8 : (set → set → set → set → set setsum (setsum X6 X7 X6 ) (λX8 : (set → set → set → (set → set → set setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ X6 ) (λX8 : set → set X6 ) ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X3 (λX8 : (set → set → set → set → set X7 (λX9 : set ⇒ X9 ) ) (λX8 : (set → set → set → (set → set → set Inj1 (Inj0 ∅ ) (λX8 : set → set ∅ ) False ) → (∀X4 : (set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : (set → set → set → set → set X2 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) (Inj0 ∅ (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ X6 X9 (λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ) ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 X8 ) (X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set ∀X6 : ((set → set → set → set → set → (set → set → (set → set → set ∀X7 : set , (Inj1 (setsum (setsum (X5 ∅ ∅ ∅ X7 (Inj0 X7 ∈ Inj0 X7 → X2 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj0 (Inj1 (setsum ∅ (setsum ∅ ∅ X7 X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set Inj1 X7 ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set , X1 (λX8 : (set → set → set λX9 : set ⇒ setsum (Inj1 X9 (setsum ∅ (Inj0 (setsum ∅ ∅ ) (Inj0 ∅ (λX8 : set → set Inj1 X5 ) X1 (λX8 : (set → set → set λX9 : set ⇒ ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ (Inj0 ∅ (X6 (λX8 : set ⇒ X8 ) ∅ (λX8 : set ⇒ X6 (λX9 : set ⇒ ∅ ) (X6 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ X7 ) (setsum ∅ ∅ ) (Inj1 ∅ (λX8 : set → set Inj1 (Inj0 X5 ) ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X1 (λX8 : (set → set → set λX9 : set ⇒ Inj0 (setsum ∅ X9 ) (Inj1 ∅ (λX8 : set → set setsum (Inj1 ∅ (Inj1 (X8 (setsum ∅ ∅ ) (setsum ∅ ∅ ∈ Inj0 (setsum (X4 (X4 ∅ (Inj1 X7 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (set → set → ((set → set → set → (set → set → set ∀X7 : set , (setsum (Inj1 (setsum (Inj0 ∅ ∅ (X5 (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) ∈ Inj0 (Inj0 ∅ → X2 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (X8 (λX11 : set ⇒ λX12 : set → set setsum ∅ X10 ) ) (setsum (Inj0 ∅ (Inj0 (setsum (Inj1 ∅ ∅ (X6 (λX8 : set ⇒ setsum X8 (X5 (λX9 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set → set setsum (Inj0 (X5 (λX9 : set ⇒ ∅ ) (Inj0 (X8 ∅ ) (λX8 : set ⇒ X8 ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set setsum (Inj0 X8 X7 ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set setsum (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X10 (λX11 : set ⇒ Inj0 ∅ ) ) (λX8 : set → set setsum (Inj0 ∅ (setsum ∅ (Inj1 (X8 ∅ ) X3 (λX8 : (set → set → set → set → set Inj0 (setsum ∅ (Inj1 (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set X6 ) (λX8 : set → set setsum X6 (Inj0 X6 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMH2RXDitK8neQHVyZ734YmDART8XFtBzDA )
∀X0 : (set → (set → set → (set → set → set → set → ((set → set → (set → set → set → (set → set → ((set → set → set → set → set → prop ∀X1 : ((set → set → set → (((set → set → (set → set → set → (set → set → set → set → set → set → prop ∀X2 : ((set → set → (set → (set → set → set → set → set → ((((set → set → set → set → set → set → prop ∀X3 : ((set → (set → set → set → set → set → set → (set → set → prop (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : set ⇒ Inj0 (Inj0 X8 ) ) → (∀X4 : ((set → set → (set → set → set → set → (set → set → set → set → set ∀X5 : (set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → (set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (Inj1 (setsum ∅ (Inj0 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (Inj1 (setsum X6 (Inj0 ∅ X5 ∈ X4 → X2 (λX8 : set → set λX9 : set → (set → set → set → set ∅ ) (λX8 : ((set → set → set → set → set ∅ ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set → set X2 (λX8 : set → set λX9 : set → (set → set → set → set Inj0 (setsum (Inj1 (setsum ∅ ∅ (X6 (X7 ∅ ) (λX8 : ((set → set → set → set → set ∅ ) (Inj1 ∅ ∈ X7 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set → (set → set → set ∀X7 : set → ((set → set → set → set → set X1 (λX8 : set → set setsum ∅ (Inj0 ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set → set λX10 : set ⇒ setsum ∅ X10 ) (Inj1 (Inj0 ∅ ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set (setsum X5 (X7 (λX8 : set → set Inj1 ∅ ) ∈ X7 (λX8 : set → set Inj1 (setsum (setsum ∅ ∅ ∅ ) → X1 (λX8 : set → set setsum (setsum (Inj1 (Inj0 ∅ (setsum X5 (Inj1 ∅ (X8 (X6 (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set → set λX10 : set ⇒ Inj0 ∅ ) ∅ X1 (λX8 : set → set Inj0 ∅ ) (λX8 : (set → set → (set → set → set λX9 : set → set → set λX10 : set ⇒ X7 (λX11 : set → set X8 (λX12 : set ⇒ ∅ ) (λX12 : set ⇒ ∅ ) ) ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → ((set → set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : (((set → set → set → set → set → ((set → set → set → (set → set → set X0 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set → set λX9 : set → set X9 (X9 (setsum ∅ (X9 ∅ ) (λX8 : set ⇒ X7 (λX9 : (set → set → set → set Inj0 (X7 (λX10 : (set → set → set → set X8 ) (λX10 : set → set X8 ) (λX10 : set ⇒ X10 ) ) (λX9 : set → set Inj1 (setsum X8 (X6 (λX10 : set → set ∅ ) ) (λX9 : set ⇒ ∅ ) ) (λX8 : set → set Inj0 ∅ ) ∅ (X5 (λX8 : (set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set setsum (setsum ∅ (Inj0 ∅ ∅ ) (X6 (λX8 : set → set X8 ∅ ) X0 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set Inj0 (Inj0 (setsum (X9 ∅ X8 ) (λX8 : set → set λX9 : set → set ∅ ) (λX8 : set ⇒ setsum (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ (Inj0 X8 ) (λX8 : set → set setsum (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ (Inj1 (X6 (λX9 : set → set ∅ ) ) (X7 (λX8 : (set → set → set → set Inj0 (X6 (λX9 : set → set X8 (λX10 : set ⇒ ∅ ) ∅ ) ) (λX8 : set → set Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 (Inj0 (Inj0 ∅ ) (X6 (λX8 : set → set setsum (Inj0 (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set → set λX9 : set → set ∅ ) (λX8 : set ⇒ X5 ∅ ) (λX8 : set → set setsum X7 ∅ ) (setsum (setsum (setsum X4 (X6 ∅ ∅ (X6 (Inj1 ∅ (Inj1 ∅ (setsum (Inj1 ∅ (Inj0 (setsum ∅ ∅ (setsum (X6 X7 (setsum ∅ (setsum ∅ ∅ (setsum (Inj0 X7 (Inj1 (setsum ∅ ∅ (Inj0 ∅ ∈ Inj0 (setsum X7 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMa4wTkpgPNupYkSy5prVPXiVoWvyGaG22h )
∀X0 : ((set → set → set → set → set → prop ∀X1 : (set → set → set → ((set → set → set → (set → set → set → (((set → set → set → set → set → set → (set → set → (set → set → set → prop ∀X2 : ((set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → set → set → ((set → set → ((set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set setsum (setsum ∅ (X5 (λX9 : set ⇒ Inj1 ∅ ) ∅ X6 ∅ ) (λX8 : set → set ∅ ) ∅ X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (Inj0 (Inj1 ∅ (setsum X10 (Inj1 ∅ ∅ ) (λX8 : set → set λX9 : (set → set → set → set setsum (Inj1 (Inj1 ∅ (Inj0 (setsum (Inj0 ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set (Inj1 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj0 ∅ ) ∈ Inj0 ∅ → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 X9 ) (λX8 : set → set λX9 : (set → set → set → set setsum (X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 ∅ ∅ ) ∅ ) (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 ∅ X12 ) ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set X7 (λX11 : set ⇒ λX12 : set ⇒ λX13 : set ⇒ Inj1 (setsum (Inj0 ∅ X12 ) ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (Inj0 (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → (set → set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set → set Inj0 (X6 (Inj0 (Inj1 ∅ (Inj1 (setsum ∅ ∅ ) ∅ (X4 (λX8 : set → set Inj0 (Inj0 ∅ ) (Inj1 (setsum (Inj1 ∅ (X4 (λX8 : set → set ∅ ) ∅ X2 (λX8 : set → set Inj1 (Inj1 (setsum (Inj1 ∅ X7 ) (λX8 : set → set Inj0 (Inj1 ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set ∀X6 : set → (set → set → set ∀X7 : set , X2 (λX8 : set → set Inj1 (setsum (setsum ∅ (setsum ∅ ∅ (setsum X7 (setsum ∅ ∅ ) (λX8 : set → set Inj1 (X8 (setsum (setsum ∅ ∅ (X5 (λX9 : set → set ∅ ) ) ∅ False ) → (∀X4 : (set → set → set ∀X5 : (set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj0 (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ setsum X9 (setsum ∅ (Inj1 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set setsum ∅ X7 ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X9 X9 ∅ ) (λX8 : set ⇒ setsum (setsum ∅ (Inj0 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set ∀X7 : set , (setsum ∅ X5 ∈ Inj0 (Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set setsum X9 X7 ) (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ (Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (Inj0 X5 X7 ) ∅ X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (X8 X9 ) (λX8 : set → set λX9 : (set → set → set → set ∅ ) (Inj0 (X6 (λX8 : (set → set → set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set X8 (X5 (λX9 : set → set → set ∅ ) ) ∅ (Inj1 (setsum (X5 (λX8 : set → set → set X8 ∅ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set ∅ ) X6 (Inj1 X6 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUpD8ydACCWjBg6qcumqBQCpHBUjSZHNKJ )
∀X0 : (((((set → set → set → set → set → set → set → ((set → set → set → set → set → set → (((set → set → set → (set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → (set → set → set → set → prop ∀X2 : ((set → set → set → set → set → set → (set → set → (((set → set → set → set → set → prop ∀X3 : (set → set → (set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : set → ((set → set → set → set → set → set X3 (λX8 : set ⇒ setsum (Inj0 (Inj1 ∅ (X6 (λX9 : set → set Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set ∅ ) X3 (λX8 : set ⇒ X7 X5 (λX9 : set → set X9 (Inj1 ∅ ) X8 (Inj0 X8 ) (λX8 : set ⇒ λX9 : (set → set → set setsum (X7 (setsum (Inj0 ∅ (Inj1 ∅ (λX10 : set → set setsum ∅ (Inj1 ∅ ) (Inj0 (setsum ∅ ∅ ∅ (Inj0 (setsum (Inj0 ∅ (Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → ((set → set → set → set → set (Inj1 (X4 (X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∈ setsum (X4 ∅ (X5 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) → X3 (λX8 : set ⇒ Inj0 (setsum (Inj0 X6 (Inj0 (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set X7 (λX10 : (set → set → set → set X10 (λX11 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (X9 (λX11 : set ⇒ Inj1 ∅ ) ) (λX10 : set → set λX11 : set ⇒ setsum ∅ X8 ) ) X1 (λX8 : set ⇒ Inj1 X6 ) (λX8 : set → set X8 (setsum (X7 (λX9 : (set → set → set → set Inj0 ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (setsum (X7 (λX9 : (set → set → set → set ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X6 (setsum X5 X7 ∈ Inj0 (setsum (X4 (setsum ∅ ∅ (λX8 : set → set X6 ) X7 → X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum ∅ ∅ ) X2 (λX8 : set → set → set → set → set Inj1 (setsum X6 (Inj1 ∅ ) (λX8 : set ⇒ setsum (Inj0 ∅ X6 ) (λX8 : (set → set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X5 ∈ Inj0 X5 → X2 (λX8 : set → set → set → set → set X7 ) (λX8 : set ⇒ setsum (setsum (Inj0 (Inj1 ∅ (Inj1 X6 X7 ) (λX8 : (set → set → set → set setsum ∅ (Inj0 (setsum (X8 (λX9 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ ) X1 (λX8 : set ⇒ setsum (setsum ∅ (setsum ∅ (Inj1 ∅ (setsum ∅ X5 ) (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum (setsum X7 (Inj0 (Inj0 ∅ (setsum (Inj0 X7 (setsum (X6 ∅ X7 ∈ Inj0 X4 → X1 (λX8 : set ⇒ X8 ) (λX8 : set → set setsum (Inj1 ∅ (setsum X7 (Inj0 (X8 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum X10 (Inj1 ∅ (setsum ∅ X9 ) X1 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set → set X8 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ (Inj0 X8 ∅ ) ) → (∀X4 : (((set → set → set → set → set → (set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set → set → set X1 (λX8 : set ⇒ X7 (λX9 : set ⇒ Inj1 (setsum (setsum ∅ ∅ X6 ) ∅ ∅ (setsum (X5 (setsum ∅ ∅ (λX9 : set → set X9 ∅ ) ∅ (X5 ∅ (λX9 : set → set ∅ ) (setsum ∅ ∅ ) (λX8 : set → set X8 (X8 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) False ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ setsum ∅ (setsum (setsum ∅ (X9 (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ ) (λX8 : (set → set → set → (set → set → set → set X5 ) ) → (∀X4 : set → ((set → set → set → set → (set → set → set → set ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : (((set → set → set → set → set → set → set λX9 : (set → set → set → set λX10 : set ⇒ setsum ∅ (Inj1 (X7 (λX11 : set ⇒ ∅ ) ) (λX8 : (set → set → set → (set → set → set → set setsum (X5 (setsum ∅ (Inj0 ∅ ∅ (λX9 : set ⇒ Inj0 ∅ ) (X5 (Inj1 ∅ X6 (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (X5 X6 ∅ (λX9 : set ⇒ ∅ ) ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTzkzbdMaH7FttENC18c5hzKQ1ZPCKBdjm )
∀X0 : (set → set → ((set → set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → (set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → (set → set → set → set → (set → set → set → (set → set → set → (set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj1 ∅ ∈ setsum X7 ∅ → X3 (λX8 : set ⇒ ∅ ) (X4 (setsum (X4 (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set → (set → set → set → set ∀X7 : (set → set → (set → set → set X3 (λX8 : set ⇒ Inj0 ∅ ) (Inj1 ∅ False ) → (∀X4 : ((set → set → (set → set → set → ((set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set → set X7 ) (λX8 : set ⇒ ∅ ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum ∅ (setsum ∅ (Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set → set → set X8 ) (λX8 : set ⇒ X8 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 X9 ) (λX8 : set ⇒ ∅ ) X1 (λX8 : ((set → set → set → set → (set → set → set λX9 : set → set → set ∅ ) ∅ (setsum (setsum X5 ∅ (Inj1 X5 ) → (∀X4 : set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set → set → set Inj1 (setsum ∅ X8 ) (λX8 : set ⇒ Inj1 (Inj0 ∅ ) X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum (Inj1 X8 (Inj1 (Inj0 ∅ ∅ ) X1 (λX8 : ((set → set → set → set → (set → set → set λX9 : set → set → set Inj1 (setsum ∅ ∅ ) (setsum (setsum (X7 (λX8 : (set → set → set → set λX9 : set ⇒ X8 (λX10 : set ⇒ ∅ ) ∅ ) (X5 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) ∅ X6 ) → (∀X4 : (((set → set → set → set → set → (set → set → set → set ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : set → set → set → set → set X1 (λX8 : ((set → set → set → set → (set → set → set λX9 : set → set → set Inj1 (setsum (setsum (Inj1 ∅ (X8 (λX10 : set → set → set ∅ ) (λX10 : set ⇒ ∅ ) (Inj1 (X9 ∅ ∅ ) ∅ (Inj1 (Inj0 (Inj1 (setsum ∅ ∅ False ) → (∀X4 : (set → (set → set → set → set → set → set → set ∀X5 : set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj0 (setsum ∅ (setsum (X5 ∅ ∅ ∅ (Inj0 ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ setsum (setsum X9 X6 (setsum X9 ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → set X0 (λX8 : set ⇒ Inj0 (X6 (X5 ∅ (λX9 : set → set ∅ ) ) (λX8 : set → set → set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ ∈ Inj1 (Inj1 X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMduohf8MbpZDbPMo4keDvVGcCiajsihd1x )
∀X0 : (set → set → (set → set → ((set → set → set → set → prop ∀X1 : (set → set → set → (((set → set → set → (set → set → set → ((set → set → set → set → prop ∀X2 : ((set → set → (set → set → set → set → set → prop ∀X3 : ((set → ((set → set → set → (set → set → set → (((set → set → set → set → set → set → (set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set → ((set → set → set → (set → set → set λX9 : ((set → set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set → set → set setsum ∅ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X4 (λX8 : set ⇒ ∅ ) ∈ X5 (Inj0 ∅ → X3 (λX8 : set → ((set → set → set → (set → set → set λX9 : ((set → set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set → set → set ∅ ) X0 (λX8 : set ⇒ Inj1 (setsum (Inj0 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ X6 ) (λX8 : set → set → set Inj0 (setsum ∅ (Inj0 (X8 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → (set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X10 ) (setsum X5 ∅ X2 (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set X2 (λX8 : set → set λX9 : set → set λX10 : set ⇒ X7 (λX11 : (set → set → set Inj1 (setsum (X11 (λX12 : set ⇒ ∅ ) (X9 ∅ ) (λX11 : set ⇒ Inj1 (setsum (Inj1 ∅ ∅ ) ) ∅ X1 (λX8 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set X6 ) (λX8 : set ⇒ Inj1 X6 ) (λX8 : (set → set → set λX9 : set → set Inj0 (setsum (Inj0 (Inj0 ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X8 (setsum X6 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → set X1 (λX8 : set ⇒ ∅ ) (setsum ∅ (Inj0 (Inj0 (Inj1 ∅ (λX8 : (set → set → set λX9 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ Inj0 (setsum (X7 (λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ Inj0 ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set → ((set → set → set → set → (set → set → set ∀X5 : set → (set → set → set ∀X6 : ((set → set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X8 ) (Inj0 (X4 (setsum (Inj1 ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ X8 (Inj0 ∅ ) (λX8 : set ⇒ Inj0 (setsum ∅ ∅ ) (λX8 : (set → set → set λX9 : set → set Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) False ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X4 (λX8 : set ⇒ X6 ) (X4 (λX8 : set ⇒ ∅ ) X7 ∈ Inj1 (setsum ∅ (Inj0 X6 → X3 (λX8 : set → ((set → set → set → (set → set → set λX9 : ((set → set → set → set → set Inj1 (Inj0 (X8 (Inj0 ∅ (λX10 : set → set X10 ∅ ) (λX10 : set ⇒ X8 ∅ (λX11 : set → set ∅ ) (λX11 : set ⇒ ∅ ) ) ) (λX8 : set ⇒ λX9 : set → set → set Inj1 ∅ ) X0 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set → set Inj0 (Inj1 (X5 (X5 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , (X5 ∈ setsum (Inj1 (Inj0 ∅ (setsum X5 (setsum X7 X7 → X0 (λX8 : set ⇒ X6 (λX9 : set → set → set X8 ) ) (λX8 : set ⇒ X6 (λX9 : set → set → set ∅ ) ) (λX8 : set → set → set ∅ ) X1 (λX8 : set ⇒ ∅ ) ∅ (λX8 : (set → set → set λX9 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMM8Zgo2HfET49AmRcEhRu1T25nTyiwJ5Fu )
∀X0 : ((set → set → set → ((set → set → set → prop ∀X1 : (set → set → set → set → set → (set → set → prop ∀X2 : (set → set → (set → set → set → (set → ((set → set → set → set → set → prop ∀X3 : ((((set → set → set → set → set → (set → set → set → set → set → (((set → set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum (X5 X4 (setsum X4 ∅ ∈ Inj1 (Inj0 (Inj0 ∅ → X3 (λX8 : ((set → set → set → set → set → (set → set → set → set setsum (Inj0 ∅ (setsum X6 X6 ) (λX8 : (set → set → set → (set → set → set X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → (set → set → set → set → set → set ∀X7 : set → set → (set → set → set → set X3 (λX8 : ((set → set → set → set → set → (set → set → set → set Inj0 (Inj0 (setsum ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set → (set → set → set X6 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj0 (setsum (setsum ∅ ∅ ∅ ) (X7 (setsum (Inj1 ∅ (Inj0 ∅ (X6 (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (setsum ∅ ∅ (Inj1 ∅ (λX9 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ (setsum (setsum (setsum ∅ ∅ (X6 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ (Inj1 ∅ ) False ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (Inj0 (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set setsum (setsum ∅ (Inj0 ∅ X8 ) (setsum ∅ (setsum (setsum ∅ (Inj1 ∅ (setsum ∅ (X7 ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : (set → set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set X8 ) ∅ X3 (λX8 : ((set → set → set → set → set → (set → set → set → set ∅ ) (λX8 : (set → set → set → (set → set → set X6 ) ) → (∀X4 : (set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → (set → set → set → set X7 ) (λX8 : (set → set → set → (set → set → set Inj1 X7 ) X1 (λX8 : set ⇒ ∅ ) (setsum (Inj1 ∅ X6 ∅ (X5 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set X1 (λX8 : set ⇒ Inj0 X8 ) ∅ (setsum X5 ∅ ∅ (λX8 : set ⇒ Inj0 (Inj0 (setsum X6 X8 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 X4 ∈ X6 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (setsum (Inj0 (Inj1 ∅ X8 ) (λX8 : set ⇒ λX9 : (set → set → set X7 ) ∅ X0 (λX8 : set → set Inj1 ∅ ) (λX8 : set → set Inj0 X7 ) ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set X8 (setsum (Inj1 (setsum ∅ ∅ (Inj0 (Inj1 ∅ ) (λX8 : set → set Inj0 (Inj1 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X10 (setsum ∅ (Inj0 X9 ) (λX8 : set ⇒ λX9 : (set → set → set X6 ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ (X4 X5 (λX8 : set ⇒ λX9 : set ⇒ X8 ) ∅ (Inj0 X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMSvtuhMbkD3oQEuYgshv9CjdavromUpk5C )
∀X0 : ((set → set → set → set → (set → (set → set → set → prop ∀X1 : (set → (set → set → ((set → set → set → set → (set → set → (set → set → set → set → prop ∀X2 : ((((set → set → set → set → set → set → (set → (set → set → set → set → ((((set → set → set → (set → set → set → set → set → set → set → set → prop ∀X3 : (set → set → (set → set → (((set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set (Inj0 ∅ ∈ setsum ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 ∅ ) → X0 (λX8 : set → set X6 ) ∅ (λX8 : set ⇒ λX9 : set → set ∅ ) X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 ) (λX8 : (set → set → set λX9 : set → set setsum (Inj1 (X9 (setsum ∅ ∅ (setsum (X9 X6 (Inj1 ∅ ) ) → (∀X4 : ((set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) (λX8 : (set → set → set λX9 : set → set X9 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : ((set → set → set → set → set → set λX9 : set → (set → set → set setsum (X8 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (Inj1 ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X8 (λX12 : set → set ∅ ) (λX12 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set X2 (λX8 : ((set → set → set → set → set → set λX9 : set → (set → set → set Inj1 (Inj1 (Inj1 ∅ ) (λX8 : ((set → set → set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 (setsum (Inj0 (Inj0 ∅ (Inj1 X6 ∈ X4 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ X7 ∈ setsum ∅ (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X9 ) X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set λX9 : set → set Inj1 (Inj0 (Inj1 X7 ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set → set ∅ ) (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set setsum ∅ X7 ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X0 (λX8 : set → set Inj1 X6 ) ∅ (λX8 : set ⇒ λX9 : set → set setsum X6 ∅ ) (setsum (Inj1 (Inj0 ∅ ∅ ∈ Inj1 (setsum (Inj0 X6 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGZaijGfKWz2EtBq9bGYmmMUrY3p6uYAe1 )
∀X0 : (set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (Inj0 (setsum ∅ ∅ ∈ Inj1 (setsum X7 (Inj1 (setsum ∅ ∅ → X3 (λX8 : set ⇒ X7 ) (setsum X6 ∅ (setsum (setsum X6 (setsum (Inj0 ∅ X6 (setsum (Inj1 (setsum ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ setsum X6 (Inj1 ∅ ) (Inj0 ∅ ∅ X2 (λX8 : set ⇒ setsum ∅ (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : ((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → (set → set → set X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X6 ) ) → (∀X4 : (((set → set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ setsum (Inj1 (setsum X7 (setsum ∅ ∅ (Inj1 (X5 (Inj0 ∅ ) (λX8 : set ⇒ Inj1 X8 ) X1 (λX8 : set ⇒ X5 (setsum (Inj0 (setsum ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ setsum (setsum (X8 ∅ (Inj1 ∅ (Inj1 ∅ ∅ ∅ ) ) → (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (setsum ∅ (setsum (setsum ∅ ∅ ∅ ∈ Inj1 ∅ → X1 (λX8 : set ⇒ Inj1 (Inj0 X8 ) (λX8 : set → set → set → set λX9 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → set → set X1 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ setsum (X8 ∅ (setsum ∅ ∅ (X8 (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 ∅ (setsum ∅ (Inj0 (Inj0 ∅ ) (Inj1 (setsum (Inj0 (setsum ∅ ∅ (Inj0 X6 ∈ Inj0 (Inj1 (X7 (λX8 : set → set λX9 : set → set ∅ ) X5 (Inj0 ∅ ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum X6 (Inj1 ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ (setsum X6 (setsum ∅ ∅ ) ∅ (setsum (setsum ∅ (setsum (setsum ∅ ∅ X6 X6 ∈ Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMVjWG7NeMEMXCeGXCfMkjas2DCPStReUV7 )
∀X0 : ((set → ((set → set → set → set → set → set → prop ∀X1 : ((set → set → set → ((set → set → set → (set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → (set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ setsum (Inj1 (Inj0 ∅ (X6 ∅ ) (λX8 : set ⇒ setsum (X5 ∅ X7 ) (λX8 : set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ Inj1 (setsum (setsum ∅ ∅ ∅ ) (X5 (λX9 : set ⇒ X7 ) (Inj1 ∅ ) (λX8 : set → set → set λX9 : set ⇒ setsum (Inj0 ∅ X9 ) (X4 ∅ ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set → (set → set → set X1 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set Inj0 (Inj1 (setsum (setsum ∅ ∅ ∅ ) (setsum ∅ X5 X2 (λX8 : set ⇒ Inj0 ∅ ) (Inj1 X5 ) → (∀X4 : set → ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ X4 X7 (λX8 : set → set Inj1 X5 ) (λX8 : set ⇒ setsum (setsum (Inj1 ∅ ∅ ∅ ) ∅ → X2 (λX8 : set ⇒ setsum X6 (Inj1 ∅ ) (Inj0 X7 X0 (λX8 : set → ((set → set → set → set Inj0 X5 ) (Inj1 (setsum (setsum (setsum ∅ ∅ ∅ (setsum (X4 ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ (Inj0 ∅ ) → (∀X4 : (((set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → (set → set → set → set X1 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set X11 (setsum (X10 (λX12 : set ⇒ setsum ∅ ∅ ) ∅ ) X5 X1 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set X11 (X11 ∅ ) ∅ ) → (∀X4 : (set → set → ((set → set → set → set ∀X5 : (set → set → set ∀X6 : (((set → set → set → set → set → ((set → set → set → set → set → set ∀X7 : set → set X1 (λX8 : set → set λX9 : set ⇒ λX10 : (set → set → set λX11 : set → set ∅ ) (Inj1 (X4 (λX8 : set ⇒ X8 ) (λX8 : set → set X6 (λX9 : (set → set → set → set setsum ∅ ∅ ) (λX9 : set → set ∅ ) ∅ (setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → ((set → set → set → set X5 (λX9 : set ⇒ λX10 : set → set X8 ∅ (λX11 : set → set ∅ ) ) ) (Inj1 X4 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , (setsum ∅ X7 ∈ X6 (λX8 : set ⇒ ∅ ) → X0 (λX8 : set → ((set → set → set → set setsum (Inj1 (Inj0 (Inj1 ∅ (Inj1 ∅ ) ∅ X2 (λX8 : set ⇒ Inj1 (Inj1 (X6 (λX9 : set ⇒ ∅ ) ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXYxXEgmNheiavLWg4KZUfAgFC386btePg )
∀X0 : (set → ((set → set → (set → set → set → set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → (set → set → (set → set → set → set → set → (set → set → (set → (set → set → set → (set → set → set → prop ∀X2 : ((set → set → set → (set → set → set → prop ∀X3 : (set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set (Inj0 X6 ∈ Inj1 (setsum X5 ∅ → X1 (λX8 : ((set → set → set → set → set → (set → set → (set → set → set → set Inj1 (Inj1 (setsum ∅ (X8 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set Inj1 (Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) X3 (λX8 : set ⇒ ∅ ) ∅ ∅ (setsum (setsum (setsum (Inj1 ∅ X6 (setsum (Inj1 ∅ (setsum ∅ ∅ (X7 (Inj0 (Inj1 ∅ (λX8 : set → set setsum X6 (setsum ∅ ∅ ) X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set → set ∀X7 : set → ((set → set → set → set X3 (λX8 : set ⇒ X8 ) ∅ (setsum X5 ∅ (Inj0 (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) X4 (Inj0 (Inj1 X5 ∈ X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj1 (setsum ∅ ∅ ) (Inj0 (setsum (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ setsum (setsum (setsum (Inj0 ∅ ∅ ∅ (Inj1 X10 ) (setsum X4 (setsum ∅ X4 ∅ X2 (λX8 : set → set X5 ) (λX8 : set ⇒ X8 ) ∅ ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set X2 (λX8 : set → set Inj1 (Inj0 X5 ) (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ) (setsum ∅ (Inj0 (setsum ∅ (Inj1 ∅ X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ setsum ∅ (setsum (setsum (setsum ∅ ∅ ∅ ∅ ) (Inj0 (X6 (setsum ∅ (X6 ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : (set → set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj1 ∅ ) (Inj1 ∅ ∅ (X6 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) ∅ X1 (λX8 : ((set → set → set → set → set → (set → set → (set → set → set → set setsum (setsum (X6 (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set ⇒ ∅ ) (setsum ∅ ∅ (X6 (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ setsum X7 (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum (X6 (λX10 : set ⇒ setsum X8 ∅ ) (λX10 : set ⇒ X7 ) (X9 (Inj1 ∅ (X6 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (X6 (λX10 : set ⇒ setsum ∅ ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) X7 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set → set ∀X6 : set → set ∀X7 : (set → (set → set → set → set (setsum (Inj0 (setsum ∅ (setsum ∅ ∅ ∅ ∈ setsum ∅ (Inj0 ∅ → X1 (λX8 : ((set → set → set → set → set → (set → set → (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ setsum (Inj1 (setsum ∅ (Inj0 ∅ (X5 (Inj1 (setsum ∅ ∅ (λX9 : set ⇒ X6 (setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 (Inj1 ∅ ) (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set setsum (X6 X8 (setsum ∅ (X9 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 (λX10 : set ⇒ λX11 : set → set ∅ ) (Inj1 X8 ) X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ X8 ) ∅ (setsum (setsum X4 (setsum ∅ X4 X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ Inj0 ∅ ) (setsum X7 (setsum (Inj0 (setsum ∅ ∅ (Inj0 ∅ (X5 ∅ ) → (∀X4 : ((set → set → set → set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set λX10 : set ⇒ X10 ) (X4 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set λX9 : set ⇒ Inj1 X9 ) ∅ X1 (λX8 : ((set → set → set → set → set → (set → set → (set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 X11 ) (λX9 : set ⇒ setsum (setsum ∅ X9 (Inj1 (Inj1 ∅ ) (λX9 : set ⇒ ∅ ) (X8 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 (Inj0 ∅ ) (λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX9 : set ⇒ X8 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) (λX10 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ setsum ∅ ∅ ) (X8 (λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ ) ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKyTtwa3Dnt9ZaZs1TWXZs2BwbMSev7gn3 )
∀X0 : ((set → (set → set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → (set → (set → set → set → set → prop ∀X2 : ((((set → set → set → set → ((set → set → set → set → (set → set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (Inj0 ∅ X3 (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) X5 ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (Inj1 X6 X1 (λX8 : set → set setsum X6 (setsum ∅ (setsum ∅ ∅ ) (X5 (λX8 : set ⇒ Inj1 ∅ ) (setsum (setsum (Inj0 ∅ X7 (setsum (setsum ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (setsum (setsum ∅ (Inj0 ∅ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set ∀X7 : (set → set → set X2 (λX8 : ((set → set → set → set → ((set → set → set → set → (set → set → set X7 (λX9 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (X7 (λX10 : set ⇒ ∅ ) ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : ((set → set → set → set → ((set → set → set → set → (set → set → set setsum X5 (Inj0 (setsum X5 (Inj1 ∅ ) (Inj0 ∅ False ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X1 (λX8 : set → set Inj1 (setsum (Inj0 (setsum ∅ ∅ ∅ ) (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) ) → (∀X4 : (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set ∀X7 : (set → set → set → set (setsum X5 (X4 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ Inj0 ∅ ) ) (setsum (X6 (λX8 : set ⇒ ∅ ) (Inj0 ∅ (Inj0 (setsum ∅ ∅ ∅ ∈ Inj0 (setsum ∅ (Inj1 (Inj1 ∅ → X1 (λX8 : set → set setsum (Inj1 (X7 (λX9 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (setsum (setsum ∅ (setsum ∅ ∅ (Inj0 ∅ ) (setsum (X6 (λX8 : set ⇒ setsum ∅ X5 ) (X6 (λX8 : set ⇒ setsum (setsum ∅ ∅ (X7 (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj0 ∅ X10 (X9 ∅ ) X0 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (X8 ∅ (λX11 : set ⇒ ∅ ) (X7 (λX11 : set ⇒ Inj0 (setsum ∅ ∅ ) X10 ) (X7 (λX8 : set ⇒ X5 ) (X7 (λX8 : set ⇒ Inj1 X5 ) ∅ ) → (∀X4 : set , ∀X5 : set → set → (set → set → set ∀X6 : set → set ∀X7 : set , (Inj0 X7 ∈ Inj0 (X6 (Inj1 ∅ → X0 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (setsum (Inj0 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (setsum (setsum (setsum ∅ ∅ ∅ (Inj1 ∅ (X7 (Inj0 (setsum ∅ ∅ (setsum (Inj1 (Inj0 X6 (setsum (Inj0 X6 (Inj1 (setsum ∅ ∅ ∈ X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMU569RurQqCCGp6v6kiAmZPMvys3La3bir )
∀X0 : ((set → set → (set → set → set → set → (set → (set → set → set → set → (set → set → set → set → set → (set → set → prop ∀X1 : (((((set → set → set → (set → set → set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → set → set → set → set → prop ∀X3 : (set → set → (((set → set → set → set → set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ Inj1 (Inj0 (setsum (setsum ∅ ∅ ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set → set → set setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ X8 ) (λX8 : (set → set → set → set → set → set Inj1 ∅ ) (X6 ∈ Inj0 (X5 (λX8 : (set → set → set → set Inj0 (setsum ∅ ∅ ) X4 X7 ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → ((set → set → set → set → set → set (Inj1 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 ∅ ∈ Inj1 ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) (Inj1 ∅ ∅ (X7 (λX8 : set → set → set ∅ ) (λX8 : set → set setsum (Inj0 (setsum ∅ ∅ (X8 (Inj0 ∅ ) (setsum (X5 (λX8 : set → set setsum ∅ ∅ ) ∅ (setsum (setsum (setsum ∅ ∅ ∅ (X5 (λX8 : set → set setsum ∅ ∅ ) ) → (∀X4 : (((set → set → set → set → set ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) X7 (setsum (setsum (X5 (λX8 : (set → set → set λX9 : set → set setsum ∅ ∅ ) (X5 (λX8 : (set → set → set λX9 : set → set Inj1 ∅ ) X6 ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ ) X6 (X5 (λX8 : (set → set → set λX9 : set → set setsum (Inj1 X7 (setsum (Inj0 ∅ (setsum ∅ ∅ ) (Inj0 ∅ ) → (∀X4 : set → set → set ∀X5 : set → set ∀X6 : (((set → set → set → set → set → (set → set → (set → set → set ∀X7 : set , (setsum (Inj0 (Inj0 (Inj1 ∅ (X4 ∅ ∅ ∈ setsum (Inj1 (Inj0 (setsum ∅ ∅ (Inj1 (Inj0 (setsum ∅ ∅ → X1 (λX8 : (((set → set → set → (set → set → set → set → set setsum (X6 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ X9 ) (Inj1 (Inj1 (X6 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (Inj1 (Inj1 (Inj0 (Inj1 ∅ (Inj1 (Inj1 (X4 ∅ (X4 ∅ ∅ X1 (λX8 : (((set → set → set → (set → set → set → set → set Inj1 (Inj0 ∅ ) (X6 (λX8 : (set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 (setsum (Inj1 ∅ (X5 ∅ ) (Inj0 (X4 ∅ (X4 (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → (set → set → set ∀X6 : (set → set → set → set ∀X7 : set → set X1 (λX8 : (((set → set → set → (set → set → set → set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) ∅ (setsum (setsum (X5 ∅ (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (X6 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (Inj0 (Inj1 (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set (Inj0 (setsum (Inj0 ∅ X6 ∈ Inj0 (setsum (Inj0 (Inj1 ∅ (Inj0 (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj0 (Inj1 ∅ ) (setsum (setsum (Inj1 ∅ ∅ (Inj1 (X4 X6 (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 X5 (Inj0 (Inj1 (X7 (Inj1 ∅ (λX8 : set ⇒ X7 ∅ (λX9 : set ⇒ ∅ ) ) X0 (λX8 : set → set → (set → set → set → set λX9 : set → (set → set → set X8 (X8 (Inj0 (Inj1 ∅ (X8 (X7 ∅ (λX10 : set ⇒ ∅ ) (X9 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ X7 ∅ (λX11 : set ⇒ ∅ ) ) (Inj1 ∅ (λX10 : set ⇒ ∅ ) (X7 (X9 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ setsum ∅ (setsum (X8 ∅ ∅ (λX11 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ ) (X7 ∅ (λX10 : set ⇒ Inj0 (Inj1 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : (set → set → set → set (setsum (Inj1 (Inj1 (Inj1 ∅ ∅ ∈ setsum (Inj0 ∅ (Inj0 (setsum (Inj1 ∅ (Inj1 ∅ → X0 (λX8 : set → set → (set → set → set → set λX9 : set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ X6 (setsum (X6 ∅ ∅ (Inj0 (Inj0 ∅ (Inj1 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum (setsum (setsum (Inj1 ∅ (Inj1 ∅ ∅ X8 ) (X7 (λX8 : set ⇒ X5 ) (Inj1 (Inj1 (Inj0 ∅ (Inj1 ∅ (Inj0 X5 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJkhGiYMh9j15WoWxN7HbpxYiNN2M6eB12 )
∀X0 : (set → set → set → (set → (set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → ((set → set → set → set → set → (((set → set → (set → set → set → set → set → set → (set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → ((set → set → set → set → set → set → set → set → prop ∀X3 : (((set → set → set → set → set → set → set → (set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X3 (λX8 : (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → set → set → set → set setsum ∅ (X6 (X6 (setsum ∅ ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ X7 (λX9 : set → set λX10 : set ⇒ Inj0 X10 ) ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X7 ) (X4 ∈ Inj0 (Inj0 (X6 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) X4 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∅ ) → (∀X4 : (((set → set → set → set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X4 (λX8 : (set → set → set X5 ) (λX8 : set → set Inj1 X5 ) ∈ setsum ∅ ∅ → X2 (λX8 : (((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (setsum (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set → ((set → set → set → set → set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ setsum (setsum (setsum ∅ (setsum ∅ ∅ (Inj0 X10 (X9 (λX13 : set ⇒ X10 ) ) (Inj0 (setsum (X5 (λX8 : set → set λX9 : set ⇒ X9 ) (Inj1 (Inj1 ∅ X3 (λX8 : (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ X8 ) ) → (∀X4 : (((set → set → set → set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : (set → set → set → set setsum (Inj0 X6 (X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : (set → set → (set → set → set Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ) ∅ (setsum (setsum X7 (Inj1 (setsum ∅ ∅ (Inj1 ∅ (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (setsum (setsum ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (setsum X7 (Inj1 ∅ (setsum (Inj1 (Inj0 ∅ (Inj0 X5 ∈ setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ → X1 (λX8 : set ⇒ λX9 : (set → set → set → set setsum X6 (Inj1 ∅ ) (λX8 : (set → set → (set → set → set setsum X5 (Inj0 (setsum ∅ (setsum ∅ ∅ ) X5 (setsum X5 ∅ (λX8 : set ⇒ setsum ∅ (Inj1 (setsum (setsum ∅ ∅ X5 ) (setsum (Inj1 (Inj1 (Inj0 ∅ (Inj0 X6 X1 (λX8 : set ⇒ λX9 : (set → set → set → set X7 ) (λX8 : (set → set → (set → set → set setsum (Inj0 (X8 (λX9 : set ⇒ X6 ) (λX9 : set ⇒ ∅ ) X7 ) X4 (Inj0 ∅ (λX8 : set ⇒ ∅ ) X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set → set → set → set ∀X7 : set → set (Inj1 (X5 (λX8 : (set → set → set setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 ∅ ∅ ∅ ) ∈ Inj0 ∅ → X0 (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 (setsum ∅ (Inj0 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 X10 ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj0 X5 ∈ Inj0 (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ → X0 (λX8 : set ⇒ X5 ) X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 ) (λX8 : set → set λX9 : set ⇒ setsum (X6 X9 ∅ ) X0 (λX8 : set ⇒ Inj0 (Inj0 (X6 X7 ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ X10 ) (λX8 : set → set λX9 : set ⇒ setsum ∅ (Inj1 (Inj1 X9 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMX3SK7EaU9yRrcZ4KoT47nrhbADsSJvYok )
∀X0 : ((set → set → set → (set → set → (((set → set → set → (set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → set → (set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → (set → set → set → set → ((set → (set → set → set → set → set → ((set → set → set → set → set → prop (∀X4 : ((set → set → set → set ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → (set → set → set X1 (λX8 : set ⇒ ∅ ) (setsum (setsum (setsum (X7 ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (X7 (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ X6 ) (λX8 : set ⇒ Inj0 ∅ ) (Inj1 ∅ X3 (λX8 : (((set → set → set → set → set → set → (set → set → set ∅ ) (λX8 : set → (set → set → set → set X6 ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → (set → set → (set → set → set → set X3 (λX8 : (((set → set → set → set → set → set → (set → set → set X8 (λX9 : (set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX9 : set ⇒ X8 (λX10 : (set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ X9 ) (λX10 : set ⇒ setsum (setsum ∅ ∅ (Inj0 ∅ ) ) ) (λX8 : set → (set → set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (Inj0 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X6 (setsum ∅ (Inj0 (setsum ∅ ∅ ∈ setsum ∅ ∅ → X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (X6 (Inj1 (Inj0 ∅ ) X1 (λX8 : set ⇒ ∅ ) (setsum X5 (setsum (Inj0 (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → set → (set → set → (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set → set (setsum (setsum ∅ (setsum ∅ X6 ∅ ∈ X6 → X1 (λX8 : set ⇒ Inj1 (X5 (λX9 : set ⇒ Inj1 ∅ ) (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ Inj1 (Inj1 ∅ ) (setsum (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum X7 (setsum (Inj0 X7 (setsum X7 ∅ ) (Inj0 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 X5 X1 (λX8 : set ⇒ X6 (Inj0 X5 ) (Inj0 X4 ) → (∀X4 : set → ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set Inj1 X7 ) (λX8 : set ⇒ Inj0 (Inj0 X7 ) (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) X0 (λX8 : set → set Inj0 (Inj0 X6 ) (λX8 : set ⇒ setsum (setsum ∅ X5 (Inj1 (setsum ∅ (setsum ∅ ∅ ) (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum (Inj1 (Inj1 (setsum ∅ ∅ (X8 (λX11 : set ⇒ setsum ∅ (setsum ∅ ∅ ) ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ (X6 (Inj1 ∅ ∈ Inj1 (setsum (setsum ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWomh74cFzdGm8eLx6axLeuygH6f3WbcK7 )
∀X0 : ((set → set → set → ((set → set → set → set → set → set → (set → set → set → (set → set → prop ∀X1 : (set → set → (set → set → set → set → ((set → set → set → set → set → set → (set → set → prop ∀X2 : (set → set → set → ((set → set → set → set → set → set → prop ∀X3 : (set → set → ((set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set setsum (Inj0 (Inj0 ∅ X7 ) (λX8 : set → set → set → set λX9 : set ⇒ setsum (setsum (setsum (Inj1 ∅ X9 (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj0 (Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ X7 ) X3 (λX8 : set ⇒ X5 ) (λX8 : set → set λX9 : set ⇒ Inj1 X7 ) (λX8 : set → set ∅ ) ) → (∀X4 : ((set → set → set → set ∀X5 : (set → set → ((set → set → set → set → (set → set → set ∀X6 : (set → set → set ∀X7 : set , X3 (λX8 : set ⇒ setsum ∅ (Inj0 X8 ) (λX8 : set → set λX9 : set ⇒ setsum ∅ X9 ) (λX8 : set → set ∅ ) (Inj0 (Inj0 X7 ∈ Inj0 (Inj0 (setsum X7 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ X7 ) X5 (λX8 : set → set → set X8 (Inj0 X7 (setsum ∅ (setsum X7 (Inj0 ∅ ) (setsum (Inj1 (X6 (setsum ∅ ∅ ∅ (Inj0 (Inj0 (setsum ∅ ∅ X2 (λX8 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) (X6 (X6 ∅ (λX8 : set → set → set setsum (X8 (setsum ∅ (setsum ∅ ∅ (setsum ∅ (Inj1 ∅ (Inj0 (X8 ∅ (Inj0 ∅ ) X4 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set X2 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set → set → set ∅ ) (setsum (Inj0 (setsum (setsum ∅ ∅ (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum X6 (X7 (λX8 : set ⇒ λX9 : set → set Inj1 (Inj1 ∅ ) False ) → (∀X4 : set → set → set → set → set ∀X5 : (((set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 ∅ ∈ Inj0 (X5 (λX8 : (set → set → set λX9 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set setsum (X7 ∅ (X10 ∅ (Inj0 X8 ) (λX8 : set → set → set → set λX9 : set ⇒ X9 ) (λX8 : set ⇒ Inj0 (setsum X6 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set Inj1 (setsum (setsum (X10 ∅ ∅ (Inj1 ∅ (X10 (X10 ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set → set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (Inj1 (Inj1 (Inj1 ∅ ) X3 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X9 ) (λX8 : set → set ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set Inj0 ∅ ) (λX8 : set → set → set → set X6 ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 (Inj0 X8 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → (set → set → set → set → ((set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → set → set ∀X6 : set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : set → set ∅ ) (λX8 : set → set → set → set setsum (X6 (Inj1 (X5 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ λX10 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) (X5 (X8 ∅ ∅ ∅ (λX9 : set → set λX10 : set ⇒ X7 ) (setsum ∅ ∅ (Inj1 ∅ ) (setsum ∅ X7 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set Inj0 (setsum (Inj1 ∅ ∅ ) (Inj0 (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) (λX8 : set → set ∅ ) (X5 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ (Inj1 (Inj0 (Inj0 ∅ ∈ Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcAyH6xMvjpdkJtxJoYJXJi4sk8vNhHhRv )
∀X0 : (set → set → set → (set → ((set → set → set → set → set → prop ∀X1 : ((((set → set → set → (set → set → set → ((set → set → set → set → set → set → set → (((set → set → set → set → ((set → set → set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → ((set → set → set → set → set → ((((set → set → set → set → set → prop ∀X3 : (set → set → (set → set → ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj1 (X7 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ X8 ) (λX8 : set → set → set λX9 : set ⇒ Inj0 (X8 ∅ (X7 (X8 ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set (Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X7 ∅ (λX8 : set → set X8 ∅ ) ∈ setsum ∅ (Inj0 ∅ → X3 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ setsum (setsum (Inj1 ∅ ∅ X5 ) (λX8 : set → set → set λX9 : set ⇒ Inj0 ∅ ) X2 (λX8 : set → set → set λX9 : (set → set → set → set ∅ ) (λX8 : ((set → set → set → set setsum (Inj0 (X7 (X7 ∅ (λX9 : set → set ∅ ) (λX9 : set → set Inj1 ∅ ) (setsum (setsum (setsum ∅ ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X6 ) X2 (λX8 : set → set → set λX9 : (set → set → set → set Inj0 (setsum X7 (setsum X6 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set setsum X7 (X8 (λX9 : set → set ∅ ) ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set → set → set → set X2 (λX8 : set → set → set λX9 : (set → set → set → set Inj0 ∅ ) (λX8 : ((set → set → set → set ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → ((set → set → set → set → set → set ∀X7 : set , X1 (λX8 : ((set → set → set → (set → set → set → ((set → set → set → set → set → set Inj0 (setsum X5 ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set X6 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set → set ∅ ) (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X8 (λX10 : set ⇒ λX11 : set ⇒ Inj1 (setsum ∅ ∅ ) ) (setsum ∅ (setsum (setsum ∅ X4 (Inj0 ∅ (Inj1 (Inj0 ∅ (λX8 : set ⇒ X5 ) X1 (λX8 : ((set → set → set → (set → set → set → ((set → set → set → set → set → set Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (Inj1 (Inj1 X4 (Inj1 ∅ (λX8 : set ⇒ X7 ) ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set X1 (λX8 : ((set → set → set → (set → set → set → ((set → set → set → set → set → set X6 ) (λX8 : (set → set → set → set λX9 : (set → set → set setsum ∅ (Inj1 (X9 (λX10 : set ⇒ ∅ ) ) (setsum (Inj0 (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (X5 (setsum (setsum ∅ ∅ ∅ (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 (X7 X9 (λX11 : set ⇒ X8 (λX12 : set ⇒ ∅ ) ) ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 (setsum ∅ (Inj0 (X5 ∅ ) (X5 (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (X7 ∅ (λX11 : set ⇒ ∅ ) ∅ ∅ ) ∈ Inj0 (setsum ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set → set → set (X6 ∈ X6 → X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum (setsum (setsum ∅ (Inj0 ∅ X6 (X9 (λX10 : set ⇒ ∅ ) (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : (set → (set → set → set → set → set → set (Inj1 (Inj1 (Inj0 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∈ setsum ∅ (setsum (Inj0 (Inj0 ∅ (setsum (Inj0 ∅ (Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum ∅ ∅ ) X1 (λX8 : ((set → set → set → (set → set → set → ((set → set → set → set → set → set X5 ) (λX8 : (set → set → set → set λX9 : (set → set → set setsum (setsum ∅ (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X10 ) (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) ∅ (setsum (setsum (X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ (setsum (Inj1 ∅ (Inj0 ∅ ) (Inj0 X4 (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) X5 (λX8 : set ⇒ X8 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMLmXzRW5FqYxiAGZzXuwoXBL2p3VpruMZ6 )
∀X0 : (set → set → (set → set → set → set → set → set → ((set → set → set → set → set → ((set → set → set → set → (set → set → prop ∀X1 : ((set → (set → set → (set → set → set → set → (((set → set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → (set → set → prop ∀X3 : (set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum (X5 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) (setsum (setsum (setsum ∅ ∅ ∅ ∅ ) X3 (λX8 : set ⇒ ∅ ) (λX8 : set → set Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set → set X8 ∅ ) (setsum (Inj1 X6 (Inj1 (setsum (setsum ∅ ∅ ∅ ∈ X5 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set (X4 ∈ X4 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) (λX8 : set ⇒ Inj1 X6 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set → set (setsum X4 X6 ∈ X6 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ X10 ) (λX8 : set ⇒ Inj1 (setsum (Inj0 (X5 ∅ (setsum ∅ (X5 ∅ ) X1 (λX8 : set → (set → set → (set → set → set Inj0 ∅ ) (λX8 : (set → set → set → set → set → set setsum ∅ (X5 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set → (set → set → (set → set → set X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X9 ∅ X7 ) ∅ ) (λX8 : (set → set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set ⇒ Inj0 X10 ) (Inj1 (setsum X5 (setsum ∅ ∅ (setsum X5 (Inj0 ∅ ) X1 (λX8 : set → (set → set → (set → set → set ∅ ) (λX8 : (set → set → set → set → set → set Inj1 (X8 (λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) X7 (Inj0 ∅ ) (X8 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set → (set → set → (set → set → set X6 (setsum (X8 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ (X8 ∅ (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) (λX8 : (set → set → set → set → set → set Inj1 ∅ ) (Inj0 X7 ∈ Inj1 X7 ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set ∀X6 : set → set ∀X7 : (set → set → set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ X12 ) (setsum ∅ (setsum (X5 (λX8 : (set → set → set → set setsum ∅ ∅ ) X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 ∅ (setsum (Inj1 (Inj0 ∅ (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ λX12 : set ⇒ Inj1 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKnac9jWVAyt7SornP3XyHzrFwNsZcm1qH )
∀X0 : ((set → (set → set → set → set → set → set → set → (((set → set → set → (set → set → set → set → (set → set → prop ∀X1 : (set → (set → set → set → set → set → set → (set → set → (((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → set → ((set → set → set → set ∀X6 : set → set ∀X7 : (set → set → set → set X3 (λX8 : set ⇒ Inj0 X8 ) (setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum ∅ ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (X6 ∅ ) X3 (λX8 : set ⇒ setsum (X6 (setsum X8 (setsum ∅ ∅ ∅ ) (setsum (Inj1 (X5 (λX8 : (set → set → set → set setsum ∅ ∅ ) (λX8 : set → set setsum ∅ ∅ ) (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (Inj0 (Inj0 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ X5 (setsum (setsum ∅ ∅ X5 ) (Inj1 ∅ X2 (λX8 : set → set ∅ ) (setsum (setsum (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ (X6 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → ((set → set → set → set X2 (λX8 : set → set Inj1 (X7 (Inj1 (Inj1 ∅ (λX9 : set → set Inj0 (setsum ∅ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → (set → set → set → (set → set → set → set ∀X7 : set , X2 (λX8 : set → set setsum X7 ∅ ) ∅ (X4 ∈ setsum X5 (setsum (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : ((set → set → set → set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set Inj1 (setsum (X5 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X10 ∅ ) ∅ ) ) → (∀X4 : set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 ∈ X5 (Inj1 X6 ∅ X1 (λX8 : set ⇒ λX9 : set → set → set → set λX10 : set ⇒ setsum X8 (setsum (Inj1 (Inj1 ∅ X8 ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set X7 ) X1 (λX8 : set ⇒ λX9 : set → set → set → set λX10 : set ⇒ X10 ) (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → set Inj1 (X8 (λX9 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) (Inj0 (Inj1 ∅ ) ) → (∀X4 : ((set → set → set → set → set → (set → set → set ∀X5 : set → ((set → set → set → set ∀X6 : (set → (set → set → set → ((set → set → set → set ∀X7 : (((set → set → set → set → set → set → set (Inj0 (Inj0 (Inj1 (Inj1 ∅ ∈ Inj1 (Inj1 (X5 (Inj0 ∅ (λX8 : set → set ∅ ) → X2 (λX8 : set → set setsum ∅ (Inj1 (Inj1 (X8 ∅ ) (setsum (Inj0 (X4 (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ (λX8 : set ⇒ Inj0 ∅ ) (setsum ∅ (setsum (X7 (λX8 : (set → set → set → set ∅ ) ∅ (Inj0 ∅ X0 (λX8 : set → (set → set → set → set → set → set X7 (λX9 : (set → set → set → set ∅ ) (setsum (X5 (Inj0 ∅ (λX9 : set → set setsum ∅ ∅ ) (X8 (Inj0 ∅ (λX9 : set ⇒ λX10 : set ⇒ X8 ∅ (λX11 : set ⇒ λX12 : set ⇒ ∅ ) ∅ ∅ ) (X8 ∅ (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ∅ ∅ ) (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ setsum ∅ X8 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → set ∀X7 : set , (Inj0 X7 ∈ X4 (X4 (Inj1 (X6 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) → X0 (λX8 : set → (set → set → set → set → set → set ∅ ) (λX8 : (set → set → set → (set → set → set ∅ ) (λX8 : set ⇒ setsum (setsum X8 X8 ∅ ) X1 (λX8 : set ⇒ λX9 : set → set → set → set λX10 : set ⇒ setsum (setsum (Inj0 X7 (Inj1 (Inj0 ∅ (Inj1 (Inj1 ∅ ) (λX8 : set ⇒ Inj1 (Inj1 (X6 (λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ X9 (λX12 : set ⇒ ∅ ) ∅ ) ) (λX8 : (set → set → set → set setsum (Inj0 ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMXRwmRowAW39d6vfxSJSkiMfSLdshhUZDH )
∀X0 : ((((set → set → set → set → set → (set → set → set → set → set → (set → set → set → (set → set → prop ∀X1 : (set → set → set → set → (set → set → set → prop ∀X2 : (set → set → ((set → set → set → set → (set → set → set → set → set → prop ∀X3 : ((set → set → set → set → (set → set → set → set → set → (set → set → set → set → prop (∀X4 : (set → (set → set → set → set → set → (set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set (Inj1 ∅ ∈ Inj1 (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 X5 → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) ∅ (setsum (setsum (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (X7 (λX8 : (set → set → set → set λX9 : set → set setsum ∅ ∅ ) (setsum ∅ (Inj1 (Inj0 ∅ (λX8 : set ⇒ X7 (λX9 : (set → set → set → set λX10 : set → set Inj0 (X9 (λX11 : set ⇒ ∅ ) ∅ ) ) (Inj1 (setsum (setsum (Inj0 ∅ (Inj0 ∅ (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (Inj1 ∅ (Inj0 ∅ (λX8 : set ⇒ Inj1 X8 ) (Inj0 (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) (Inj0 (setsum ∅ ∅ X5 (Inj1 (X6 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) ∅ ∈ Inj1 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → ((set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum ∅ (Inj1 (X8 X10 ) ∅ (setsum (Inj0 X7 (setsum (Inj0 (setsum ∅ ∅ ∅ (λX8 : set ⇒ setsum (setsum X8 ∅ (X5 (λX9 : (set → set → set Inj0 (Inj0 ∅ ) (λX9 : set → set ∅ ) ) ∅ (Inj1 (setsum (Inj0 ∅ X4 X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ X11 X9 ) X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set → set ∀X7 : set , (setsum ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X6 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ∅ ) (Inj1 (setsum ∅ ∅ ∈ X7 → X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set λX12 : set ⇒ X9 ) ∅ X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set X10 ) ∅ (X5 ∅ (λX8 : set ⇒ X7 ) ∅ X4 ) → (∀X4 : ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set → set → set (Inj1 (setsum X6 (Inj0 ∅ ∈ Inj1 (Inj1 (Inj0 ∅ → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set ∅ ) (X4 (λX8 : set → set → set λX9 : set ⇒ Inj1 (X7 (X8 ∅ ∅ (X8 ∅ ∅ (Inj0 ∅ (setsum ∅ ∅ ) (setsum ∅ ∅ X5 (λX8 : set ⇒ Inj0 (setsum (X7 (setsum ∅ ∅ X6 (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) ∅ ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ setsum X8 X8 ) ∅ (λX8 : set ⇒ X5 ) (X7 X6 (Inj1 (setsum X6 (Inj1 ∅ (setsum X5 ∅ X5 ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → (set → set → set → set → set ∀X7 : set , (X4 (Inj0 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (Inj0 (X5 (setsum ∅ ∅ X7 ∈ Inj1 ∅ → X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ Inj0 (setsum (setsum ∅ ∅ ∅ ) (setsum ∅ (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 ∅ ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (Inj1 (Inj0 (Inj1 ∅ ) X7 (X4 (setsum (X4 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (X4 ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) (X6 (λX8 : set → set → set λX9 : set → set λX10 : set ⇒ setsum (X8 ∅ ∅ (Inj1 ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ X8 ) (setsum ∅ (setsum ∅ (setsum (setsum ∅ ∅ (X4 ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set ∀X6 : set → set → set ∀X7 : set → set (Inj1 (X5 (λX8 : set ⇒ λX9 : set → set Inj1 (X9 ∅ ) ∅ ∈ Inj0 ∅ → X0 (λX8 : ((set → set → set → set → set → (set → set → set → set X5 (λX9 : set ⇒ λX10 : set → set setsum ∅ ∅ ) (setsum (Inj1 ∅ (X8 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X6 ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) X0 (λX8 : ((set → set → set → set → set → (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum X9 (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ X6 (setsum ∅ (Inj0 (X5 (λX9 : set ⇒ λX10 : set → set ∅ ) ∅ (Inj1 ∅ ) ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 ∅ ∈ Inj0 (setsum ∅ (Inj0 (Inj1 ∅ → X0 (λX8 : ((set → set → set → set → set → (set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ setsum X11 ∅ ) (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ setsum X8 X7 ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum (X11 ∅ X10 ) (Inj0 ∅ ∅ (λX8 : set ⇒ X7 ) (setsum ∅ X6 (Inj1 (setsum (setsum (setsum ∅ ∅ (X5 ∅ (Inj0 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMhGzbcdXEEgj5uQ8vBLc4gegfdA2qF8UU )
∀X0 : ((set → set → set → (set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → set → ((((set → set → set → set → set → set → (set → set → set → set → prop ∀X2 : (set → set → set → ((set → set → set → ((set → set → (set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set ∀X7 : set , (Inj1 X5 ∈ setsum (setsum ∅ (Inj1 (Inj1 ∅ X7 → X0 (λX8 : set → set Inj0 (setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 X9 ) ∅ X3 (λX8 : set ⇒ ∅ ) (setsum X7 (Inj1 (setsum (Inj1 ∅ (X6 (λX8 : set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : (((set → set → set → set → set → (set → set → set X3 (λX8 : set ⇒ Inj1 X5 ) X4 False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → (set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , (X6 X4 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ ∅ ∈ X7 → X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (X6 ∅ (setsum ∅ ∅ ∅ ) (λX8 : set → set Inj0 (Inj0 ∅ ) (λX8 : set → set λX9 : set → set X8 (setsum (X8 X7 (Inj0 (X9 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set → set Inj0 (Inj0 X7 ) (λX8 : set → set λX9 : set → set X8 (Inj0 ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ∈ Inj0 (setsum (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj1 ∅ (Inj0 (setsum ∅ ∅ ) (λX8 : set → set ∅ ) (λX8 : set → set λX9 : set → set ∅ ) X1 (λX8 : (((set → set → set → set → set → set X7 (setsum (X8 (λX9 : (set → set → set → set ∅ ) ∅ (λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ) (Inj1 ∅ ) (λX8 : ((set → set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj0 (Inj1 X6 ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum (setsum (Inj1 (Inj1 ∅ ∅ (Inj1 (setsum (X7 ∅ (setsum ∅ ∅ ∈ Inj0 ∅ → X1 (λX8 : (((set → set → set → set → set → set X5 ) (λX8 : ((set → set → set → set → set X5 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X1 (λX8 : (((set → set → set → set → set → set Inj1 (Inj1 (Inj1 (setsum ∅ ∅ ) (λX8 : ((set → set → set → set → set X5 ) (λX8 : set ⇒ λX9 : set ⇒ X7 (setsum ∅ X9 ) (setsum ∅ (X4 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set → set Inj0 (setsum X5 ∅ ) (λX8 : set → set λX9 : set → set ∅ ) X0 (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (Inj0 ∅ ∅ X7 ) ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → (set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , (Inj1 X7 ∈ setsum ∅ X7 → X0 (λX8 : set → set setsum ∅ (Inj1 (X8 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (X5 (λX8 : set ⇒ ∅ ) X4 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) X3 (λX8 : set ⇒ Inj1 (setsum ∅ (Inj0 (Inj0 ∅ ) (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQPBVwvxHrbTh46AGwhZXdkR6UyB8TdhsJ )
∀X0 : (set → ((set → set → (set → set → set → set → set → set → (((set → set → set → set → (set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : ((((set → set → set → (set → set → set → set → set → set → (set → (set → set → set → set → prop ∀X3 : ((set → set → ((set → set → set → set → set → (set → set → set → ((set → set → set → (set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set → set ∀X7 : (set → (set → set → set → (set → set → set → set (Inj1 (X5 (λX8 : (set → set → set Inj0 ∅ ) (Inj1 (Inj1 ∅ (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 ∅ ∈ Inj0 (Inj1 (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) → X3 (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set → set X9 (λX12 : set ⇒ λX13 : set ⇒ Inj1 X13 ) ) (λX8 : set → set Inj1 (Inj1 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set ⇒ λX11 : set → set setsum ∅ ∅ ) (λX10 : set ⇒ setsum (setsum (Inj0 ∅ X8 ∅ ) (setsum (setsum (setsum ∅ ∅ (X7 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (setsum (X6 ∅ (setsum ∅ ∅ ) X3 (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set → set setsum (setsum (Inj1 (Inj1 ∅ (X11 (setsum ∅ ∅ (X8 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → (set → set → set → set X3 (λX8 : set → set λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set → set Inj1 (Inj0 (X8 (Inj1 ∅ ) (λX8 : set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set setsum (setsum (Inj1 ∅ (Inj0 ∅ (setsum X8 (setsum ∅ ∅ ) (setsum ∅ (setsum X5 (Inj1 ∅ (λX8 : (set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ X7 ∅ (λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 ∅ ) ) (setsum (Inj0 (setsum ∅ ∅ (X8 (λX10 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X4 ∈ Inj0 X7 → X2 (λX8 : ((set → set → set → (set → set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set → set → set Inj0 X6 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set → set → set ∀X7 : set , X2 (λX8 : ((set → set → set → (set → set → set → set → set Inj1 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set → set → set X6 (Inj1 (Inj1 (setsum ∅ ∅ ∅ (Inj0 (Inj1 (Inj0 ∅ (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (setsum (Inj0 ∅ ∅ ∈ setsum (setsum (Inj0 ∅ ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → (set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ setsum (Inj1 X8 ∅ ) (Inj1 (setsum (Inj1 X5 X7 (setsum ∅ (setsum (Inj1 (Inj1 ∅ (setsum ∅ (X6 (λX8 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set → set → (set → set → set → set X1 (λX8 : set ⇒ Inj1 X6 ) (Inj1 (Inj1 (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (Inj1 (Inj1 (X7 (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ X6 (λX8 : set ⇒ Inj1 ∅ ) ∅ (Inj1 ∅ ∈ Inj0 (setsum (X5 X6 (X5 (Inj0 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : ((set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set ∅ ) (setsum (X5 (λX8 : set → set λX9 : set → set setsum ∅ (Inj0 ∅ ) (X5 (λX8 : set → set λX9 : set → set X8 (X7 ∅ ) (λX8 : (set → set → set → set λX9 : set → set X6 (λX10 : set → set → set X8 (λX11 : set ⇒ Inj0 (Inj0 ∅ ) (X9 (setsum ∅ ∅ ) (Inj1 (setsum (X6 (λX10 : set → set → set ∅ ) ∅ ∅ ) X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set setsum (Inj0 (setsum (Inj0 ∅ (X7 ∅ (X9 (λX10 : set ⇒ setsum (Inj1 ∅ X10 ) (λX10 : set ⇒ X7 (X9 (λX11 : set ⇒ ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) (X6 (λX10 : set → set → set setsum ∅ ∅ ) (X6 (λX10 : set → set → set ∅ ) ∅ ) (X6 (λX8 : set → set → set X7 (Inj0 (Inj1 ∅ ) ∅ (λX8 : (set → set → set → set λX9 : set → set setsum ∅ (X7 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : set , (Inj0 ∅ ∈ Inj1 (Inj0 (setsum X7 (setsum ∅ ∅ → X0 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set setsum X8 X8 ) (setsum (X6 (λX8 : set → set ∅ ) (setsum ∅ (setsum (X6 (λX8 : set → set ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set → set X7 ) X2 (λX8 : ((set → set → set → (set → set → set → set → set X7 ) (λX8 : set ⇒ λX9 : set → set → set X6 (λX10 : set → set Inj0 (setsum (Inj1 ∅ X7 ) ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMdSVkuZ5HWPTLdBktb4xECEoSMM8BZWz3 )
∀X0 : (((set → set → set → set → set → prop ∀X1 : (set → (set → set → set → set → prop ∀X2 : (set → set → set → set → (set → set → set → prop ∀X3 : (set → (set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : (((set → set → set → set → set → (set → set → set → (set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , X0 (λX8 : (set → set → set Inj1 ∅ ) X7 X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set X8 ) (setsum ∅ (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) → (∀X4 : ((set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set X7 ∅ (λX10 : set → set ∅ ) X8 ) (Inj1 (X4 (λX8 : set → set setsum ∅ (setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ X6 → X2 (λX8 : set ⇒ setsum (Inj0 ∅ (setsum ∅ (Inj1 (setsum ∅ ∅ ) X7 X6 (λX8 : set ⇒ λX9 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set ⇒ setsum ∅ X5 ) X5 X5 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj0 ∅ X7 ) X2 (λX8 : set ⇒ setsum (Inj1 (Inj0 (Inj0 ∅ ∅ ) X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → (set → set → set → set → (set → set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ setsum (Inj0 (setsum (Inj0 ∅ (X7 ∅ (Inj0 (Inj0 ∅ ) (setsum (Inj0 (X5 (X5 ∅ ∅ ∅ (Inj0 (setsum (setsum ∅ ∅ (X5 ∅ ∅ (setsum (Inj1 (setsum ∅ (Inj0 ∅ X6 (λX8 : set ⇒ λX9 : set ⇒ X9 ) X1 (λX8 : set ⇒ λX9 : set → set setsum X6 (Inj0 (Inj1 ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X1 (λX8 : set ⇒ λX9 : set → set X6 ) (setsum ∅ ∅ (Inj1 ∅ ∈ Inj1 (X7 (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ (λX8 : set → set λX9 : set ⇒ Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ ) ∈ X6 → X3 (λX8 : set ⇒ λX9 : set → (set → set → set → set Inj1 (Inj1 ∅ ) (Inj0 (X4 (setsum ∅ (setsum ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum X9 (Inj0 ∅ ) X0 (λX8 : (set → set → set Inj1 (Inj1 (setsum X5 X5 ) (setsum X5 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set → set ∀X7 : set , X0 (λX8 : (set → set → set Inj0 ∅ ) (setsum ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcW3aNwx1GnSRdxN9KQsKecm458CuXxAKw )
∀X0 : (set → set → (set → set → set → ((set → set → set → (set → set → prop ∀X1 : (((((set → set → set → set → set → set → set → set → set → (set → set → (set → set → set → set → (set → set → (set → set → prop ∀X2 : ((((set → set → set → set → set → (set → set → set → set → set → ((set → set → set → set → ((set → set → set → set → set → prop ∀X3 : (set → ((set → set → set → set → ((set → set → set → set → (set → ((set → set → set → set → set → set → set → (set → set → ((set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X5 ∈ setsum X7 X6 → X3 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : (set → set → set X9 (λX11 : set ⇒ setsum ∅ ∅ ) (Inj1 (X10 (λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) X3 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : (set → set → set Inj0 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X10 ) (λX8 : set ⇒ Inj1 (Inj0 X6 ) (λX8 : set → set λX9 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : (set → set → set X7 (λX11 : set ⇒ λX12 : set ⇒ setsum (X9 (λX13 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (X9 (λX13 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum X5 (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj1 (Inj1 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum (X8 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ ∅ ) X0 (λX8 : set ⇒ X6 ∅ ) (λX8 : set ⇒ X6 (setsum ∅ (setsum ∅ ∅ ) (setsum X5 (X6 (X6 ∅ (λX8 : set → set setsum X5 (Inj0 ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (Inj0 ∅ (X6 ∅ X5 (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ∈ setsum X7 X7 → X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X7 (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (setsum ∅ (setsum ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) X2 (λX8 : ((set → set → set → set → set → (set → set → set → set ∅ ) (λX8 : set → set → set → set λX9 : (set → set → set → set X8 (Inj0 ∅ (Inj0 (Inj1 (X8 ∅ ∅ ∅ (X6 ∅ ) ) → (∀X4 : ((set → set → set → set → ((set → set → set → set → set ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set → set ∀X7 : (set → set → set X2 (λX8 : ((set → set → set → set → set → (set → set → set → set ∅ ) (λX8 : set → set → set → set λX9 : (set → set → set → set setsum (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (setsum (X9 (λX10 : set ⇒ ∅ ) ∅ ∅ (X7 (λX10 : set ⇒ X7 (λX11 : set ⇒ ∅ ) ) ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set , (Inj1 (setsum ∅ ∅ ∈ setsum X7 (Inj1 (Inj1 ∅ → X1 (λX8 : (((set → set → set → set → set → set → set → set X8 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum (X9 (λX12 : set ⇒ ∅ ) ∅ (Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) (λX8 : set ⇒ X6 (λX9 : set ⇒ ∅ ) (λX9 : set → set setsum X8 (Inj1 (setsum ∅ ∅ ) X5 ) (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) X1 (λX8 : (((set → set → set → set → set → set → set → set setsum ∅ (setsum (X6 (λX9 : set ⇒ ∅ ) (λX9 : set → set ∅ ) (Inj0 ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum X8 (X6 (λX9 : set ⇒ Inj0 ∅ ) (λX9 : set → set ∅ ) (setsum ∅ ∅ (Inj0 (setsum (setsum ∅ ∅ X8 ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : set → set ∀X7 : set → set (X6 (Inj0 (setsum ∅ ∅ ∈ X7 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ → X1 (λX8 : (((set → set → set → set → set → set → set → set setsum (X7 (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ (X10 (setsum (Inj0 ∅ (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) X2 (λX8 : ((set → set → set → set → set → (set → set → set → set ∅ ) (λX8 : set → set → set → set λX9 : (set → set → set → set X9 (λX10 : set ⇒ ∅ ) (setsum ∅ (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set (Inj1 (setsum ∅ (Inj0 ∅ ∈ setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 (Inj1 ∅ ) (Inj1 (setsum ∅ (setsum ∅ ∅ → X0 (λX8 : set ⇒ X7 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set ⇒ Inj1 ∅ ) (setsum (X4 ∅ ∅ (λX8 : set → set X6 ) (λX8 : set ⇒ X6 ) ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : (set → set → set ∀X6 : set → (set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ → X0 (λX8 : set ⇒ Inj0 (Inj0 (setsum (Inj0 ∅ ∅ ) (λX8 : set ⇒ X5 (λX9 : set ⇒ setsum ∅ X9 ) ) ∅ (λX8 : set → set ∅ ) (λX8 : set ⇒ setsum X8 (X5 (λX9 : set ⇒ setsum (setsum ∅ ∅ (Inj1 ∅ ) ) X1 (λX8 : (((set → set → set → set → set → set → set → set setsum (Inj0 (setsum (setsum ∅ ∅ (X5 (λX9 : set ⇒ ∅ ) (X8 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 X8 ) (λX8 : set ⇒ setsum ∅ (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ Inj1 (X6 (Inj1 (Inj1 ∅ (λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcX7tGT2RLXgHVcfwE5cvLiMjCekL4XbRk )
∀X0 : (set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → (set → (set → set → set → set → set → (((set → set → set → set → (set → set → set → prop ∀X2 : (((set → (set → set → set → set → set → set → set → ((((set → set → set → set → (set → set → set → set → ((set → set → set → set → set → (set → set → set → set → ((set → set → set → set → prop ∀X3 : (set → (set → set → set → set → set → ((((set → set → set → set → set → prop (∀X4 : (((set → set → set → (set → set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set → set Inj1 ∅ ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : (set → set → set → set Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum X7 (Inj0 (Inj0 ∅ ) (λX8 : set → set λX9 : set ⇒ X8 ∅ ) X3 (λX8 : set ⇒ λX9 : set → set → set → set setsum (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ X7 ) (λX8 : ((set → set → set → set X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set → set → set → set X3 (λX8 : set ⇒ λX9 : set → set → set → set X6 X8 (setsum (Inj1 (X9 ∅ ∅ ∅ ∅ ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → set Inj0 (X8 (λX9 : set → set ∅ ) ) (X4 ∈ Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum ∅ X7 X2 (λX8 : (set → (set → set → set → set → set → set X5 ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → (set → set → set → set → set → set X8 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (X10 X11 ) X7 ) (λX8 : ((set → set → set → set → (set → set → set → set λX9 : (set → set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (X5 (Inj0 X4 ∈ Inj0 X4 ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set → set (setsum ∅ ∅ ∈ setsum ∅ (X4 (λX8 : set ⇒ λX9 : set → set X9 (setsum ∅ ∅ ) → X1 (λX8 : ((set → set → set → set → set X6 (λX9 : set ⇒ ∅ ) (Inj0 (Inj0 (X8 (λX9 : set → set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : set → set Inj0 ∅ ) ) → (∀X4 : (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set → set X5 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ X9 X8 ) (λX8 : (set → set → set → set λX9 : set → set Inj0 X6 ) (Inj1 (setsum ∅ (setsum ∅ ∅ ∈ X7 ) → (∀X4 : (((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set → set X6 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set → set λX9 : set → set setsum (Inj0 (Inj0 (X8 (λX10 : set ⇒ ∅ ) ∅ (Inj1 X6 ) X0 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (setsum (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (X4 (λX8 : (set → set → set λX9 : set ⇒ Inj1 ∅ ) (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (setsum (setsum (Inj0 ∅ (Inj1 ∅ X6 ∅ ∈ X7 → X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X4 X3 (λX8 : set ⇒ λX9 : set → set → set → set ∅ ) (λX8 : ((set → set → set → set X6 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWxHuX8ecX31TTiaJkzLWhHZM3LDPq5iA8 )
∀X0 : ((set → set → (((set → set → set → set → (set → set → set → set → set → ((set → set → set → set → (set → set → set → prop ∀X1 : ((set → set → set → (((set → set → set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → (set → set → set → set → set → set → set → (set → set → (set → (set → set → set → set → prop ∀X3 : ((set → (set → set → set → (set → (set → set → set → set → set → (((set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set → (set → set → set λX9 : set → (set → set → set → set setsum ∅ (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set X5 ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : set → set X3 (λX8 : set → (set → set → set λX9 : set → (set → set → set → set X7 (setsum (setsum ∅ ∅ (setsum (X8 ∅ (λX10 : set ⇒ ∅ ) ∅ ) (λX8 : (set → set → (set → set → set ∅ ) (setsum (Inj1 (X6 (λX8 : (set → set → set setsum ∅ ∅ ) (setsum ∅ ∅ ∈ Inj0 (Inj0 (Inj1 X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj0 (Inj0 (Inj0 (Inj1 ∅ ∈ Inj0 (setsum X7 ∅ → X3 (λX8 : set → (set → set → set λX9 : set → (set → set → set → set Inj0 (Inj1 (X9 (X9 ∅ (λX10 : set ⇒ ∅ ) ∅ (λX10 : set ⇒ Inj0 ∅ ) (setsum ∅ ∅ ) (λX8 : (set → set → (set → set → set ∅ ) X2 (λX8 : (((set → set → set → set → set → set → (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ Inj0 X7 ) (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set → (set → set → set → set → set → set ∅ ) (λX8 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set → set Inj1 ∅ ) (setsum X4 ∅ X3 (λX8 : set → (set → set → set λX9 : set → (set → set → set → set X8 (setsum (X9 (setsum ∅ ∅ (λX10 : set ⇒ ∅ ) ∅ (X8 ∅ (λX10 : set ⇒ Inj0 ∅ ) (λX10 : set ⇒ setsum (setsum (Inj1 ∅ (X9 ∅ (λX11 : set ⇒ ∅ ) ∅ (setsum X7 ∅ ) ) (λX8 : (set → set → (set → set → set ∅ ) ) → (∀X4 : (set → (set → set → set → (set → set → set ∀X5 : (set → set → (set → set → set ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ X6 → X1 (λX8 : set → set → set λX9 : ((set → set → set → set → set ∅ ) (Inj0 (Inj1 (setsum (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → ((set → set → set → set ∀X6 : set → ((set → set → set → set → set → set ∀X7 : (set → set → set X1 (λX8 : set → set → set λX9 : ((set → set → set → set → set setsum (Inj1 (X9 (λX10 : set → set λX11 : set ⇒ X9 (λX12 : set → set λX13 : set ⇒ ∅ ) ) (setsum (Inj0 ∅ (Inj0 (Inj0 ∅ ) (setsum (Inj1 (Inj0 (Inj0 ∅ (setsum (Inj0 (X4 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ False ) → (∀X4 : set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , (X6 ∈ X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum (X9 (X9 ∅ X10 ) → X1 (λX8 : set → set → set λX9 : ((set → set → set → set → set Inj0 ∅ ) (Inj0 (setsum X6 (Inj1 (setsum ∅ ∅ X0 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set X7 ) (Inj0 ∅ (λX8 : set → set setsum (setsum ∅ ∅ X7 ) ∅ (λX8 : set ⇒ ∅ ) (Inj0 (Inj1 (setsum (Inj1 ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set → set ∀X7 : set → ((set → set → set → set → set → set → set X0 (λX8 : set → set λX9 : ((set → set → set → set → (set → set → set X6 ∅ ) (X5 (λX8 : set ⇒ Inj1 (Inj1 (X7 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set → set Inj0 ∅ ) (setsum ∅ (setsum ∅ (setsum ∅ (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) (X7 (Inj0 X4 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (setsum (Inj0 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (Inj0 ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMGNGcdwbcEJXUFAGfwa62T1HcZizyxyuL )
∀X0 : (set → set → ((((set → set → set → (set → set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → (set → set → set → prop ∀X2 : ((set → set → set → set → prop ∀X3 : (set → set → set → prop (∀X4 : ((set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ Inj1 ∅ ) (setsum (Inj0 (Inj1 (Inj1 ∅ (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set → set X3 (λX8 : set ⇒ ∅ ) (setsum (setsum (setsum X4 (Inj0 ∅ (setsum (setsum ∅ ∅ X4 (setsum ∅ (Inj0 (X7 (λX8 : set ⇒ ∅ ) ∅ ∅ ∅ (Inj0 X5 ∈ setsum (setsum (Inj1 (setsum ∅ ∅ (X6 (Inj1 ∅ ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : set → ((set → set → set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set → set X6 X7 ) ∅ ) → (∀X4 : set → set → (set → set → set ∀X5 : (((set → set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : set → set ∅ ) (Inj0 ∅ X3 (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set → set → set X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set Inj1 (setsum (setsum ∅ (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set ∀X6 : set → set → set ∀X7 : (set → set → set → set X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set → set setsum ∅ (setsum X9 (setsum ∅ (setsum ∅ ∅ ) False ) → (∀X4 : (((set → set → set → set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ Inj0 (setsum X7 (X6 X5 (λX9 : set ⇒ setsum ∅ ∅ ) ) (λX8 : ((set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (λX11 : set → set X11 (setsum (X11 ∅ ∅ ) (λX11 : set ⇒ ∅ ) ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMYUNHfcfdD4UVjNdWeAr2rnYYMCx3kGGAR )
∀X0 : (set → set → set → (((set → set → set → set → set → set → set → prop ∀X1 : (set → (((set → set → set → set → set → ((set → set → set → set → set → ((((set → set → set → set → set → set → prop ∀X2 : (set → (set → set → set → (set → (set → set → (set → set → set → prop ∀X3 : ((set → set → set → set → set → prop (∀X4 : set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , (setsum (Inj1 (Inj0 (X6 ∅ ∅ ∈ setsum (Inj0 ∅ (Inj0 (X5 ∅ → X2 (λX8 : set ⇒ λX9 : set → set X9 (X6 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set X8 ) X3 (λX8 : set → set Inj1 ∅ ) (Inj1 (X5 ∅ ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X3 (λX8 : set → set setsum X6 ∅ ) ∅ ∅ False ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set setsum ∅ X7 ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set Inj1 ∅ ) X2 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set → set ∀X7 : set → set (X7 (Inj0 (X6 (setsum ∅ ∅ (Inj1 ∅ (λX8 : set ⇒ Inj0 ∅ ) ∅ ∈ Inj1 X5 → X2 (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set → set Inj1 X8 ) X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : ((set → set → set → set → set setsum X5 (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) ) ) → (∀X4 : ((set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , (Inj0 (Inj1 ∅ ∈ Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : ((set → set → set → set → set X6 ∅ ) X3 (λX8 : set → set Inj1 (X5 ∅ ) (setsum ∅ (setsum (X5 ∅ (X6 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set X0 (λX8 : set ⇒ X7 (λX9 : (set → set → set → set λX10 : set ⇒ X8 ) ) X6 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ setsum ∅ ∅ ) X6 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj1 (Inj0 ∅ ) X3 (λX8 : set → set X6 ) (Inj1 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTCaeutXwBad9HD54KmtSSaCamLXDQvJik )
∀X0 : (set → set → (set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → (set → set → set → (set → set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → (set → set → set → (((set → set → set → set → set → set → (set → set → (set → set → (set → set → (set → set → prop ∀X3 : (set → set → set → set → ((set → set → set → set → prop (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj0 ∅ X8 ) (Inj0 (Inj0 X7 (λX8 : set → set → set Inj0 (Inj0 (setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj1 X5 ∈ Inj0 (setsum ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ setsum X7 X8 ) (setsum (Inj1 X5 ∅ (λX8 : set → set → set Inj0 (X6 (Inj1 X7 ) X2 (λX8 : (((set → set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ setsum (setsum (Inj0 ∅ X8 X8 ) (λX8 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → (set → set → set X2 (λX8 : (((set → set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set λX10 : set ⇒ ∅ ) (λX8 : set ⇒ X6 ) (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (X7 (λX9 : set ⇒ X6 ) (λX9 : set ⇒ Inj1 X9 ) ) (λX8 : set ⇒ setsum (X5 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 ∅ (setsum (setsum (Inj1 ∅ X6 (setsum (setsum ∅ ∅ (Inj1 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set → set ∀X6 : (set → set → set → set ∀X7 : set → set X2 (λX8 : (((set → set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set λX10 : set ⇒ Inj1 (setsum (X9 (λX11 : set → set ∅ ) (X8 (λX11 : (set → set → set → set λX12 : set ⇒ setsum ∅ ∅ ) X10 (λX11 : set ⇒ X10 ) ) (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) False ) → (∀X4 : set → ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 (Inj1 ∅ (λX8 : set → set ∅ ) ∈ setsum (setsum ∅ ∅ (setsum (Inj0 X5 X7 → X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → (set → set → set Inj1 X5 ) (Inj1 (Inj0 (Inj1 ∅ (Inj0 (setsum (X4 (Inj1 ∅ (λX8 : set → set X8 ∅ ) (Inj0 X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (((set → set → set → set → set → set → (set → set → set → (set → set → set ∅ ) (Inj1 (Inj1 X6 ∅ (X5 ∈ Inj0 (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set → set ∀X6 : ((set → set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (setsum (X4 (Inj1 ∅ ∅ (λX8 : set → set → set Inj0 (setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) X0 (λX8 : set ⇒ setsum X7 ∅ ) (λX8 : set ⇒ Inj1 (Inj1 (Inj1 ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ Inj0 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ X8 ) ∅ (Inj1 (setsum ∅ (Inj0 (setsum ∅ ∅ ∈ Inj1 (Inj0 (Inj0 (setsum ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMLyKZ7SDUxA91YZJ31eJnjtj5KvwWSEp3b )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → (set → set → set → prop ∀X2 : ((set → set → set → set → (set → set → set → prop ∀X3 : (set → set → (set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : (set → set → set → set (Inj1 (Inj0 (X6 (X4 ∅ (setsum ∅ ∅ ∈ setsum (X7 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) X5 → X3 (λX8 : set ⇒ setsum (X7 (λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (setsum (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj0 X9 (Inj1 X9 ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) (Inj0 ∅ ∈ Inj1 ∅ ) → (∀X4 : set → set ∀X5 : (((set → set → set → (set → set → set → set → set ∀X6 : (set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set , (setsum ∅ X7 ∈ Inj0 X7 → X2 (λX8 : set → set → set X5 (λX9 : (set → set → set λX10 : set → set X8 ∅ ∅ ) (setsum (Inj1 (Inj0 ∅ (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (setsum X7 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set → set Inj1 (setsum ∅ ∅ ) (λX8 : set ⇒ Inj1 ∅ ) X4 False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 X8 ) ) → (∀X4 : (((set → set → set → set → set → set → set → set ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X7 ∈ setsum (setsum (Inj0 (Inj1 ∅ ∅ (setsum (setsum (Inj1 ∅ ∅ (setsum X6 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ X5 ) (Inj0 (Inj0 X5 X0 (λX8 : set ⇒ setsum X5 (setsum X8 ∅ ) (Inj0 (setsum (Inj1 ∅ (Inj0 (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : ((set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ ∅ ) (Inj1 (Inj1 X5 False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRGjRdKxh4sFDULLvpa3YyYKNVUrc6emjy )
∀X0 : (set → set → (set → ((set → set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → ((set → (set → set → set → set → set → prop ∀X2 : (set → ((set → set → set → set → set → (((set → set → set → set → set → set → prop ∀X3 : (set → set → set → (set → (set → set → set → set → ((set → set → set → prop (∀X4 : set → set ∀X5 : ((set → set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ Inj0 (setsum (setsum ∅ ∅ (setsum (Inj1 ∅ (X5 (λX9 : set → set ∅ ) ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (setsum (setsum (Inj0 ∅ X8 ∅ (Inj0 (Inj1 (setsum ∅ ∅ ) (λX8 : set → set setsum (Inj1 (Inj1 (X8 ∅ (setsum (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : (set → set → set ∀X7 : set , (setsum ∅ ∅ ∈ Inj1 X7 → X3 (λX8 : set ⇒ setsum (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (X6 (λX9 : set ⇒ setsum ∅ ∅ ) ∅ ) X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (λX8 : set → set X8 (Inj0 (Inj1 ∅ ) X1 (λX8 : (((set → set → set → set → set Inj1 (setsum (setsum ∅ (X6 (λX9 : set ⇒ ∅ ) (X8 (λX9 : (set → set → set setsum ∅ ∅ ) ) (λX8 : set → (set → set → set → set Inj0 (Inj0 (X6 (λX9 : set ⇒ Inj1 ∅ ) ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set (X7 (λX8 : (set → set → set → set λX9 : set → set X8 (λX10 : set ⇒ ∅ ) ∅ ) ∈ Inj1 (setsum X6 (Inj1 (Inj0 ∅ → X2 (λX8 : set ⇒ λX9 : (set → set → set ∅ ) ∅ (λX8 : (set → set → set → set Inj0 (X7 (λX9 : (set → set → set → set λX10 : set → set X7 (λX11 : (set → set → set → set λX12 : set → set ∅ ) ) ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : (set → (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : (set → set → set setsum (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj0 (setsum ∅ ∅ ) (Inj1 ∅ ) (setsum ∅ (Inj1 (X4 X5 (λX8 : (set → set → set → set Inj0 (X7 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 ∅ ) ) (Inj1 (Inj1 ∅ False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → set → set → set ∀X7 : set , (Inj0 (Inj1 (Inj1 (Inj0 ∅ ∈ Inj0 (setsum ∅ (setsum ∅ (setsum ∅ ∅ → X2 (λX8 : set ⇒ λX9 : (set → set → set setsum X7 (setsum ∅ ∅ ) (setsum ∅ ∅ (λX8 : (set → set → set → set Inj1 (Inj1 ∅ ) (Inj1 (setsum (setsum X4 (setsum ∅ ∅ (Inj0 ∅ X1 (λX8 : (((set → set → set → set → set Inj0 (setsum ∅ (X6 (λX9 : set ⇒ X6 (λX10 : set ⇒ ∅ ) ∅ ) ∅ ) (λX8 : set → (set → set → set → set setsum (X5 ∅ (X8 X7 (λX9 : set ⇒ setsum ∅ (Inj0 ∅ ) (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → set (Inj1 (setsum (Inj1 (setsum ∅ ∅ (setsum (Inj1 ∅ ∅ ∈ Inj1 X4 → X1 (λX8 : (((set → set → set → set → set Inj1 ∅ ) (λX8 : set → (set → set → set → set X6 ) X3 (λX8 : set ⇒ Inj1 X6 ) (setsum ∅ (setsum (Inj0 (Inj1 ∅ (Inj0 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set → set ∀X5 : ((set → set → set → set → set ∀X6 : ((set → set → set → set → ((set → set → set → set → set → set ∀X7 : set , (Inj0 X7 ∈ X4 (Inj0 ∅ → X0 (λX8 : set ⇒ Inj0 (Inj0 (Inj0 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 (Inj0 X7 ) ) → (∀X4 : (((set → set → set → (set → set → set → set → set → set → set ∀X5 : (set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : set , (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 ∅ ) (setsum (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) (X4 (λX8 : (set → set → set λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ (Inj0 ∅ (setsum (X5 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ ∈ Inj1 ∅ → X0 (λX8 : set ⇒ setsum X8 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set setsum X8 (setsum X6 (X9 (λX10 : set ⇒ ∅ ) ∅ ) X0 (λX8 : set ⇒ setsum X7 X6 ) (λX8 : set ⇒ λX9 : (set → set → set → set X6 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMWH9ZHtCyGsg7vN7mVBQq2ybpzvHhAunqq )
∀X0 : ((((set → set → set → set → set → set → (set → set → set → set → set → ((set → set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → (set → set → set → set → set → ((set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → (set → set → set → (((set → set → set → set → (set → set → set → (set → set → set → set → (set → set → (set → set → set → set → prop ∀X3 : (set → set → set → (((set → set → set → set → ((set → set → set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set → set → set → set ∀X6 : (set → set → set ∀X7 : set → ((set → set → set → (set → set → set → set (X6 (λX8 : set ⇒ setsum (setsum (Inj0 ∅ (Inj1 ∅ X8 ) ∈ Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ X7 (Inj0 (setsum ∅ X9 (λX10 : set → set ∅ ) (λX10 : set ⇒ setsum (setsum (Inj1 ∅ (setsum ∅ ∅ X10 ) (Inj0 ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set → set setsum (X7 (Inj0 (X9 (λX10 : set ⇒ ∅ ) ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ X9 (λX11 : set ⇒ Inj0 ∅ ) (Inj1 ∅ ) (Inj1 (X7 ∅ (λX10 : set → set ∅ ) (λX10 : set ⇒ ∅ ) ∅ (setsum (setsum (Inj0 ∅ (X6 (λX10 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) ) → (∀X4 : ((set → set → set → (set → set → set → ((set → set → set → set → set ∀X5 : ((set → set → set → (set → set → set → set → set ∀X6 : set → set ∀X7 : set → (set → set → set → set (setsum (X6 ∅ ∅ ∈ Inj1 (setsum (Inj1 ∅ (setsum ∅ (X6 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : (set → set → set → set λX9 : (set → set → set → set Inj1 ∅ ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum ∅ (X6 ∅ ) X1 (λX8 : ((set → set → set → set → set → set → (set → set → set → set X8 (λX9 : set → set → set λX10 : set ⇒ ∅ ) (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X9 ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) (X8 (λX9 : set → set → set λX10 : set ⇒ X8 (λX11 : set → set → set λX12 : set ⇒ Inj1 ∅ ) (Inj1 ∅ (λX11 : set ⇒ Inj0 ∅ ) (X9 ∅ ∅ ) (setsum (setsum ∅ ∅ (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) (λX9 : set ⇒ setsum (setsum ∅ ∅ ∅ ) ∅ ) (λX8 : set → set setsum (X5 (λX9 : set → set → set λX10 : set → set λX11 : set ⇒ X9 (setsum ∅ ∅ X11 ) ∅ ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (Inj0 (setsum (Inj1 ∅ ∅ ∈ X5 → X1 (λX8 : ((set → set → set → set → set → set → (set → set → set → set setsum X7 X6 ) (λX8 : set → set X6 ) X2 (λX8 : (((set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set → (set → set → set λX10 : set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : (((set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set → (set → set → set λX10 : set → set → set X9 (λX11 : set → set λX12 : set ⇒ setsum (setsum ∅ (Inj0 ∅ (setsum (X9 (λX13 : set → set λX14 : set ⇒ ∅ ) (λX13 : set ⇒ ∅ ) (setsum ∅ ∅ ) (λX11 : set ⇒ setsum (setsum ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ (X8 (λX12 : (set → set → set → set ∅ ) ∅ (λX12 : set ⇒ ∅ ) ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) X2 (λX8 : (((set → set → set → set → set → set → (set → set → set λX9 : ((set → set → set → set → (set → set → set λX10 : set → set → set setsum (X8 (λX11 : (set → set → set → set X10 ∅ (Inj0 ∅ ) (Inj1 (X10 ∅ ∅ (λX11 : set ⇒ setsum (setsum ∅ ∅ (X9 (λX12 : set → set λX13 : set ⇒ ∅ ) (λX12 : set ⇒ ∅ ) ) (Inj1 (X9 (λX11 : set → set λX12 : set ⇒ ∅ ) (λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ setsum (Inj1 (Inj1 (Inj0 ∅ ∅ ) ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X5 ∈ Inj1 (X4 (Inj1 (Inj0 ∅ (λX8 : set ⇒ setsum (setsum ∅ ∅ (setsum ∅ ∅ ) → X1 (λX8 : ((set → set → set → set → set → set → (set → set → set → set setsum (Inj0 (Inj1 ∅ (X8 (λX9 : set → set → set λX10 : set ⇒ Inj1 ∅ ) (setsum (setsum ∅ ∅ X7 (λX9 : set ⇒ X9 ) (setsum (X6 ∅ (setsum ∅ ∅ ) (λX8 : set → set Inj1 (Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : ((set → set → set → set → set → set → (set → set → set → set setsum (X8 (λX9 : set → set → set λX10 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ Inj0 ∅ ) X5 (Inj1 (Inj0 ∅ ) (λX8 : set → set ∅ ) X1 (λX8 : ((set → set → set → set → set → set → (set → set → set → set Inj0 ∅ ) (λX8 : set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : ((set → set → set → set → set → set → (set → set → set Inj1 ∅ ) (Inj1 (setsum ∅ (X7 (Inj1 ∅ (setsum ∅ ∅ (λX8 : set → set → set setsum (setsum (setsum ∅ ∅ (Inj0 (Inj1 ∅ (Inj0 ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : ((set → set → set → set → set → set → (set → set → set ∅ ) X6 (λX8 : set → set → set X6 ) (setsum (setsum X7 (setsum (setsum ∅ ∅ (X4 (λX8 : (set → set → set ∅ ) ∅ ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMV8m7UhNukzgViceNEWpT58oT2NVaXxSDF )
∀X0 : (((set → set → set → set → (set → set → (set → set → set → prop ∀X1 : (((set → set → set → set → set → (set → set → ((set → set → set → (set → set → set → (set → set → set → prop ∀X2 : (set → set → set → (set → set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → (set → set → set → set (Inj1 (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ∈ Inj0 (X5 ∅ → X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (Inj0 (Inj1 (Inj1 ∅ ∅ ) ∅ (Inj1 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set ∀X6 : (set → set → set → (set → set → set → set ∀X7 : set → set → set → set → set X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) ∅ (X5 (λX8 : set → set Inj0 (Inj0 (Inj1 ∅ ) False ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X1 (λX8 : (set → set → set → set → set λX9 : set → set λX10 : (set → set → set λX11 : set → set X9 ∅ ) (λX8 : set ⇒ Inj0 X5 ) (setsum (X4 (λX8 : set ⇒ Inj1 (Inj0 ∅ ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj1 X9 ) (setsum (X7 (X4 (λX8 : set ⇒ ∅ ) X5 ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ X10 ) (setsum X4 (setsum (Inj0 (Inj0 ∅ ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : (set → set → set → set → set λX9 : set → set λX10 : (set → set → set λX11 : set → set setsum (Inj0 (X11 (Inj0 ∅ (setsum (X8 (λX12 : set ⇒ λX13 : set ⇒ λX14 : set ⇒ ∅ ) (X10 (λX12 : set ⇒ Inj1 ∅ ) ) (λX8 : set ⇒ Inj0 (Inj1 (Inj1 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set X1 (λX8 : (set → set → set → set → set λX9 : set → set λX10 : (set → set → set λX11 : set → set X11 (X10 (λX12 : set ⇒ X12 ) ) (λX8 : set ⇒ ∅ ) ∅ False ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set X5 (λX9 : set ⇒ λX10 : set → set Inj0 ∅ ) (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set X9 ) ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : (set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , X0 (λX8 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set ∅ ) X3 (λX8 : (set → (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X10 ) ∅ (Inj0 (X6 (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdyDMeKPXKhGRKZ5vi7ShrncUqQwwhC1MV )
∀X0 : (((set → set → set → set → ((((set → set → set → set → set → set → set → ((set → set → set → (set → set → set → prop ∀X1 : (set → set → (set → set → set → prop ∀X2 : ((set → set → set → set → set → ((set → set → (set → set → set → set → prop ∀X3 : (set → set → ((((set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : set , X0 (λX8 : (set → set → set setsum ∅ (setsum ∅ (Inj0 ∅ ) (λX8 : ((set → set → set → set → set X7 ) (setsum X4 (Inj0 (Inj0 (Inj1 ∅ (λX8 : set → set setsum X5 (setsum X7 (Inj0 (X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) (λX8 : set ⇒ setsum (Inj1 X8 (X6 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ ) (setsum (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ X7 X7 X3 (λX8 : set ⇒ Inj0 (Inj0 (setsum (Inj1 ∅ ∅ ) (λX8 : ((set → set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ ∅ ) ) X7 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → (set → set → set → set X3 (λX8 : set ⇒ X8 ) (λX8 : ((set → set → set → set → set setsum ∅ (Inj1 (setsum (Inj0 ∅ X5 ) ∅ (setsum (setsum (setsum X6 ∅ (Inj1 (setsum ∅ ∅ ∅ ∈ X4 (setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (Inj0 (Inj0 ∅ ) → (∀X4 : (set → set → set → set → ((set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (setsum (Inj0 (setsum (setsum ∅ ∅ ∅ ∅ ∈ Inj1 (setsum (setsum X7 ∅ ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (Inj0 X7 X2 (λX8 : set → set → set → set setsum ∅ (X8 ∅ (Inj1 (Inj1 ∅ ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set → set → set Inj1 X7 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum (Inj1 ∅ (Inj0 (X8 ∅ ∅ ) X2 (λX8 : set → set → set → set ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ setsum (setsum (X9 (Inj0 ∅ X10 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set → ((set → set → set → set → set → set ∀X7 : (set → set → set → set → set (Inj0 (Inj1 (setsum ∅ ∅ ∈ Inj0 X5 → X1 (λX8 : set ⇒ setsum (setsum (setsum (Inj1 ∅ (Inj1 ∅ X5 ∅ ) (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ X5 ) (Inj1 (Inj1 (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (set → (set → set → set → ((set → set → set → set → set ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X6 (X6 (Inj1 (X6 ∅ ∅ (λX9 : set ⇒ ∅ ) (setsum X7 (Inj0 ∅ (λX9 : set ⇒ setsum (Inj0 ∅ ∅ ) (Inj0 (setsum X8 X7 (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj0 X5 ) (X4 (λX8 : set ⇒ λX9 : set → set X8 ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set ∀X7 : set → set X2 (λX8 : set → set → set → set ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) X0 (λX8 : (set → set → set X5 ) (λX8 : ((set → set → set → set → set setsum (setsum (Inj1 (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ (setsum (X8 (λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ) X4 (λX8 : set → set setsum (Inj0 (setsum (X6 ∅ (λX9 : set → set ∅ ) ∅ ∅ (setsum (X7 (X6 ∅ (λX9 : set → set ∅ ) ∅ ∅ ) (λX8 : set ⇒ ∅ ) (X7 ∅ ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set X6 ) ∅ (λX8 : set → set setsum (setsum (setsum (X8 ∅ ∅ X6 ∅ ) (λX8 : set ⇒ X7 X6 (setsum (setsum ∅ (setsum ∅ ∅ ∅ ) ∅ X1 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ ∅ ) (setsum (Inj0 ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUSPgKJxhUW1s5Q9sgi8gGMW6C1kQRpvaw )
∀X0 : (((((set → set → set → set → set → set → set → set → (set → set → prop ∀X1 : ((set → set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → (set → set → set → (set → set → prop ∀X3 : (((set → (set → set → set → ((set → set → set → set → (set → set → set → ((set → set → set → set → set → set → set → (set → set → (set → set → prop (∀X4 : set → (set → set → set → set → set → set ∀X5 : set → (set → set → set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , X3 (λX8 : (set → (set → set → set → ((set → set → set → set λX9 : set → set Inj0 (setsum (X9 (X6 (λX10 : set → set ∅ ) ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X9 ) (X4 (Inj1 (X5 ∅ (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (X6 (λX10 : set → set X8 ) (setsum X8 ∅ ) (X4 (Inj1 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ X7 ) (setsum (Inj1 ∅ (Inj0 ∅ (Inj1 (Inj0 ∅ (X6 (λX8 : set → set ∅ ) (λX8 : set ⇒ X6 (λX9 : set → set setsum ∅ (X9 (setsum ∅ ∅ ) ) (λX8 : set ⇒ X8 ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → (set → set → set → ((set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) ∅ (λX8 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ Inj1 (Inj0 (Inj0 ∅ ) False ) → (∀X4 : (set → set → set ∀X5 : set → ((set → set → set → set → (set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : (set → set → set X0 (λX8 : (((set → set → set → set → set → set → set Inj0 (X6 ∅ (λX9 : set → set ∅ ) ) (λX8 : set ⇒ Inj1 X8 ) X2 (λX8 : set ⇒ λX9 : set → set X7 (λX10 : set ⇒ Inj1 (setsum (setsum ∅ ∅ ∅ ) ) (λX8 : set ⇒ X5 (X7 (λX9 : set ⇒ setsum X9 (setsum ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ Inj0 (setsum (Inj0 ∅ (Inj1 ∅ ) (X5 ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) (λX9 : set ⇒ X6 (X6 ∅ (λX10 : set → set ∅ ) (λX10 : set → set setsum ∅ ∅ ) ) ∅ ) ) → (∀X4 : set → set ∀X5 : (((set → set → set → set → (set → set → set → set → ((set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set X7 ) (λX8 : set ⇒ Inj1 (setsum (setsum (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set → set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ X8 ) X1 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (X11 ∅ X9 ) (Inj1 ∅ ∅ ∅ ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → ((set → set → set → set → set → set (X6 ∈ Inj0 (X5 (λX8 : set ⇒ λX9 : set → set X9 (Inj1 ∅ ) → X1 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set Inj1 (setsum (X11 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) (setsum (Inj1 (X4 (Inj1 ∅ ∅ X6 ∅ X2 (λX8 : set ⇒ λX9 : set → set setsum ∅ (Inj1 (Inj1 X8 ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : ((set → set → (set → set → set → ((set → set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set → set ∅ ) (λX8 : set ⇒ setsum (setsum (X6 (λX9 : set → set λX10 : set → set X9 ∅ ) (λX9 : set → set X7 ) ∅ (Inj1 (setsum (Inj0 ∅ (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X0 (λX8 : (((set → set → set → set → set → set → set X7 (X5 (λX9 : set ⇒ ∅ ) (Inj1 ∅ (λX9 : set → set Inj0 (setsum (X7 ∅ (λX10 : set → set ∅ ) ∅ ∅ ) ∅ ) (λX8 : set ⇒ Inj0 (X5 (λX9 : set ⇒ setsum X9 (setsum ∅ ∅ ) (X5 (λX9 : set ⇒ ∅ ) ∅ ) (setsum X6 ∅ ∈ X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQaiWUEmFtp9LKHToDT33HMxVyQhG3ZgAY )
∀X0 : (((set → (set → set → set → set → set → set → set → set → prop ∀X1 : (set → (set → set → set → set → set → set → prop ∀X2 : ((((set → set → set → set → (set → set → (set → set → set → set → (set → set → set → (set → set → (set → set → set → prop ∀X3 : ((set → ((set → set → set → set → ((set → set → set → (set → set → set → set → ((((set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (X6 ∈ Inj1 (setsum X5 (X7 X4 → X3 (λX8 : set → ((set → set → set → set λX9 : (set → set → set λX10 : set → set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) (λX8 : ((set → set → set → set Inj0 (setsum (Inj1 ∅ (setsum (X8 (λX9 : set → set ∅ ) ∅ ) ) → (∀X4 : (set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X5 ∅ ∈ X7 → X3 (λX8 : set → ((set → set → set → set λX9 : (set → set → set λX10 : set → set → set ∅ ) (λX8 : ((set → set → set → set ∅ ) X2 (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set → set X8 (λX11 : set → set setsum (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) (λX8 : set ⇒ setsum (X5 (setsum ∅ (setsum ∅ ∅ (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ setsum (Inj1 ∅ (setsum ∅ X8 ) (setsum (Inj1 ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 ∈ Inj0 (Inj0 (Inj1 (Inj0 ∅ X2 (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set → set setsum (X9 (Inj1 X7 (X10 ∅ (setsum (Inj0 ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X5 ) (λX8 : set ⇒ X6 ) (setsum X5 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X2 (λX8 : ((set → set → set → set λX9 : set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 (X6 (X6 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (λX8 : set ⇒ X6 X8 ) (X5 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (X6 ∈ Inj1 ∅ → X0 (λX8 : (set → (set → set → set → set → set X5 ) (Inj1 ∅ (Inj0 ∅ X1 (λX8 : set ⇒ λX9 : set → set → set → set Inj1 (setsum X7 (X9 ∅ X7 (Inj1 ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set → set → set → set ∅ ) ∅ (Inj1 ∅ ∈ Inj1 (Inj0 ∅ ) → (∀X4 : ((set → set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ setsum X10 ∅ ) ∅ (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ∈ X4 (λX8 : set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ (setsum X7 (setsum (setsum ∅ ∅ (Inj0 ∅ → X1 (λX8 : set ⇒ λX9 : set → set → set → set ∅ ) (setsum (Inj0 ∅ (Inj1 X6 X0 (λX8 : (set → (set → set → set → set → set ∅ ) (Inj1 (Inj0 X5 X7 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : (set → (set → set → set → set → set X7 ) (Inj1 (Inj1 ∅ (setsum X5 X5 X3 (λX8 : set → ((set → set → set → set λX9 : (set → set → set λX10 : set → set → set ∅ ) (λX8 : ((set → set → set → set setsum (Inj1 X5 (Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNNRnNzzeGqxv2HnqHnnM3JtBxWcAah9hR )
∀X0 : (set → set → set → set → prop ∀X1 : ((((set → set → set → set → set → set → (set → ((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → prop ∀X3 : (set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ setsum X8 X6 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (Inj1 (Inj1 (Inj0 ∅ X4 ) → (∀X4 : (set → (set → set → set → set → (set → set → set → set ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ setsum (setsum ∅ ∅ (Inj0 X7 ) (λX8 : set ⇒ λX9 : set ⇒ setsum X7 ∅ ) (Inj0 (X5 (λX8 : set ⇒ Inj1 (X5 (λX9 : set ⇒ ∅ ) ∅ ∅ ) (Inj1 ∅ ∅ X0 (λX8 : set ⇒ setsum X6 X6 ) (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ ∅ ) (setsum X5 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → (set → set → set → set ∀X7 : (set → (set → set → set → set → set X2 (λX8 : set → set λX9 : set ⇒ Inj1 (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set ∀X7 : set , (setsum (setsum X7 X7 (Inj0 (Inj1 (Inj1 ∅ ∈ X7 → X1 (λX8 : ((set → set → set → set → set setsum (setsum ∅ X5 (setsum X7 (X8 (λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : (set → set → set Inj0 (Inj0 X8 ) (setsum (setsum ∅ (Inj0 (X6 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ (setsum (setsum (Inj0 ∅ ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : ((set → set → set → set → set X7 ) (λX8 : set ⇒ λX9 : (set → set → set setsum (setsum ∅ (X9 (λX10 : set ⇒ setsum ∅ ∅ ) ∅ ) X5 False ) → (∀X4 : set → set → set ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : set → set → (set → set → set (X6 ∈ X5 X6 (λX8 : set → set setsum (setsum (Inj1 ∅ ∅ ∅ ) → X2 (λX8 : set → set λX9 : set ⇒ setsum (X8 (Inj1 (X7 ∅ ∅ (λX10 : set ⇒ ∅ ) ∅ ) (X5 (X7 (Inj0 (Inj0 ∅ (Inj0 ∅ (λX8 : set ⇒ Inj1 (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : set → set X7 (Inj0 (Inj0 ∅ (setsum (X5 ∅ (λX9 : set → set ∅ ) (Inj1 ∅ (λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ) X0 (λX8 : set ⇒ X7 (Inj0 ∅ ∅ (λX9 : set ⇒ setsum (setsum ∅ X6 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) X6 (X7 (Inj1 (Inj0 (Inj0 ∅ X6 (λX8 : set ⇒ setsum ∅ (setsum ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : (set → set → set X0 (λX8 : set ⇒ setsum ∅ ∅ ) (Inj1 (Inj0 X4 X5 (setsum ∅ (setsum (Inj0 (setsum ∅ ∅ (X6 (λX8 : set ⇒ ∅ ) ∈ Inj0 (setsum (X6 (λX8 : set ⇒ setsum ∅ ∅ ) (X6 (λX8 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMaiLz7RkEq2BgPq87Kj8ds3JdMj7j8G7Av )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → (set → (set → set → set → set → ((set → (set → set → set → set → ((set → set → set → set → (set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → (set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set → set (Inj1 ∅ ∈ Inj0 (Inj0 (Inj0 ∅ → X3 (λX8 : set ⇒ λX9 : set → set → set ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ λX9 : set → set → set setsum (setsum (Inj0 (setsum ∅ ∅ ∅ (Inj0 (X7 X8 ) (λX8 : set → set setsum ∅ (setsum (Inj0 (setsum ∅ ∅ (X5 (λX9 : set → set → set Inj1 ∅ ) ∅ ) False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set → set ∀X7 : (((set → set → set → set → set X2 (λX8 : set ⇒ setsum (X7 (λX9 : (set → set → set setsum (X9 (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ) ∅ ) (Inj0 (Inj1 ∅ X2 (λX8 : set ⇒ ∅ ) (X5 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ ∅ ) (setsum (setsum ∅ ∅ (setsum X6 ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ ∅ ) X7 X1 (λX8 : set ⇒ λX9 : set → (set → set → set setsum ∅ ∅ ) (λX8 : set → (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set → (set → set → set X7 ) (λX8 : set → (set → set → set Inj0 (X6 (X8 (Inj1 ∅ (λX9 : set ⇒ Inj1 ∅ ) ) (λX8 : set → set λX9 : set ⇒ X8 (X6 (Inj0 X7 ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (set → (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ X7 ) (Inj1 (Inj1 ∅ (setsum (setsum X7 (setsum (Inj1 ∅ (setsum ∅ ∅ (Inj0 X4 (Inj1 ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : set , (setsum X7 (setsum (setsum (setsum ∅ ∅ ∅ ∅ ∈ Inj1 (X5 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ setsum (setsum ∅ ∅ X8 ) → X0 (λX8 : set ⇒ ∅ ) (setsum (X5 (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ X5 ∅ (λX9 : set ⇒ X7 ) ) (X5 (Inj0 (Inj0 ∅ (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (setsum (setsum (setsum X4 ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj0 X4 X4 (Inj1 X6 X3 (λX8 : set ⇒ λX9 : set → set → set setsum ∅ (setsum (setsum X8 (Inj1 ∅ (X9 (setsum ∅ ∅ (X9 ∅ ∅ ) (λX8 : set → set ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMK9ibgUhVJ3YEeo7iRfT9MkinxHfeWhjvw )
∀X0 : (((((set → set → set → set → set → set → set → ((set → set → set → set → set → ((set → (set → set → set → set → set → prop ∀X1 : ((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → (set → set → set → set → set → set → set → (set → (set → set → set → set → prop (∀X4 : ((set → set → set → set → set → (set → set → set → (set → set → set ∀X5 : (set → set → set ∀X6 : ((set → set → set → set ∀X7 : set , (X6 (λX8 : set → set setsum (X8 (setsum ∅ ∅ (X8 (setsum ∅ ∅ ) ∈ Inj1 (setsum (setsum X7 (Inj0 ∅ (Inj1 (X6 (λX8 : set → set ∅ ) → X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X10 ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (Inj1 ∅ X12 ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X9 X10 ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X5 ∅ (Inj1 (setsum ∅ ∅ (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum X8 (Inj1 (X9 X7 ) X0 (λX8 : (((set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set X10 (λX11 : set ⇒ Inj0 (setsum (setsum ∅ ∅ ∅ ) ∅ ) (λX8 : set → (set → set → set → set X7 ) ) → (∀X4 : (set → set → ((set → set → set → (set → set → set ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set → set → set X2 (λX8 : set → set setsum (X7 (Inj0 X6 (Inj0 ∅ (X8 ∅ ) (X7 (Inj0 (setsum (Inj1 ∅ (Inj1 ∅ ∅ (X7 ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum X9 (setsum (Inj0 (X7 ∅ ∅ (setsum X6 X6 ) ) → (∀X4 : set → set → (set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : set → set setsum X7 (Inj1 X6 ) (X4 ∅ (X4 X7 (X5 (λX8 : (set → set → set → set λX9 : set → set setsum ∅ ∅ ) (λX8 : set ⇒ setsum (X5 (λX9 : (set → set → set → set λX10 : set → set ∅ ) (Inj1 ∅ ) (Inj0 ∅ (λX8 : set ⇒ setsum (Inj0 ∅ (Inj0 ∅ ) (setsum (setsum (X4 ∅ ∅ (λX8 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ (setsum (setsum ∅ (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (setsum (Inj1 (Inj1 (setsum ∅ ∅ (X5 (λX8 : (set → set → set → set λX9 : set → set X6 ) ∈ setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 ∈ Inj0 X6 X1 (λX8 : set → set X6 ) (Inj1 ∅ (setsum (Inj0 (Inj1 (Inj0 ∅ ∅ X1 (λX8 : set → set setsum ∅ (Inj0 ∅ ) (setsum X6 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X1 (λX8 : set → set X7 (λX9 : set → set X7 (λX10 : set → set setsum (setsum ∅ ∅ (X10 ∅ ) ∅ ) ∅ ) ∅ X6 (Inj1 (Inj0 (setsum ∅ (setsum ∅ ∅ ∈ setsum (X5 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → ((set → set → set → set → set ∀X7 : set → set X0 (λX8 : (((set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set ∅ ) (λX8 : set → (set → set → set → set setsum X5 ∅ ) ) → (∀X4 : (set → set → ((set → set → set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (((set → set → set → set → set → set λX9 : set ⇒ λX10 : (set → set → set → set X10 (λX11 : set ⇒ X8 (λX12 : (set → set → set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) ∅ ) (λX8 : set → (set → set → set → set ∅ ) X3 (λX8 : set → set λX9 : set ⇒ λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 (setsum X12 ∅ ) ∅ (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj0 X8 (setsum X7 (Inj1 (setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMdpYSg3vhN3bqaY2VpziLvWWCGdpCcQWpe )
∀X0 : ((set → set → set → (set → set → set → set → ((set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → set → set → ((set → set → set → set → set → set → set → prop ∀X3 : (((set → set → ((set → set → set → set → ((set → set → set → set → (set → set → set → set → (set → set → (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set → set X3 (λX8 : (set → set → ((set → set → set → set λX9 : (set → set → set → set λX10 : set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ X8 ) ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : (set → set → ((set → set → set → set λX9 : (set → set → set → set λX10 : set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 (setsum (Inj1 X8 (Inj0 ∅ ) (setsum ∅ (setsum (Inj0 (setsum ∅ ∅ ∅ ∈ Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → (set → set → set → set → set (X7 (λX8 : set ⇒ λX9 : set → set setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ ) (setsum (X7 (λX8 : set ⇒ λX9 : set → set ∅ ) (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ X5 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ X6 → X2 (λX8 : (((set → set → set → set → set → set → set → ((set → set → set → set → set Inj1 ∅ ) (setsum ∅ (setsum ∅ (Inj1 (Inj0 ∅ X2 (λX8 : (((set → set → set → set → set → set → set → ((set → set → set → set → set setsum (Inj1 (Inj1 (setsum ∅ ∅ (X7 (λX9 : set ⇒ λX10 : set → set Inj0 (Inj1 ∅ ) (X7 (λX9 : set ⇒ λX10 : set → set ∅ ) (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , (setsum (setsum (setsum ∅ X6 X7 X7 ∈ Inj1 (Inj0 X7 → X2 (λX8 : (((set → set → set → set → set → set → set → ((set → set → set → set → set Inj1 X7 ) (Inj0 ∅ X0 (λX8 : set → set X7 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum X6 (Inj1 ∅ (Inj1 (setsum ∅ ∅ X8 ) X4 (λX8 : set → set λX9 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → (set → set → set X3 (λX8 : (set → set → ((set → set → set → set λX9 : (set → set → set → set λX10 : set → set → set X10 (setsum (X8 (λX11 : set ⇒ setsum ∅ ∅ ) (λX11 : set → set X9 (λX12 : set ⇒ ∅ ) ∅ ) (X10 ∅ ∅ (X8 (λX11 : set ⇒ Inj0 X11 ) (λX11 : set → set setsum (Inj1 ∅ (setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj0 (X10 (setsum ∅ (Inj1 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ setsum (setsum (setsum ∅ ∅ X8 (Inj1 (X7 ∅ (λX11 : set ⇒ ∅ ) ) ) ∅ (setsum X4 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ setsum (setsum (X6 (λX9 : set ⇒ ∅ ) X5 (setsum (setsum ∅ ∅ X5 ) (setsum (setsum X7 X5 (Inj1 (setsum (setsum ∅ ∅ (Inj1 ∅ X0 (λX8 : set → set X5 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (setsum (setsum X8 X8 ∅ ) (Inj1 (setsum (setsum ∅ ∅ ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set , (Inj0 X7 ∈ Inj1 (Inj0 X5 → X0 (λX8 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 X9 ) (setsum X7 (setsum (Inj0 (setsum ∅ ∅ (Inj0 X7 (λX8 : set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → set X0 (λX8 : set → set X7 (λX9 : set → set λX10 : set → set λX11 : set ⇒ setsum ∅ (Inj0 (setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) (Inj1 (X4 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum ∅ (Inj0 (Inj0 ∅ ∅ ) X3 (λX8 : (set → set → ((set → set → set → set λX9 : (set → set → set → set λX10 : set → set → set Inj1 (setsum (X10 (X10 ∅ ∅ (X10 ∅ ∅ (Inj1 (X8 (λX11 : set ⇒ ∅ ) (λX11 : set → set ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMY56YqTza3dpvH8Uep1wd289Y9Rx2usiY3 )
∀X0 : (((((set → set → set → set → (set → set → set → set → set → ((set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → set → (set → set → set → set → set → set → ((set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → (set → set → set → prop ∀X3 : ((((set → set → set → set → set → set → (((set → set → set → (set → set → set → set → set → set → set → prop (∀X4 : (set → set → set ∀X5 : (set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set , (Inj1 (X4 (λX8 : set ⇒ ∅ ) ∈ X4 (λX8 : set ⇒ ∅ ) → X2 (λX8 : set → set → set X6 ) X7 (λX8 : set ⇒ X8 ) X6 X3 (λX8 : ((set → set → set → set → set → set λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ setsum ∅ (setsum (setsum (Inj0 ∅ ∅ (setsum (setsum ∅ ∅ ∅ ) (setsum (Inj0 ∅ X7 ) → (∀X4 : ((set → set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → set λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ X9 (λX11 : set → set ∅ ) (λX11 : set ⇒ setsum (X8 (λX12 : set → set → set λX13 : set ⇒ Inj1 ∅ ) X10 ) ∅ ) (Inj0 (Inj1 (setsum X6 (X5 ∅ ∅ X3 (λX8 : ((set → set → set → set → set → set λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ ∅ ) (X5 (setsum ∅ (Inj1 (setsum ∅ ∅ (Inj0 (setsum (X4 (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : (((set → set → set → set → set → set ∀X7 : set , (Inj0 (setsum ∅ (setsum (setsum ∅ ∅ (X5 ∅ ∈ Inj1 (Inj1 ∅ → X0 (λX8 : (((set → set → set → set → (set → set → set → set setsum (setsum (setsum (Inj0 ∅ (X8 (λX9 : (set → set → set → set λX10 : set → set ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ (Inj0 (setsum (Inj0 ∅ (Inj1 ∅ ) (λX8 : set → set → set ∅ ) X2 (λX8 : set → set → set X7 ) (Inj1 (setsum (Inj0 (setsum ∅ ∅ ∅ (λX8 : set ⇒ ∅ ) X7 ) → (∀X4 : set → set → set → set ∀X5 : (set → set → set → set ∀X6 : set → ((set → set → set → set → set ∀X7 : ((set → set → set → set → set → set → (set → set → set X2 (λX8 : set → set → set X6 (X5 (λX9 : set ⇒ X8 ∅ (X6 ∅ (λX10 : set → set λX11 : set ⇒ ∅ ) ) ∅ (λX9 : set → set λX10 : set ⇒ ∅ ) ) (Inj0 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (setsum (X6 ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (Inj1 (Inj1 ∅ ∈ X6 ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → (set → set → set → ((set → set → set → set → set ∀X7 : set → set (Inj1 ∅ ∈ X5 → X1 (λX8 : (((set → set → set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum X9 (setsum (Inj0 (Inj1 ∅ (setsum X10 (setsum ∅ ∅ ) (λX8 : set → set → set → set setsum (X6 (λX9 : set → set → set λX10 : set → set Inj1 (X9 ∅ ∅ ) (λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : (set → set → set → set X1 (λX8 : (((set → set → set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set → set → set Inj0 ∅ ) False ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : ((set → set → set → set → set → set λX9 : ((set → set → set → (set → set → set → set λX10 : set ⇒ setsum ∅ (Inj0 X10 ) (Inj0 (X5 (X4 (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ X6 ∅ ) X0 (λX8 : (((set → set → set → set → (set → set → set → set X8 (λX9 : (set → set → set → set λX10 : set → set X8 (λX11 : (set → set → set → set λX12 : set → set ∅ ) ) ) (λX8 : set → set → set Inj0 (setsum (setsum (setsum ∅ ∅ ∅ (setsum (X8 ∅ ∅ (X8 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : (((set → set → set → set → (set → set → set → set setsum (setsum (setsum (X8 (λX9 : (set → set → set → set λX10 : set → set ∅ ) X5 (Inj1 (Inj1 ∅ (Inj0 (Inj1 ∅ ) (λX8 : set → set → set setsum (setsum (setsum (setsum ∅ ∅ ∅ (X8 ∅ (setsum ∅ ∅ X7 ) X2 (λX8 : set → set → set X5 ) X5 (λX8 : set ⇒ setsum X8 X8 ) ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKeiipjB917cP3FkcA7cNhLiZeWfL25sso )
∀X0 : (((set → set → set → (set → set → set → set → set → (((set → set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → set → set → set → prop ∀X2 : (((set → set → set → set → set → set → (set → set → set → set → prop ∀X3 : (set → set → (set → set → set → (set → set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set → ((set → set → set → (set → set → set ∀X6 : set → set ∀X7 : set , (setsum ∅ (X5 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set → set Inj1 ∅ ) (λX8 : set ⇒ X5 (setsum ∅ ∅ (λX9 : set → set X9 ∅ ) (λX9 : set ⇒ ∅ ) ) ∈ X5 (setsum ∅ ∅ (λX8 : set → set setsum ∅ (setsum X7 (X6 ∅ ) (λX8 : set ⇒ Inj1 X8 ) → X0 (λX8 : (set → set → set → (set → set → set → set ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ setsum (Inj1 (Inj1 X9 X9 ) X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set → set λX12 : set ⇒ Inj1 X9 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → ((set → set → set → set → (set → set → set → set ∀X7 : set → (set → set → set → set → set → set (X4 ∅ ∈ X7 (X6 (λX8 : (set → set → set Inj0 (setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj1 ∅ X9 ) (λX8 : set ⇒ ∅ ) (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 ∅ ) (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum (Inj1 (Inj0 ∅ (Inj1 (X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set → set λX12 : set ⇒ X12 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum (Inj1 (Inj1 (Inj0 ∅ (Inj1 ∅ ) X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ Inj1 X8 ) ∅ ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : ((set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ ∅ ) (setsum (Inj0 (X5 (λX8 : set → set ∅ ) (λX8 : set → set X6 ) (X4 (λX8 : set → set → set λX9 : set → set setsum ∅ ∅ ) X2 (λX8 : (set → set → set → set setsum (setsum (setsum (X8 (λX9 : set ⇒ ∅ ) ∅ ∅ (Inj1 (setsum ∅ ∅ (X5 (λX9 : set → set Inj0 X6 ) (λX9 : set → set Inj0 (setsum ∅ ∅ ) ) (setsum (setsum (setsum (X4 (λX8 : set → set → set λX9 : set → set ∅ ) (Inj0 ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) ) → (∀X4 : (set → set → set → (set → set → (set → set → set ∀X5 : set → set → (set → set → set → set ∀X6 : (set → (set → set → set → ((set → set → set → set → (set → set → set ∀X7 : set → set (X7 (setsum (Inj1 (setsum ∅ ∅ (X4 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ X7 ∅ ) ∈ Inj1 (Inj0 (X5 (Inj1 ∅ (Inj1 ∅ (λX8 : set ⇒ X7 ∅ ) (X7 ∅ → X2 (λX8 : (set → set → set → set ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X2 (λX8 : (set → set → set → set setsum ∅ (Inj0 ∅ ) (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum (setsum ∅ ∅ ∅ ) (setsum (X4 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set → set ∅ ) (λX10 : set → set λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ X9 ) (setsum (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set (X5 ∈ Inj0 (setsum (Inj1 X6 X6 → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set λX11 : set ⇒ X10 (λX12 : set ⇒ ∅ ) ) (Inj0 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X7 (λX11 : (set → set → set → set Inj0 (setsum ∅ (Inj1 ∅ ) ∅ ) ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set → set → (set → set → set ∀X6 : set → set → set ∀X7 : (set → set → set → set → set (X7 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum X10 (Inj0 ∅ ) ∈ Inj0 ∅ → X0 (λX8 : (set → set → set → (set → set → set → set Inj1 ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : (set → set → set → (set → set → set → set Inj0 (Inj1 (setsum (X5 (λX9 : set → set → set ∅ ) ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ ∅ ) (setsum X4 (setsum (Inj0 (Inj0 ∅ (Inj1 (Inj1 ∅ ∈ X6 (Inj1 (setsum ∅ (Inj0 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMbm1EcNRaFhKez8WWb4gTTjKhxcSJZC6kp )
∀X0 : (set → set → set → set → prop ∀X1 : (set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → (set → set → set → (set → set → prop ∀X3 : (set → set → (set → set → set → ((set → set → set → prop (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (Inj0 (setsum ∅ (Inj1 ∅ (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ∈ setsum (Inj0 (Inj1 (setsum ∅ ∅ (Inj1 (setsum X7 (setsum ∅ ∅ → X3 (λX8 : set ⇒ X6 ) (λX8 : set ⇒ ∅ ) X5 (λX8 : set → set setsum (setsum (setsum (Inj0 ∅ ∅ (Inj0 (setsum ∅ ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set (setsum (setsum (Inj0 ∅ (X4 (λX8 : set → set → set ∅ ) (Inj1 (Inj1 (X4 (λX8 : set → set → set ∅ ) ∈ Inj1 (Inj0 X5 → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X6 ) (X7 ∅ (λX8 : set → set ∅ ) X2 (λX8 : set → set ∅ ) (setsum (setsum ∅ (Inj0 ∅ ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj1 ∅ X6 ) (λX8 : set ⇒ Inj1 (setsum X8 (setsum ∅ X5 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : set → ((set → set → set → set ∀X7 : set , (setsum ∅ (Inj0 (X5 (λX8 : (set → set → set X7 ) ∈ X4 → X2 (λX8 : set → set setsum (X6 (setsum ∅ (setsum ∅ ∅ (λX9 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (X8 (Inj1 (X6 ∅ (λX9 : set → set ∅ ) ) (setsum X7 (X6 ∅ (λX8 : set → set setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X5 (λX9 : (set → set → set X7 ) ) ) → (∀X4 : ((set → set → set → set → set → (set → set → set ∀X5 : set → set ∀X6 : (set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set ∅ ) (X5 (Inj0 (Inj1 X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 X7 ) (setsum (setsum (Inj1 (Inj1 ∅ (setsum (Inj1 ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj1 ∅ ) ∈ setsum (Inj1 (setsum ∅ (Inj0 ∅ (setsum ∅ (X5 (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X7 ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (setsum (X6 ∅ (Inj0 (setsum ∅ ∅ ∅ ∈ X5 → X1 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ X2 (λX8 : set → set ∅ ) (setsum (setsum (setsum (Inj0 ∅ (Inj0 ∅ (Inj0 (X4 (λX8 : set ⇒ ∅ ) ∅ ∅ (setsum ∅ (Inj1 (Inj0 ∅ (setsum (Inj1 (Inj0 (setsum ∅ ∅ (setsum X7 ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X8 ) ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , (Inj0 ∅ ∈ Inj1 (Inj0 (setsum (Inj1 ∅ (Inj0 ∅ → X3 (λX8 : set ⇒ setsum X7 ∅ ) (λX8 : set ⇒ setsum X7 (setsum (X6 (Inj0 ∅ (Inj1 (setsum ∅ ∅ ) ∅ (λX8 : set → set setsum (setsum (setsum (X8 ∅ (Inj1 ∅ (setsum (X8 ∅ (Inj0 ∅ (X8 X5 ) X0 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (X6 (Inj1 (setsum ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ X7 ) (setsum ∅ ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMN7ob7wBCAntZT93XczT8xd4WuWs39qRqB )
∀X0 : (set → set → set → (set → set → (((set → set → set → set → (set → set → set → prop ∀X1 : ((set → (set → set → set → set → set → prop ∀X2 : (set → set → set → set → set → prop ∀X3 : (((set → set → (set → set → set → set → set → (set → set → set → ((set → set → set → set → set → ((set → set → (set → set → set → set → prop (∀X4 : (set → (set → set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → (set → set → set → set → set λX9 : set → set X9 (Inj1 (Inj1 (Inj1 ∅ ) (λX8 : set → set → set → set ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj0 (Inj1 ∅ ) ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set ∀X7 : (((set → set → set → set → (set → set → set → set X3 (λX8 : (set → set → (set → set → set → set → set λX9 : set → set setsum ∅ (Inj0 ∅ ) (λX8 : set → set → set → set Inj0 (setsum (setsum ∅ (setsum ∅ ∅ (Inj1 (X8 ∅ ∅ ∅ ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ X9 ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : (set → set → set Inj0 ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (X7 (λX8 : (set → set → set Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum (X4 X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (X4 (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : (set → set → set λX11 : set → set setsum ∅ ∅ ) ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : (set → set → set → (set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : (((set → set → set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (Inj0 (X4 (λX8 : set ⇒ Inj1 (setsum ∅ ∅ ) ∅ (λX8 : set ⇒ X8 ) ∅ ) → (∀X4 : set , ∀X5 : (set → set → (set → set → set → (set → set → set → set ∀X6 : (set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ setsum (setsum (Inj1 ∅ X8 (X7 X8 ) ) (setsum (Inj0 (X6 (λX8 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ ∅ ) (X5 (λX8 : set ⇒ Inj1 (X7 (X6 (λX9 : set ⇒ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X4 False ) → (∀X4 : set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → set → (set → set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set → set → set X7 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) X1 (λX8 : set → (set → set → set setsum ∅ (setsum (setsum ∅ X6 (Inj1 (setsum ∅ ∅ ) (X5 ∅ X7 ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set → (set → set → set setsum (setsum (setsum (setsum ∅ ∅ X7 X6 (Inj1 (setsum ∅ ∅ ) ∅ (X5 (λX8 : set ⇒ Inj1 (setsum X8 ∅ ) ∈ Inj0 (Inj1 X6 ) → (∀X4 : (set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (X4 (λX8 : set ⇒ Inj1 (Inj0 X5 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (setsum X5 (Inj0 (Inj1 ∅ ∈ setsum ∅ (Inj1 (Inj1 ∅ → X0 (λX8 : set ⇒ λX9 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ Inj1 ∅ ) (λX8 : (set → set → set → set λX9 : set → set X9 (X8 (λX10 : set ⇒ setsum (Inj1 ∅ ∅ ) ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (setsum X9 (X7 ∅ (Inj1 (X6 ∅ (setsum (setsum ∅ (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ Inj0 X5 ) (λX8 : (set → set → set → set λX9 : set → set setsum (Inj1 ∅ ∅ ) X3 (λX8 : (set → set → (set → set → set → set → set λX9 : set → set X9 (Inj0 (X6 ∅ ) (λX8 : set → set → set → set Inj0 X5 ) (λX8 : set → set λX9 : set → set λX10 : set ⇒ Inj0 (setsum ∅ X10 ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMNzzLdRuUe3jFZ3Vf8ngPqhWAGvp8FVwQL )
∀X0 : ((set → set → set → set → (set → set → prop ∀X1 : (set → set → ((set → set → set → set → (set → set → set → prop ∀X2 : (set → set → (set → set → set → ((set → set → set → prop ∀X3 : (set → set → (set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ X5 ) (λX8 : set ⇒ Inj1 (setsum (setsum (setsum ∅ ∅ X7 (Inj0 (setsum ∅ ∅ ) (setsum (setsum ∅ (X6 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ X3 (λX8 : set ⇒ Inj0 (Inj0 (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ setsum ∅ (Inj0 ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set setsum ∅ (setsum ∅ (Inj0 ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : ((set → set → (set → set → set → set → set → set X3 (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ Inj1 X5 ) ∅ X2 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X5 ) (setsum ∅ (X7 (λX8 : set → set λX9 : set → set λX10 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ (λX8 : set → set X6 (setsum (Inj1 ∅ (Inj0 ∅ ) ) → (∀X4 : set → set → set ∀X5 : set → ((set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → (set → set → set → set (setsum (X7 (λX8 : set ⇒ Inj1 (X7 (λX9 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) (Inj1 (Inj1 ∅ (λX8 : set ⇒ ∅ ) (X7 (λX8 : set ⇒ setsum ∅ ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (X7 (λX8 : set ⇒ X8 ) ∅ (λX8 : set ⇒ Inj0 (Inj0 ∅ ) (setsum ∅ ∅ ∈ X4 ∅ ∅ → X2 (λX8 : set ⇒ Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (X5 (setsum ∅ ∅ (λX9 : set → set X9 ∅ ) ) (λX8 : set ⇒ ∅ ) (X4 ∅ ∅ (λX8 : set → set ∅ ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set → set → set → set ∀X6 : (set → set → set ∀X7 : set , X2 (λX8 : set ⇒ X6 (λX9 : set ⇒ setsum ∅ (setsum (Inj1 ∅ (X6 (λX10 : set ⇒ ∅ ) ) ) (λX8 : set ⇒ ∅ ) ∅ (λX8 : set → set X5 (setsum ∅ (Inj0 (Inj1 ∅ X7 (setsum (setsum ∅ (Inj0 ∅ (Inj1 (X5 ∅ ∅ ∅ ) X2 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ Inj1 ∅ ) (Inj1 (X4 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set → set Inj0 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ X7 ) (λX8 : set → set → set → set λX9 : set → set ∅ ) ) → (∀X4 : (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set → set λX9 : set → set Inj1 ∅ ) False ) → (∀X4 : set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set → set → set → set (Inj0 (X7 (λX8 : set ⇒ Inj1 (X6 ∅ ) ∅ (X6 (setsum ∅ ∅ ∅ ∈ Inj1 (X7 (λX8 : set ⇒ setsum (Inj1 ∅ ∅ ) (X4 X5 (X4 ∅ ∅ ∅ (Inj0 ∅ (X4 (setsum ∅ ∅ (setsum ∅ ∅ (Inj1 ∅ (Inj1 (X6 ∅ → X0 (λX8 : set → set X8 (Inj0 (setsum ∅ ∅ ) (Inj1 (setsum ∅ (Inj1 ∅ (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set → (set → set → set → set X0 (λX8 : set → set setsum (X8 (X7 (Inj1 ∅ (Inj1 ∅ (λX9 : set ⇒ setsum ∅ ∅ ) ∅ (setsum ∅ (setsum (X7 ∅ ∅ (λX9 : set ⇒ ∅ ) ∅ X6 ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMJiwSr1Tzzzt9wQSUXm7vMqUzeQcfopz25 )
∀X0 : ((set → set → set → (((set → set → set → set → set → set → set → (set → (set → set → set → prop ∀X1 : ((set → set → (set → set → set → set → set → set → ((set → set → set → set → prop ∀X2 : ((set → set → ((set → set → set → set → ((((set → set → set → set → set → set → (set → set → set → (set → set → set → ((set → set → set → set → set → (set → set → prop ∀X3 : ((set → set → set → ((set → set → set → set → set → ((set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : (set → set → set Inj0 (Inj1 (Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set λX10 : set → set X10 (X10 X7 ) (λX8 : set → set → set ∅ ) ∅ (λX8 : set ⇒ Inj0 (setsum (Inj0 X5 (Inj0 ∅ ) X3 (λX8 : set → set → set λX9 : (set → set → set → set setsum (setsum (Inj1 (X6 (λX10 : set → set → set ∅ ) (setsum (Inj1 ∅ (setsum ∅ ∅ (X8 X7 ∅ ) (λX8 : set → set setsum (Inj1 (Inj0 (Inj1 ∅ (X6 (λX9 : set → set → set setsum (X9 ∅ ∅ (setsum ∅ ∅ ) ) ) → (∀X4 : ((set → set → (set → set → set → (set → set → (set → set → set → set ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set → set λX9 : (set → set → set → set Inj0 (Inj0 ∅ ) (λX8 : set → set ∅ ) X0 (λX8 : set → set X5 ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → (set → set → set ∀X6 : set , ∀X7 ∈ Inj1 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ X2 (λX8 : set → set λX9 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set λX10 : set → set ∅ ) (λX8 : set → set → set ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) ) → (∀X4 : set → ((set → set → set → set → set ∀X5 : (set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X2 (λX8 : set → set λX9 : (set → set → set ∅ ) (λX8 : ((set → set → set → set → set → set λX9 : set → set → set λX10 : set → set Inj1 X7 ) (λX8 : set → set → set setsum ∅ (Inj1 (X6 (λX9 : set ⇒ λX10 : set → set λX11 : set ⇒ ∅ ) ) (Inj0 (setsum (X5 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ setsum X7 (setsum (Inj0 (setsum ∅ ∅ ∅ ) (Inj1 (X4 ∅ (λX8 : set → set λX9 : set ⇒ setsum X9 (setsum ∅ ∅ ) ∈ X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ) → (∀X4 : (set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set ∀X7 : (set → (set → set → set → set → set → set (Inj0 X5 ∈ X4 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) → X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set → set → set setsum ∅ ∅ ) X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) (λX8 : set → set → set setsum (Inj1 (X6 ∅ (λX9 : set → set λX10 : set ⇒ X9 ∅ ) (Inj0 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : (((set → set → set → (set → set → set → set → set → set ∀X7 : set , X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X9 (setsum (setsum (Inj0 ∅ ∅ (setsum X11 (setsum ∅ ∅ ) (λX8 : set → set → set X8 (setsum X7 (Inj1 (X6 (λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ ∅ ) ∅ (Inj0 (X5 (setsum ∅ ∅ ∅ ) False ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set → set λX9 : (set → set → set → set Inj0 ∅ ) (λX8 : set → set setsum (setsum ∅ ∅ (setsum ∅ (setsum (setsum ∅ ∅ X7 ) X0 (λX8 : set → set X6 ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) ) → (∀X4 : set → set → (set → set → set ∀X5 : (((set → set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set → set ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 X10 ) (λX8 : set ⇒ λX9 : set → set ∅ ) X1 (λX8 : set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj0 (Inj0 ∅ ) (λX8 : set → set → set X8 ∅ (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum (X5 (λX9 : (set → set → set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ (Inj0 ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUsAzpnFWXo8Kv6ESiga72NFgB64YeRYFi )
∀X0 : ((set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : (((((set → set → set → set → (set → set → set → set → set → (set → set → set → set → set → prop ∀X3 : (set → set → (set → set → set → (set → set → set → set → set → prop (∀X4 : (set → set → set → set → set → set ∀X5 : set → set ∀X6 : set , ∀X7 : set , (Inj1 (X5 ∅ ∈ setsum X7 (Inj1 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set → set λX12 : set ⇒ Inj1 ∅ ) (Inj1 X7 ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set → set → set ∀X6 : set , ∀X7 : ((set → set → set → set → set X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set → set λX11 : set → set λX12 : set ⇒ X11 (X11 (X11 (setsum ∅ ∅ ) (setsum ∅ (setsum (X7 (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) (Inj0 (setsum ∅ ∅ (Inj0 (Inj0 (X5 (λX8 : (set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ ∅ ) (Inj0 ∅ ∈ X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X2 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set → set X8 (λX10 : (set → set → set X10 (λX11 : set ⇒ Inj0 (X8 (λX12 : (set → set → set ∅ ) (λX12 : set ⇒ ∅ ) ∅ ∅ ) ) (λX10 : set ⇒ Inj1 (Inj0 (Inj1 ∅ ) (Inj1 (setsum (setsum ∅ ∅ (Inj0 ∅ ∅ ) X4 ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set → set (Inj1 (Inj0 (setsum ∅ (Inj1 ∅ ∈ Inj0 ∅ → X2 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set → set Inj1 X6 ) (Inj1 (setsum (setsum (Inj0 ∅ ∅ ∅ X1 (λX8 : set → set ∅ ) X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → (set → set → set → set → set → set (setsum ∅ ∅ ∈ Inj1 X4 → X2 (λX8 : (((set → set → set → set → (set → set → set → set → set λX9 : set → set → set ∅ ) (setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ X1 (λX8 : set → set ∅ ) X6 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set ∀X7 : (set → (set → set → set → set X1 (λX8 : set → set Inj1 (Inj1 (X6 X5 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj1 ∅ → X1 (λX8 : set → set X8 ∅ ) (Inj1 (setsum (Inj1 X4 X7 X0 (λX8 : set → set → set → set setsum (X8 ∅ ∅ ∅ (X8 ∅ (Inj0 (setsum ∅ ∅ (setsum X6 ∅ ) (Inj1 X5 ) → (∀X4 : (set → set → set → set ∀X5 : set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set → set → set → set ∅ ) X6 (Inj1 (setsum (Inj0 (Inj0 ∅ X7 ∈ X5 (setsum ∅ (setsum (Inj0 ∅ (Inj0 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKmMrFuUbaNVkbWj51GKRByY9Lq7xTbRXm )
∀X0 : (set → (set → set → ((set → set → set → (set → set → set → set → set → ((set → set → set → set → set → (set → set → set → prop ∀X1 : (set → set → (set → (set → set → set → set → (set → set → set → prop ∀X2 : (set → (set → (set → set → set → ((set → set → set → set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set → (set → set → set ∀X7 : set → set → set (setsum (setsum ∅ (setsum ∅ (Inj1 ∅ (X6 (setsum (setsum ∅ ∅ X4 ∅ (λX8 : set ⇒ Inj1 ∅ ) ∈ setsum X4 ∅ → X3 (λX8 : set ⇒ λX9 : set ⇒ X7 ∅ (setsum X8 (Inj0 (Inj0 ∅ ) ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : (((set → set → set → set → (set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (Inj1 ∅ (setsum (X4 (λX8 : (set → set → set → set λX9 : set ⇒ setsum (X6 (λX10 : set → set λX11 : set ⇒ ∅ ) (setsum ∅ ∅ ) X7 ∈ setsum (Inj0 (X5 (λX8 : (set → set → set → set λX9 : set → set X6 (λX10 : set → set λX11 : set ⇒ ∅ ) ) (setsum ∅ (X5 (λX8 : (set → set → set → set λX9 : set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 X7 ) (λX8 : set ⇒ λX9 : set ⇒ X9 ) X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set Inj0 (setsum (Inj0 (X9 ∅ (λX11 : set ⇒ ∅ ) (Inj0 (setsum ∅ ∅ ) (setsum X6 (setsum ∅ (setsum X5 (Inj1 ∅ X5 ) → (∀X4 : ((set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set setsum ∅ (X10 (λX11 : set ⇒ X11 ) ) (setsum (setsum X6 ∅ (setsum (Inj1 X5 (Inj0 (X7 ∅ (setsum X5 (X7 (Inj1 (Inj1 ∅ X1 (λX8 : set ⇒ setsum (Inj0 (setsum X5 (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (setsum (setsum ∅ ∅ X7 ∈ Inj1 (Inj1 ∅ → X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 X8 ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) X3 (λX8 : set ⇒ λX9 : set ⇒ setsum (Inj1 (Inj0 X9 (setsum X9 (setsum ∅ X6 ) X6 ) → (∀X4 : set → (set → set → set → (set → set → set ∀X5 : set , ∀X6 : set → set → set ∀X7 : set → set → set (setsum (setsum (Inj1 (setsum ∅ ∅ (setsum (setsum ∅ ∅ ∅ (Inj0 ∅ ∈ X6 (Inj0 (X4 (setsum ∅ ∅ (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) (λX8 : set ⇒ setsum ∅ ∅ ) (setsum (X7 (setsum ∅ ∅ ∅ (Inj1 (Inj1 ∅ → X0 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X12 ) (Inj1 (Inj1 (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) X5 (λX8 : set ⇒ ∅ ) (setsum (Inj1 (Inj0 (Inj0 ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → (set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X12 ) (setsum ∅ (Inj0 ∅ (λX8 : set → set λX9 : set ⇒ Inj0 ∅ ) (setsum (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (setsum (setsum X7 (setsum ∅ ∅ (Inj0 ∅ (λX8 : set ⇒ setsum X8 ∅ ) (Inj0 (X6 ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj1 ∅ ) (λX8 : set ⇒ X6 X7 (λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) (λX9 : set ⇒ setsum ∅ ∅ ) ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcwmf4GWzEzRaFpFkhcFMnTxTSgDe9FGbf )
∀X0 : (set → set → (set → ((set → set → set → set → set → (set → set → set → set → (set → set → prop ∀X1 : ((set → set → set → (set → set → set → set → set → set → prop ∀X2 : (set → set → (set → set → (set → set → set → set → prop ∀X3 : (((set → set → set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : (((set → set → set → set → ((set → set → set → set → set (setsum (X6 (λX8 : set → set ∅ ) (Inj0 (setsum ∅ ∅ (setsum (X7 (λX8 : (set → set → set setsum ∅ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum ∅ ∅ ) ∅ ∈ Inj1 (setsum ∅ (setsum (setsum ∅ ∅ (X7 (λX8 : (set → set → set ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) → X3 (λX8 : (set → set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (X6 (λX10 : set → set ∅ ) X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set setsum ∅ (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) (Inj0 (setsum (setsum X6 ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → (set → set → set → set ∀X6 : set → set → set ∀X7 : set → ((set → set → set → (set → set → set → set (Inj1 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ ∅ ∈ setsum ∅ ∅ → X2 (λX8 : set ⇒ Inj0 (X7 (setsum X8 ∅ (λX9 : set → set X6 (setsum ∅ ∅ (Inj1 ∅ ) (λX9 : set ⇒ Inj0 ∅ ) (setsum (X7 ∅ (λX9 : set → set ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set Inj1 (Inj0 (setsum (setsum ∅ ∅ (X7 ∅ (λX11 : set → set ∅ ) (λX11 : set ⇒ ∅ ) ∅ ) ∅ X3 (λX8 : (set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 X8 ) ) → (∀X4 : ((set → set → set → ((set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X7 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (X6 (λX10 : (set → set → set → set λX11 : set ⇒ λX12 : set ⇒ X11 ) ) (Inj0 (setsum X5 ∅ (λX8 : set ⇒ ∅ ) X1 (λX8 : set → set X6 (λX9 : (set → set → set → set λX10 : set ⇒ λX11 : set ⇒ Inj0 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) (X6 (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set → set Inj1 X7 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum X9 ∅ ) ∅ False ) → (∀X4 : (set → set → set → set ∀X5 : (set → set → set → set → set ∀X6 : ((set → set → set → set → set → set ∀X7 : set , (Inj1 (Inj0 (X5 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 ∅ ) ∈ Inj1 (setsum (Inj1 X7 ∅ → X0 (λX8 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : (set → set → set → set Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ∅ (λX8 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (X7 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set X6 (λX10 : set → set → set Inj0 ∅ ) ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 X5 (λX8 : set ⇒ setsum ∅ ∅ ) (Inj1 (X7 X5 ∈ Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMH1DUK4EhShoFFUR66o5euZWGgWACzpKjE )
∀X0 : (set → (set → (set → set → set → ((set → set → set → set → set → ((set → (set → set → set → set → set → prop ∀X1 : (set → (((set → set → set → set → set → set → set → set → set → set → prop ∀X2 : ((set → set → set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : (((set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set X8 ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj0 (X8 (X8 (setsum ∅ ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) ) X3 (λX8 : set ⇒ setsum (Inj1 (Inj0 ∅ ∅ ) (X7 ∅ (Inj0 ∅ ) → (∀X4 : (((set → set → set → set → (set → set → set → set ∀X5 : (((set → set → set → set → set → (set → set → (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ X8 ) (setsum ∅ (Inj1 ∅ (Inj1 (X5 (λX8 : (set → set → set → set X6 ) (λX8 : set ⇒ setsum X6 (Inj0 ∅ ) (λX8 : set ⇒ ∅ ) (X6 ∈ Inj0 (Inj0 X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set → set X8 ∅ ) (Inj1 X6 X5 ) → (∀X4 : set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X6 ∈ setsum X7 (Inj1 X6 → X2 (λX8 : set → set ∅ ) ∅ ∅ X2 (λX8 : set → set Inj0 (Inj0 ∅ ) ∅ X5 ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : (((set → set → set → set → (set → set → set → ((set → set → set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set → set λX10 : set ⇒ Inj1 (setsum ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ ) (Inj1 (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set → set → ((set → set → set → set → set ∀X6 : ((set → set → set → set → set ∀X7 : set → (set → set → set → set → set X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set → set → set λX10 : set ⇒ Inj1 (setsum ∅ (setsum ∅ ∅ ) (Inj1 ∅ (setsum X4 ∅ ∈ setsum (Inj1 (X6 (λX8 : set → set → set Inj0 ∅ ) ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set X2 (λX8 : set → set Inj0 (Inj1 ∅ ) (Inj1 (setsum (setsum (setsum ∅ ∅ ∅ (Inj0 (setsum ∅ ∅ X6 X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ Inj0 (setsum X9 (X7 (λX10 : set → set → set Inj0 ∅ ) ) ) → (∀X4 : (((set → set → set → set → set → set → set → ((set → set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set (X6 ∈ setsum (Inj1 (Inj1 (Inj1 ∅ (Inj0 ∅ → X0 (λX8 : set ⇒ λX9 : set → (set → set → set λX10 : (set → set → set → set ∅ ) (λX8 : set → (set → set → set λX9 : set ⇒ X7 (λX10 : set ⇒ Inj0 ∅ ) ) X2 (λX8 : set → set X8 (Inj1 (Inj1 (Inj1 ∅ ) (X5 (λX8 : set → set → set setsum (setsum ∅ (setsum ∅ ∅ (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) X6 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMUoTbd38143ow9Gj2UiqK29C9ipa2xtSZK )
∀X0 : ((set → set → (set → set → set → set → set → (((set → set → set → set → (set → set → set → ((set → set → set → prop ∀X1 : (set → set → (set → set → set → prop ∀X2 : (set → (set → set → set → (set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → (set → set → set → set ∀X7 : set , X0 (λX8 : set → set → (set → set → set ∅ ) X7 (λX8 : (set → set → set → set λX9 : set → set setsum (setsum (setsum (setsum ∅ ∅ (X8 (λX10 : set ⇒ ∅ ) ∅ (setsum ∅ (X8 (λX10 : set ⇒ ∅ ) ∅ (X8 (λX10 : set ⇒ Inj1 (X9 ∅ ) (Inj1 ∅ ) (λX8 : set → set setsum ∅ (Inj1 (Inj1 (Inj1 ∅ ) X3 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set setsum (X6 (λX9 : set ⇒ setsum ∅ ∅ ) (λX9 : set → set setsum ∅ ∅ ) (λX9 : set ⇒ ∅ ) ∅ ∅ ) (λX8 : set ⇒ ∅ ) (setsum ∅ (Inj1 (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) (λX8 : set ⇒ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → (set → set → set ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ setsum X6 (setsum ∅ X9 ) (setsum ∅ X4 (X6 ∈ Inj0 (Inj0 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : (set → set → set ∀X6 : (set → set → set → set ∀X7 : set → set (Inj0 (setsum ∅ (Inj0 (setsum ∅ ∅ ∈ X5 (λX8 : set ⇒ X5 (λX9 : set ⇒ X8 ) ) → X2 (λX8 : set ⇒ λX9 : set → set Inj1 (X7 (setsum (Inj0 ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ ∅ ) X2 (λX8 : set ⇒ λX9 : set → set Inj0 X8 ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj1 ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) X2 (λX8 : set ⇒ λX9 : set → set ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X6 ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set → set → set → set → set ∀X6 : (((set → set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set → set ∀X7 : (set → set → set X1 (λX8 : set ⇒ setsum ∅ X8 ) (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 (λX10 : set ⇒ Inj1 ∅ ) ∅ ) (Inj1 ∅ ∈ setsum ∅ (setsum ∅ (X7 (λX8 : set ⇒ setsum ∅ ∅ ) ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∅ X0 (λX8 : set → set → (set → set → set Inj0 ∅ ) (setsum (setsum ∅ ∅ (X6 (setsum (Inj1 ∅ (setsum ∅ ∅ (λX8 : (set → set → set → set λX9 : set → set X7 ) (λX8 : set → set X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set → set → (set → set → set Inj0 (setsum (Inj1 ∅ ∅ ) X4 (λX8 : (set → set → set → set λX9 : set → set ∅ ) (λX8 : set → set ∅ ) (setsum ∅ (X6 (setsum (Inj1 ∅ (Inj0 ∅ ∈ setsum (setsum (setsum (Inj0 ∅ ∅ (Inj1 (setsum ∅ ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMbJfAZYz9JpKdHj3uR3w1vt4QDLx4CnAE5 )
∀X0 : (set → set → (set → set → set → (((set → set → set → set → prop ∀X1 : (((((set → set → set → set → set → ((set → set → set → set → (set → set → set → set → set → set → (set → ((set → set → set → set → set → set → prop ∀X2 : ((set → ((set → set → set → set → set → set → (set → set → (set → set → set → set → set → (((set → set → set → set → prop ∀X3 : (set → ((set → set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 X4 ∈ Inj1 (setsum ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ → X0 (λX8 : set ⇒ Inj0 (setsum ∅ (Inj0 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj0 (Inj0 (setsum ∅ X8 ) (λX8 : (set → set → set ∅ ) X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X8 ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set ∀X7 : set → ((set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (Inj0 (Inj0 (setsum (X7 ∅ (λX8 : set → set ∅ ) ∅ X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (setsum (Inj1 X11 ∅ ) X5 ) → (∀X4 : ((set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : set , X2 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set λX12 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ) (Inj0 (X4 (λX8 : set → set → set λX9 : set → set X9 (Inj1 ∅ ) (λX8 : (set → set → set setsum (Inj1 (Inj1 (X8 (λX9 : set ⇒ ∅ ) X5 ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set → set ∀X7 : set → (set → set → set X2 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ λX10 : set → set λX11 : set → set λX12 : set ⇒ Inj1 (Inj0 (setsum (setsum ∅ ∅ X12 ) (setsum ∅ ∅ (λX8 : (set → set → set setsum ∅ (Inj1 (X6 (X6 ∅ ) (Inj1 (X5 (setsum (X7 ∅ (λX8 : set ⇒ ∅ ) (Inj1 ∅ ∈ Inj1 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X0 (λX8 : set ⇒ X6 X5 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : (set → set → set ∅ ) X1 (λX8 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ X7 ) (λX8 : set ⇒ λX9 : (set → set → set ∅ ) ∅ (Inj0 (X6 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set (Inj1 ∅ ∈ Inj0 (setsum (Inj0 (setsum ∅ ∅ (Inj1 (setsum ∅ ∅ → X1 (λX8 : (((set → set → set → set → set → ((set → set → set → set → (set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (setsum ∅ (Inj0 (Inj1 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set X9 (λX10 : set ⇒ X8 ) ) (X7 (setsum (Inj1 X5 X6 (setsum (setsum ∅ (Inj0 (Inj1 ∅ ∅ X0 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 (setsum ∅ (X7 ∅ ) (λX8 : (set → set → set Inj0 (setsum (setsum ∅ (X8 (λX9 : set ⇒ ∅ ) (X7 (Inj0 ∅ ) ) → (∀X4 : set → ((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set ∀X7 : (set → set → (set → set → set (setsum ∅ (X7 (λX8 : set ⇒ Inj0 (X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : set ⇒ Inj0 (X7 (λX9 : set ⇒ ∅ ) (λX9 : set ⇒ ∅ ) ) ∈ setsum (setsum ∅ (Inj0 (X4 ∅ (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ∅ ∅ → X3 (λX8 : set ⇒ λX9 : (set → set → set → set → set λX10 : set ⇒ λX11 : set ⇒ X9 (λX12 : set ⇒ setsum X10 (setsum ∅ (Inj1 ∅ ) ∅ X10 ) (setsum (Inj0 ∅ ∅ X0 (λX8 : set ⇒ Inj1 (Inj1 (Inj1 X8 ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (λX8 : (set → set → set setsum ∅ (Inj1 (setsum (setsum ∅ ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → (set → set → set → set ∀X6 : set , ∀X7 : set → set → set X0 (λX8 : set ⇒ setsum ∅ (Inj1 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X7 (Inj0 X9 (Inj0 X8 ) (λX8 : (set → set → set X6 ) (setsum (setsum (setsum (X7 ∅ ∅ (X5 (λX8 : set ⇒ λX9 : set → set ∅ ) ∅ (setsum (X5 (λX8 : set ⇒ λX9 : set → set X7 ∅ ∅ ) (X5 (λX8 : set ⇒ λX9 : set → set X9 ∅ ) ∈ Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMKugUQiTkZgcmvzTFvjogU6vHySG7A4aBM )
∀X0 : (set → set → set → prop ∀X1 : (set → set → set → ((set → set → set → prop ∀X2 : ((set → ((set → set → set → set → set → set → (set → set → set → set → set → ((set → set → set → set → prop ∀X3 : ((set → set → set → (set → set → (set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , X3 (λX8 : set → set Inj0 (X8 ∅ ) (λX8 : set ⇒ X5 ) (λX8 : set ⇒ X6 ∅ (λX9 : set ⇒ ∅ ) ) (Inj1 ∅ ) → (∀X4 : set → (set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set → set Inj1 (Inj1 (X6 (λX9 : (set → set → set λX10 : set → set λX11 : set ⇒ setsum ∅ ∅ ) ) (λX8 : set ⇒ setsum ∅ (Inj1 X8 ) (λX8 : set ⇒ ∅ ) (Inj0 (Inj1 ∅ (Inj1 ∅ ∈ setsum (setsum ∅ ∅ ∅ ) → (∀X4 : set → set → set ∀X5 : ((set → set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : (set → set → set → set → set X2 (λX8 : set → ((set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (Inj0 ∅ (Inj0 X12 ) (setsum (Inj1 (Inj1 ∅ ∅ (λX8 : set → set λX9 : set ⇒ setsum X9 (X7 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) ) → (∀X4 : (set → (set → set → set → set → set ∀X5 : set , ∀X6 : set → ((set → set → set → set → set → set ∀X7 : set , (Inj0 (Inj1 X7 ∈ X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) → X2 (λX8 : set → ((set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj0 (Inj0 (setsum ∅ (Inj0 ∅ ) (setsum (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) X2 (λX8 : set → ((set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ Inj0 (Inj0 ∅ ) ∅ (λX8 : set → set λX9 : set ⇒ Inj0 (Inj0 (setsum (Inj0 ∅ ∅ ) ) → (∀X4 : set , ∀X5 : (set → set → set → set → set ∀X6 : (set → set → set → set → set ∀X7 : set → set (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ Inj1 X9 ) ∈ setsum (Inj0 (Inj1 (setsum ∅ ∅ (setsum (Inj1 (setsum ∅ ∅ (Inj0 (setsum ∅ ∅ → X0 (λX8 : set ⇒ X8 ) (setsum (setsum (setsum ∅ (setsum ∅ ∅ ∅ (Inj1 (Inj1 ∅ X1 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum (Inj1 X9 (Inj1 ∅ (setsum ∅ (X7 (X7 ∅ ) (λX8 : set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ X8 ) (λX8 : set → set setsum (setsum (Inj0 (setsum ∅ ∅ ∅ (Inj0 (Inj0 (Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → ((set → set → set → set → set ∀X7 : set → set X0 (λX8 : set ⇒ X8 ) (Inj0 ∅ ) → (∀X4 : (set → set → ((set → set → set → set → set ∀X5 : set → set → set ∀X6 : set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ X8 ) (X6 (setsum (Inj1 (Inj0 ∅ (X5 ∅ ∅ (setsum (setsum ∅ (setsum ∅ ∅ (X6 (Inj0 ∅ (Inj1 ∅ (setsum ∅ ∅ (X4 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ setsum X9 (setsum ∅ ∅ ) (Inj0 ∅ ∈ X4 (λX8 : set ⇒ X8 ) (λX8 : set → set λX9 : set ⇒ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMPYfiYvV2FiFGaZd2kJTRGu117iPKhfmVn )
∀X0 : (set → set → ((set → set → set → set → set → set → prop ∀X1 : (set → set → ((set → set → set → prop ∀X2 : (set → (set → set → ((set → set → set → (set → set → set → set → set → (set → set → prop ∀X3 : (set → set → (((set → set → set → (set → set → set → set → set → prop (∀X4 : set → (set → set → (set → set → set ∀X5 : (set → set → set → set → set ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ Inj0 (setsum (X7 (setsum ∅ ∅ (X7 ∅ ) X3 (λX8 : set ⇒ X5 (λX9 : set ⇒ X8 ) (setsum (Inj1 (setsum ∅ ∅ (X7 X6 (Inj0 ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ setsum ∅ (setsum (Inj0 (X8 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX10 : set ⇒ ∅ ) X9 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ setsum (setsum (Inj0 (Inj0 ∅ (setsum (X7 ∅ ∅ (Inj1 (Inj0 (setsum ∅ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ setsum (Inj1 (X8 (λX10 : set ⇒ λX11 : set ⇒ X10 ) (λX10 : set ⇒ ∅ ) (X8 (λX10 : set ⇒ λX11 : set ⇒ Inj1 (setsum ∅ ∅ ) (λX10 : set ⇒ ∅ ) ) (Inj1 (Inj1 ∅ ∈ Inj1 X6 ) → (∀X4 : (set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ ∅ ) (Inj0 (X4 (λX8 : set ⇒ λX9 : set → set Inj0 (Inj0 ∅ ) (λX8 : set ⇒ setsum (Inj1 (Inj1 (Inj1 ∅ (setsum (Inj1 ∅ X6 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : ((set → set → set → set → set ∀X7 : set → (set → set → set → (set → set → set → set (Inj0 ∅ ∈ setsum (Inj1 (Inj1 (Inj1 ∅ (X7 (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ setsum ∅ X5 ) X4 → X2 (λX8 : set ⇒ λX9 : set → set λX10 : (set → set → set λX11 : set → set λX12 : set ⇒ X9 ∅ ) ∅ (λX8 : set ⇒ Inj0 ∅ ) X3 (λX8 : set ⇒ Inj1 (Inj0 (setsum (Inj1 ∅ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X5 (Inj0 (Inj1 (Inj1 ∅ ∈ Inj1 X7 → X1 (λX8 : set ⇒ setsum (setsum (setsum (setsum ∅ ∅ X6 (setsum X6 ∅ ∅ ) (λX8 : set → set X5 (setsum (Inj1 X6 ∅ ) ) → (∀X4 : ((set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → (set → set → set → set → set → (set → set → set → set X1 (λX8 : set ⇒ ∅ ) (λX8 : set → set ∅ ) False ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : (set → set → set → (set → set → set λX9 : set ⇒ Inj0 (Inj0 ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set Inj1 (setsum (setsum (Inj0 ∅ (Inj1 ∅ ∅ ) (Inj1 (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X7 ) ) → (∀X4 : (set → set → set ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set ∀X7 : set → (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set Inj1 (setsum (X7 ∅ (λX11 : set ⇒ setsum ∅ ∅ ) (X10 (λX11 : set ⇒ X9 ) (setsum ∅ ∅ ) (X6 (λX8 : set ⇒ ∅ ) (λX8 : set → set λX9 : set ⇒ X7 (X7 ∅ (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ Inj0 (Inj0 ∅ ) ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMLA89SfsTrpRQuHiSAJVTXTbpQ7qfUsSHV )
∀X0 : (set → set → set → set → prop ∀X1 : (set → ((set → set → set → (set → set → set → set → set → ((((set → set → set → set → set → set → set → prop ∀X2 : (set → set → set → set → prop ∀X3 : (((set → (set → set → set → set → set → set → set → set → set → ((set → (set → set → set → ((set → set → set → set → set → set → prop (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → set → set → set → set → set ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → (set → set → set λX9 : (set → set → set → set X7 ) (setsum (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 (Inj0 ∅ ) (setsum (setsum ∅ ∅ (setsum ∅ ∅ X5 (setsum X7 ∅ ∅ X3 (λX8 : (set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 X9 ) (λX8 : set → (set → set → set λX9 : (set → set → set → set ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 X8 ) (setsum (setsum ∅ ∅ (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ ∅ (setsum (Inj0 ∅ (Inj1 ∅ (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ ∅ ) ∅ ∅ ∅ (Inj1 ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set → (set → set → set → set ∀X6 : set , ∀X7 : ((set → set → (set → set → set → set → (set → set → set → set X3 (λX8 : (set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ X9 ) (λX8 : set → (set → set → set λX9 : (set → set → set → set setsum ∅ (Inj1 (setsum X6 ∅ ) X6 (setsum (X7 (λX8 : set → set λX9 : set → set X8 (Inj0 ∅ ) (setsum X4 (Inj0 ∅ (λX8 : set ⇒ setsum X8 (setsum ∅ ∅ ) ∅ ∅ ∈ X5 ∅ (X7 (λX8 : set → set λX9 : set → set Inj1 ∅ ) (Inj1 ∅ (λX8 : set ⇒ ∅ ) (Inj1 (setsum ∅ ∅ (λX8 : set ⇒ Inj0 (Inj0 (Inj0 ∅ ) X6 ) → (∀X4 : set → (set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : (set → (set → set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (λX8 : set → (set → set → set λX9 : (set → set → set → set setsum X6 (Inj1 (setsum (X8 ∅ (λX10 : set ⇒ ∅ ) (setsum ∅ ∅ ) ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj0 ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : set ⇒ Inj1 (Inj0 (setsum (setsum ∅ ∅ ∅ ) (Inj0 X5 X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) (Inj1 (Inj1 (Inj0 (Inj1 ∅ ) → (∀X4 : set → (set → set → set → set ∀X5 : set → set → (set → set → set ∀X6 : (set → (set → set → set → set → (set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (setsum ∅ (setsum X9 (Inj1 ∅ ∅ ) (Inj0 (Inj0 (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X8 ) (λX8 : set ⇒ λX9 : set ⇒ X6 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) X1 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set Inj0 ∅ ) (λX8 : ((set → set → set → set → set → set ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set X1 (λX8 : set ⇒ λX9 : (set → set → set → (set → set → set → set X8 ) (λX8 : ((set → set → set → set → set → set setsum (setsum ∅ ∅ ∅ ) False ) → (∀X4 : set → set ∀X5 : (set → (set → set → set → ((set → set → set → set ∀X6 : set → set ∀X7 : set , (setsum (setsum (X4 (setsum ∅ ∅ (Inj0 (Inj0 ∅ (setsum (setsum X7 (setsum ∅ ∅ (setsum (Inj0 ∅ (setsum ∅ ∅ ∈ X7 → X0 (λX8 : set ⇒ λX9 : set ⇒ Inj0 (setsum (Inj0 (Inj0 ∅ ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → ((set → set → set → set ∀X6 : set , ∀X7 : (set → set → set X0 (λX8 : set ⇒ λX9 : set ⇒ X6 ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMRk3Jnc97mQMgYFTZ2xiowjTQEfGJdWCTw )
∀X0 : ((set → (set → set → set → (set → set → set → set → set → set → (set → set → set → set → prop ∀X1 : (set → (set → set → set → set → set → set → (set → set → prop ∀X2 : (set → (set → set → set → set → set → set → prop ∀X3 : (set → set → ((set → set → set → set → (set → set → set → ((((set → set → set → set → set → set → prop (∀X4 : set → set ∀X5 : ((set → set → set → set → set ∀X6 : set , ∀X7 : (set → set → set → set (X7 (λX8 : set ⇒ ∅ ) (X7 (λX8 : set ⇒ X8 ) X6 ∈ setsum (X5 (λX8 : set → set λX9 : set ⇒ ∅ ) (Inj1 (setsum (X4 ∅ (Inj1 ∅ → X0 (λX8 : set → (set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (Inj1 (setsum (Inj1 ∅ X11 ) (λX8 : set ⇒ Inj0 X6 ) (setsum (setsum ∅ (X7 (λX8 : set ⇒ ∅ ) X6 (Inj0 (Inj0 ∅ (Inj0 (X4 (Inj1 (setsum ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set Inj1 (Inj0 (X10 (λX12 : set ⇒ ∅ ) ∅ ) (λX8 : ((set → set → set → set → set X8 (λX9 : set → set λX10 : set ⇒ Inj1 X10 ) ) ) → (∀X4 : set , ∀X5 : (set → set → set → set ∀X6 : set → set ∀X7 : set , X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set X9 ) (λX8 : ((set → set → set → set → set Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum X7 (Inj0 (Inj1 ∅ ∈ Inj0 (setsum X7 (setsum (Inj0 ∅ X4 → X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ setsum ∅ (setsum ∅ (setsum (Inj1 ∅ ∅ ) (λX8 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ X9 (setsum (Inj1 (Inj0 ∅ X7 ∅ ) ∅ ) → (∀X4 : ((set → set → (set → set → set → ((set → set → set → set → set ∀X5 : ((set → set → set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ setsum ∅ (X7 ∅ ) (X7 (setsum (setsum ∅ (Inj0 ∅ ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set setsum (Inj1 ∅ (X10 (λX12 : set ⇒ ∅ ) (Inj0 (Inj0 ∅ ) (λX8 : ((set → set → set → set → set Inj1 (X5 (λX9 : set → set → set Inj0 (Inj1 ∅ ) (X5 (λX9 : set → set → set ∅ ) (Inj0 ∅ (Inj1 ∅ (X7 ∅ (Inj0 (Inj1 ∅ (Inj1 (setsum ∅ ∅ ) ) → (∀X4 : ((set → set → set → set → set → set → ((set → set → set → set ∀X5 : (((set → set → set → set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set (Inj0 ∅ ∈ Inj1 (X4 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (λX8 : set → set Inj0 (setsum ∅ ∅ ) → X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set setsum (Inj0 ∅ ∅ ) (λX8 : ((set → set → set → set → set ∅ ) X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ setsum ∅ (setsum (X5 (λX9 : (set → set → set → set X6 ∅ ) (X7 (λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ X11 ) ) ) → (∀X4 : (set → set → set ∀X5 : set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → ((set → set → set → set X1 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ λX11 : set ⇒ ∅ ) (λX8 : set ⇒ Inj0 ∅ ) X2 (λX8 : set ⇒ λX9 : set → set → set λX10 : set ⇒ ∅ ) (setsum (X7 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ X8 (X8 ∅ ∅ (X7 (λX11 : set → set → set λX12 : set ⇒ λX13 : set ⇒ ∅ ) (λX11 : set → set ∅ ) ) (λX8 : set → set setsum (setsum ∅ ∅ ∅ ) (setsum (Inj1 (Inj1 ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj1 (Inj1 (Inj1 (setsum ∅ ∅ → X0 (λX8 : set → (set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ X11 ) (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (setsum (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ ∅ (setsum X6 ∅ ) → (∀X4 : (((set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj0 (setsum (Inj1 (Inj1 ∅ X6 ∈ Inj0 (setsum ∅ ∅ → X0 (λX8 : set → (set → set → set λX9 : set → set λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ Inj1 (X9 X10 ) (λX8 : set ⇒ setsum X6 ∅ ) (setsum (setsum ∅ (Inj0 ∅ (setsum (setsum X6 (setsum ∅ ∅ X5 (Inj1 (Inj0 ∅ X3 (λX8 : set ⇒ λX9 : set ⇒ λX10 : (set → set → set → set λX11 : set → set setsum (setsum (Inj1 ∅ (X10 (λX12 : set ⇒ ∅ ) ∅ (Inj0 (setsum X9 (X11 ∅ ) (λX8 : ((set → set → set → set → set setsum ∅ ∅ ) ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMZxGQh6BpHp6andBtU327tzayfZ93KQvHr )
∀X0 : (set → set → (set → (set → set → set → prop ∀X1 : ((set → set → set → set → (set → set → set → prop ∀X2 : (((set → set → set → set → set → prop ∀X3 : ((set → set → set → set → prop (∀X4 : set → (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 (setsum X7 X6 ∈ setsum (X4 X5 (λX8 : set ⇒ X5 ) (setsum ∅ (Inj1 ∅ X5 → X3 (λX8 : set → set X8 (Inj1 X5 ) (Inj0 ∅ X3 (λX8 : set → set ∅ ) (Inj1 (setsum (setsum (X4 ∅ (λX8 : set ⇒ ∅ ) ∅ (X4 ∅ (λX8 : set ⇒ ∅ ) ∅ (setsum (setsum ∅ ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set → set ∅ ) (setsum X6 ∅ False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → (set → set → set → set ∀X6 : set , ∀X7 : (set → set → (set → set → set → (set → set → set → set (Inj0 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum ∅ ∅ ∈ Inj1 (Inj1 ∅ → X2 (λX8 : (set → set → set X5 (λX9 : set → set ∅ ) (X8 (λX9 : set ⇒ setsum ∅ (setsum ∅ ∅ ) (λX9 : set ⇒ Inj1 ∅ ) (setsum ∅ (Inj1 (X5 (λX9 : set → set ∅ ) ∅ (λX9 : set ⇒ ∅ ) ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X2 (λX8 : (set → set → set Inj1 (X8 (λX9 : set ⇒ setsum ∅ X6 ) ) (Inj0 ∅ (X5 X7 ∈ X6 ) → (∀X4 : ((set → set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set (setsum (Inj0 (X4 (λX8 : set → set → set λX9 : set ⇒ Inj0 ∅ ) ∅ ∈ Inj0 (Inj1 ∅ → X2 (λX8 : (set → set → set setsum (X7 (λX9 : (set → set → set setsum (setsum ∅ ∅ ∅ ) X5 ) (setsum (setsum X6 (setsum (setsum ∅ ∅ ∅ X5 X1 (λX8 : set → set Inj1 (Inj0 ∅ ) X6 (λX8 : set ⇒ setsum (X7 (λX9 : (set → set → set setsum (Inj0 ∅ (setsum ∅ ∅ ) (Inj0 (Inj0 ∅ ) (X4 (λX8 : set → set → set λX9 : set ⇒ setsum (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum X6 X6 ) ) → (∀X4 : set → set → set ∀X5 : (set → set → set ∀X6 : ((set → set → set → set → set → set → set ∀X7 : set , (Inj0 (X6 (λX8 : set → set setsum (Inj0 ∅ (Inj1 ∅ ) (setsum ∅ (Inj1 ∅ (Inj1 (X6 (λX8 : set → set ∅ ) ∅ ∅ ∅ ∅ ∈ Inj1 (Inj1 (X4 ∅ (X4 ∅ ∅ → X1 (λX8 : set → set Inj1 X7 ) (X5 (λX8 : set ⇒ Inj1 (setsum (setsum ∅ ∅ (setsum ∅ ∅ ) (λX8 : set ⇒ setsum (setsum (Inj0 (setsum ∅ ∅ ∅ ∅ ) X7 X3 (λX8 : set → set X5 (λX9 : set ⇒ ∅ ) ) (Inj1 (Inj1 (X4 X7 (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , (X5 (Inj1 (Inj0 (setsum ∅ ∅ ∈ X5 (Inj0 (Inj0 ∅ → X0 (λX8 : set ⇒ setsum (setsum (Inj1 ∅ X6 (Inj0 ∅ ) (λX8 : set ⇒ λX9 : set → set Inj0 ∅ ) X0 (λX8 : set ⇒ X5 (setsum ∅ (setsum (X5 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set setsum X6 (Inj0 X7 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → (set → set → set → set → set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ setsum (Inj0 (Inj0 (Inj0 ∅ ∅ ) (λX8 : set ⇒ λX9 : set → set ∅ ) X3 (λX8 : set → set Inj0 X5 ) (X6 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum X8 ∅ ) (setsum X5 (Inj1 (Inj0 ∅ ∅ (setsum (setsum ∅ (Inj1 ∅ ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcxuavfw9EHmaofciPbbpQpXdW6DWhXmii )
∀X0 : (set → set → ((set → (set → set → set → set → set → prop ∀X1 : (set → set → set → prop ∀X2 : (set → (set → set → (set → set → set → set → set → set → (set → ((set → set → set → set → (set → set → set → set → prop ∀X3 : (set → set → ((set → set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 ∅ ∈ setsum ∅ X6 → X3 (λX8 : set ⇒ Inj0 X5 ) (λX8 : set → set → set → set λX9 : set → set Inj0 (setsum (Inj1 ∅ (Inj0 X7 ) (Inj0 (X4 (X4 X5 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set → set (Inj1 (X7 X5 ∈ Inj0 (X6 ∅ → X3 (λX8 : set ⇒ ∅ ) (λX8 : set → set → set → set λX9 : set → set ∅ ) (Inj1 (Inj0 X4 X0 (λX8 : set ⇒ setsum (Inj1 (setsum ∅ (setsum ∅ ∅ (Inj1 (Inj0 X8 ) (λX8 : set → (set → set → set → set ∅ ) ) → (∀X4 : ((set → set → set → set → set ∀X5 : (set → set → (set → set → set → (set → set → set ∀X6 : set → set → (set → set → set ∀X7 : (set → (set → set → set → set → set X2 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ setsum (setsum (X9 (setsum ∅ ∅ (setsum ∅ (X9 ∅ (Inj1 (Inj1 (X10 ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ setsum (Inj1 (X10 (Inj1 ∅ (Inj0 (setsum (X10 ∅ X11 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X2 (λX8 : set ⇒ λX9 : set → set λX10 : set → set → set λX11 : set ⇒ λX12 : set ⇒ Inj0 ∅ ) (λX8 : set ⇒ λX9 : (set → set → set → set λX10 : set → set λX11 : set ⇒ Inj1 ∅ ) False ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , (X5 (λX8 : set → set → set X6 ) X4 (λX8 : set ⇒ setsum (setsum ∅ (setsum ∅ ∅ (X5 (λX9 : set → set → set ∅ ) (setsum ∅ ∅ (λX9 : set ⇒ ∅ ) ) ∈ Inj0 (Inj0 X4 → X1 (λX8 : set ⇒ Inj1 (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (Inj1 ∅ ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X1 (λX8 : set ⇒ setsum (Inj0 (X7 (setsum ∅ ∅ ∅ ) (setsum ∅ (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum (Inj1 ∅ (setsum ∅ ∅ X3 (λX8 : set ⇒ setsum (Inj1 (setsum (setsum ∅ ∅ X8 (setsum (Inj1 (setsum ∅ ∅ (setsum X8 (setsum ∅ ∅ ) (λX8 : set → set → set → set λX9 : set → set X8 (Inj0 (setsum ∅ (Inj1 ∅ ∅ ∅ ) (setsum ∅ (Inj1 X6 ) → (∀X4 : set → set ∀X5 : (set → set → ((set → set → set → set → set → set ∀X6 : set , ∀X7 : set → set X0 (λX8 : set ⇒ setsum ∅ (setsum (Inj0 (Inj1 ∅ (X7 (setsum ∅ ∅ ) (λX8 : set → (set → set → set → set Inj1 (Inj1 (X7 (setsum ∅ ∅ ) ) → (∀X4 : set , ∀X5 : ((set → set → set → set → (set → set → set → (set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ X7 ) (λX8 : set → (set → set → set → set X7 ) False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTQNAiJw2DsaH36UHwDxAVEbU46Kr2NeiM )
∀X0 : ((((set → set → set → set → set → (set → (set → set → set → set → (set → ((set → set → set → set → set → (((set → set → set → set → set → set → set → prop ∀X1 : ((set → set → set → set → prop ∀X2 : (((((set → set → set → set → set → (set → set → set → set → set → set → set → (set → set → set → prop ∀X3 : (set → set → (set → set → prop (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → set ∀X7 : set , (X7 ∈ X6 (λX8 : (set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj1 (setsum X7 (setsum ∅ ∅ ) → X3 (λX8 : set ⇒ X8 ) (λX8 : set ⇒ Inj1 (setsum ∅ (setsum (setsum ∅ ∅ (Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum (Inj0 (Inj0 (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ∈ X5 → X3 (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ X9 (λX11 : set ⇒ ∅ ) ) (λX8 : (set → set → set → set X5 ) ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X6 ∈ X7 → X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj1 (setsum (setsum X7 (Inj0 ∅ ∅ ) (λX8 : (set → set → set → set ∅ ) (setsum ∅ (setsum X7 (setsum (Inj0 ∅ X6 ∅ X2 (λX8 : (((set → set → set → set → set → (set → set → set → set → set X7 ) (Inj1 (setsum (Inj0 X4 ∅ (λX8 : set ⇒ setsum (setsum (setsum X7 X6 X7 (setsum ∅ ∅ ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (setsum ∅ X6 ∈ Inj0 (Inj0 ∅ → X2 (λX8 : (((set → set → set → set → set → (set → set → set → set → set setsum X7 X5 ) ∅ (λX8 : set ⇒ Inj0 (setsum X5 ∅ ) ∅ X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set setsum ∅ (setsum (setsum (setsum ∅ ∅ X7 X6 ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj1 (Inj1 ∅ ) (λX8 : (set → set → set → set setsum (Inj1 (X8 (λX9 : set ⇒ X6 ) (setsum ∅ ∅ X7 ) ∅ (setsum (setsum (Inj0 (Inj0 ∅ X4 (Inj0 (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → (set → set → set → set → (set → set → set → set (Inj1 (Inj1 ∅ ∈ Inj0 (setsum (Inj0 (X7 (λX8 : (set → set → set → set λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ ∅ → X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ setsum (Inj0 (Inj1 (Inj1 ∅ (Inj0 (Inj1 (setsum ∅ ∅ ) (λX8 : (set → set → set → set X8 (λX9 : set ⇒ setsum (X7 (λX10 : (set → set → set → set λX11 : set → set setsum ∅ ∅ ) ∅ (λX10 : set ⇒ Inj0 ∅ ) X9 (setsum ∅ (Inj1 ∅ ) ∅ ) (setsum ∅ (Inj1 (setsum (X7 (λX8 : (set → set → set → set λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (setsum ∅ ∅ ∅ X1 (λX8 : set → set setsum (Inj1 (setsum ∅ (X8 ∅ (setsum (setsum (X8 ∅ (Inj0 ∅ ∅ ) (Inj1 ∅ ) → (∀X4 : (set → (set → set → set → set → set → set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → set → set (Inj1 (setsum (setsum (Inj1 ∅ (setsum ∅ ∅ (setsum ∅ (setsum ∅ ∅ ∈ Inj0 (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (setsum ∅ ∅ (Inj0 ∅ (Inj0 ∅ → X1 (λX8 : set → set X6 (Inj0 (Inj1 (setsum ∅ ∅ ) (setsum (X7 (λX8 : set ⇒ Inj1 (Inj1 ∅ ) (Inj0 (Inj1 (Inj0 ∅ X1 (λX8 : set → set Inj1 (setsum (X8 (setsum ∅ ∅ (setsum (Inj1 ∅ (X7 (λX9 : set ⇒ ∅ ) ) ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set ∀X7 : set , (X4 ∈ Inj0 ∅ → X2 (λX8 : (((set → set → set → set → set → (set → set → set → set → set setsum ∅ X5 ) (Inj0 X7 (λX8 : set ⇒ setsum ∅ X8 ) ∅ X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set ∅ ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ ∅ ) (λX8 : (set → set → set → set setsum (Inj1 ∅ X5 ) (Inj0 ∅ X7 ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set , X0 (λX8 : ((set → set → set → set → set λX9 : set → (set → set → set X9 (setsum (X8 (λX10 : set → set → set Inj0 ∅ ) (setsum (Inj0 ∅ ∅ (λX10 : set ⇒ X9 (X8 (λX11 : set → set → set ∅ ) (λX11 : set ⇒ X9 (X9 ∅ (λX12 : set ⇒ ∅ ) (λX12 : set ⇒ ∅ ) ) ) ) (λX8 : set ⇒ λX9 : (set → set → set λX10 : set ⇒ Inj0 (setsum X10 (Inj1 (Inj1 ∅ ) (λX8 : (set → set → set → set Inj1 X5 ) (Inj0 X7 (setsum ∅ (setsum (setsum (X6 (λX8 : set ⇒ ∅ ) ∅ (setsum ∅ X5 (X4 ∈ setsum (Inj1 (Inj1 ∅ (setsum (setsum (Inj0 ∅ (setsum ∅ ∅ (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMTrDW3WaGgYkX4ARCv2nwjonBY9ukeZtEe )
∀X0 : (((set → set → set → set → set → set → set → prop ∀X1 : (set → (((set → set → set → set → set → ((set → set → set → set → set → (set → set → prop ∀X2 : ((set → set → set → (set → set → (set → set → (set → set → set → prop ∀X3 : (((((set → set → set → set → set → set → set → set → (((set → set → set → set → set → set → set → (set → set → (set → set → set → prop (∀X4 : set → set → set ∀X5 : set , ∀X6 : (set → (set → set → set → ((set → set → set → set → set ∀X7 : set , X3 (λX8 : (((set → set → set → set → set → set → set → set λX9 : ((set → set → set → set Inj0 (Inj1 (X6 (λX10 : set ⇒ λX11 : set → set setsum ∅ ∅ ) (λX10 : set → set λX11 : set ⇒ X8 (λX12 : (set → set → set → set λX13 : set ⇒ λX14 : set ⇒ ∅ ) ) ) ∅ (X6 (λX8 : set ⇒ λX9 : set → set X6 (λX10 : set ⇒ λX11 : set → set X10 ) (λX10 : set → set λX11 : set ⇒ setsum (Inj0 ∅ (setsum ∅ ∅ ) ) (λX8 : set → set λX9 : set ⇒ ∅ ) (λX8 : set ⇒ X5 ) (λX8 : set ⇒ Inj1 X8 ) (setsum (X6 (λX8 : set ⇒ λX9 : set → set X9 (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ ∅ ) ∅ ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : (((set → set → set → set → (set → set → set → set ∀X7 : set → ((set → set → set → set (setsum ∅ (X7 X5 (λX8 : set → set Inj0 (X8 ∅ ) ∈ setsum ∅ X5 → X3 (λX8 : (((set → set → set → set → set → set → set → set λX9 : ((set → set → set → set ∅ ) (X7 (Inj0 (setsum ∅ ∅ (λX8 : set → set setsum ∅ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ X8 ) ∅ X3 (λX8 : (((set → set → set → set → set → set → set → set λX9 : ((set → set → set → set ∅ ) (X4 (λX8 : set → set → set ∅ ) ∅ (λX8 : set ⇒ Inj0 X8 ) (λX8 : set ⇒ setsum (Inj0 (X7 (Inj1 ∅ (λX9 : set → set setsum ∅ ∅ ) (Inj0 ∅ ) (setsum (Inj0 ∅ ∅ ) → (∀X4 : (set → set → set → set → set → set ∀X5 : set → set ∀X6 : ((set → set → set → set ∀X7 : set , (Inj1 (Inj1 (Inj1 X7 ∈ Inj1 ∅ → X2 (λX8 : set → set Inj1 (Inj1 (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ setsum X8 (Inj0 (setsum (setsum ∅ ∅ (Inj1 ∅ ) X2 (λX8 : set → set setsum (X8 (Inj1 ∅ (Inj1 X7 ) (λX8 : set ⇒ X8 ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set → (set → set → set ∀X7 : set , X2 (λX8 : set → set X7 ) (λX8 : set ⇒ setsum (Inj1 X5 ∅ ) (λX8 : set ⇒ Inj0 (setsum (Inj0 X5 (setsum ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) (Inj0 (setsum (setsum (setsum ∅ ∅ (Inj0 ∅ (X6 (Inj0 ∅ (λX8 : set ⇒ setsum ∅ ∅ ) ∈ Inj0 (X6 (setsum ∅ (X4 ∅ (λX8 : set ⇒ X7 ) ) → (∀X4 : set , ∀X5 : (set → set → set → (set → set → set → set ∀X6 : (set → set → set → set → set ∀X7 : (set → (set → set → set → set → set (setsum ∅ (setsum (X7 (λX8 : set ⇒ λX9 : set → set setsum ∅ ∅ ) (X5 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (X5 (λX8 : set ⇒ setsum ∅ ∅ ) ∅ (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ ∈ Inj0 (Inj0 (X5 (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ setsum ∅ ∅ ) (X5 (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ → X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set Inj0 ∅ ) (setsum (Inj0 (setsum (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (Inj0 (setsum ∅ ∅ (Inj1 ∅ (λX8 : set ⇒ setsum (X5 (λX9 : set ⇒ setsum ∅ X9 ) ∅ (λX9 : set ⇒ Inj0 (X6 (λX10 : set ⇒ λX11 : set ⇒ λX12 : set ⇒ ∅ ) ) X8 ∅ ) ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : ((set → set → set → set → set λX10 : (set → set → set Inj1 (Inj1 (setsum ∅ (Inj1 ∅ ) ∅ (λX8 : set ⇒ X8 ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → ((set → set → set → set → set → set → set ∀X7 : set , (setsum ∅ (Inj1 (Inj0 ∅ ∈ Inj0 ∅ → X0 (λX8 : (set → set → set → set → set Inj0 (Inj0 (setsum (Inj0 ∅ ∅ ) (Inj0 X4 ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → set → set → set → set setsum (X5 (setsum (setsum ∅ ∅ (Inj1 ∅ (setsum (X8 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ setsum ∅ ∅ ) (setsum ∅ X6 ) (setsum ∅ ∅ (Inj1 (Inj0 ∅ ∈ X4 ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMMYNTELFa6GShLZx4W3v8yb6xhMh6ZcLTP )
∀X0 : ((set → ((set → set → set → set → set → set → set → set → set → ((((set → set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (set → ((set → set → set → set → set → ((((set → set → set → set → (set → set → set → set → prop ∀X3 : (set → set → ((((set → set → set → set → (set → set → set → set → prop (∀X4 : set → set ∀X5 : set , ∀X6 : set → set ∀X7 : (set → (set → set → set → set (Inj0 ∅ ∈ Inj1 ∅ → X3 (λX8 : set ⇒ Inj1 ∅ ) (λX8 : ((set → set → set → set → (set → set → set ∅ ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X3 (λX8 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → (set → set → set ∅ ) False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → ((set → set → set → (set → set → set → set ∀X7 ∈ Inj0 (setsum (setsum X4 ∅ ∅ X2 (λX8 : set ⇒ λX9 : (set → set → set → set X8 ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set ⇒ X10 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X2 (λX8 : set ⇒ λX9 : (set → set → set → set X9 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set λX9 : set → set λX10 : set ⇒ setsum ∅ (X8 (λX11 : set → set X11 ∅ ) ) (setsum ∅ (setsum X7 X6 ∈ X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ Inj0 X6 ) (Inj0 ∅ ) → (∀X4 : set , ∀X5 : ((set → set → (set → set → set → set → set ∀X6 : set , ∀X7 : set , X1 (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) ∅ False ) → (∀X4 : ((set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set → set → set → set → set (setsum X6 (setsum (X4 (λX8 : set → set X8 ∅ ) (setsum ∅ ∅ (X4 (λX8 : set → set setsum ∅ ∅ ) ∅ ∈ Inj1 (setsum (X4 (λX8 : set → set ∅ ) ∅ ∅ → X0 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X8 (setsum (X8 (setsum ∅ ∅ (λX12 : set → set λX13 : set ⇒ Inj0 ∅ ) (Inj0 (Inj0 ∅ (λX12 : set → set λX13 : set ⇒ ∅ ) ) (λX8 : ((set → set → set → set → set Inj1 ∅ ) ) → (∀X4 : set , ∀X5 : (((set → set → set → set → set ∀X6 : (set → (set → set → set → set ∀X7 : (((set → set → set → (set → set → set → ((set → set → set → set → set → set X0 (λX8 : set → ((set → set → set → set → set λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj0 ∅ ) (λX8 : ((set → set → set → set → set ∅ ) (X7 (λX8 : (set → set → set λX9 : set → set Inj1 (setsum (X6 (λX10 : set ⇒ λX11 : set → set ∅ ) ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 ∅ ) (X6 (λX8 : set ⇒ λX9 : set → set X6 (λX10 : set ⇒ λX11 : set → set Inj0 ∅ ) ) ∈ Inj1 (Inj0 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMGUuUvLQKqvUUCccjv8wbtBb6vuxMbH7jL )
∀X0 : (set → set → (set → set → (set → set → set → set → set → prop ∀X1 : (set → (set → set → set → set → set → ((set → set → set → set → ((set → set → set → set → set → prop ∀X2 : (set → set → set → set → (set → set → set → set → prop ∀X3 : (set → ((set → set → (set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → ((set → set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set Inj1 (Inj0 (Inj1 ∅ ) X4 ) → (∀X4 : set → set ∀X5 : (set → set → set → set → ((set → set → set → (set → set → set → set ∀X6 : (((set → set → set → (set → set → set → set → set ∀X7 : ((set → set → set → set → set → ((set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set setsum (setsum (X9 (λX10 : set ⇒ ∅ ) (λX10 : set ⇒ Inj0 ∅ ) (Inj0 ∅ X8 (Inj1 ∅ ) (X4 ∅ X2 (λX8 : set ⇒ λX9 : set ⇒ X7 (λX10 : set → set → set λX11 : set ⇒ Inj1 ∅ ) (λX10 : set → set X8 ) ) (Inj0 (Inj1 (Inj1 (Inj1 ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set ∀X6 : set , ∀X7 : set → (set → set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ setsum (X7 X6 (λX10 : set ⇒ λX11 : set ⇒ ∅ ) (setsum X9 (setsum (setsum ∅ ∅ X8 ) ∅ (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → set → set → set → set ∀X6 : set , ∀X7 : set → set (Inj0 (X7 X4 ∈ setsum ∅ (setsum (setsum (Inj1 ∅ (Inj1 ∅ (setsum (setsum ∅ ∅ ∅ → X2 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set X11 (Inj0 (Inj0 (X10 ∅ ) (Inj1 ∅ (Inj0 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (set → (set → set → set → set → set X3 (λX8 : set ⇒ λX9 : (set → set → (set → set → set → set X8 ) X5 X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum X8 (Inj1 ∅ ) (setsum (Inj1 (X7 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj1 ∅ ) (setsum ∅ (setsum (setsum ∅ ∅ (Inj0 ∅ (λX8 : set → set → set X8 (Inj1 (Inj0 ∅ (Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (Inj0 (Inj1 ∅ (Inj1 (X7 (λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum ∅ ∅ ) ) X5 ) → (∀X4 : (set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : ((set → set → set → set → set → set (setsum (X4 (λX8 : set ⇒ X5 ) (setsum (setsum ∅ ∅ (X4 (λX8 : set ⇒ ∅ ) ∅ ∅ ∈ X5 → X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (Inj1 ∅ ∅ ) X5 (λX8 : set → set → set Inj1 ∅ ) (λX8 : set → set λX9 : set ⇒ setsum (setsum (X7 (λX10 : set → set → set λX11 : set ⇒ X11 ) (X8 (X8 ∅ (Inj0 (X8 (setsum ∅ ∅ ) ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set setsum ∅ (Inj0 (Inj1 (Inj0 ∅ ) (setsum (setsum X6 X5 ∅ (Inj0 (X7 (λX8 : set → set → set λX9 : set ⇒ Inj0 (setsum ∅ ∅ ) ) → (∀X4 : (set → set → set → (set → set → set → set ∀X5 : set , ∀X6 : (set → set → set → set → set → (set → set → set → set ∀X7 : set , (Inj0 (Inj0 ∅ ∈ Inj1 (setsum (Inj0 (setsum ∅ ∅ ∅ → X1 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ setsum (X9 (Inj0 ∅ (setsum ∅ X7 ) ∅ (λX8 : set → set → set X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ X10 ) (Inj0 (setsum ∅ (Inj1 ∅ (λX9 : set ⇒ X9 ) ∅ ) (λX8 : set → set λX9 : set ⇒ Inj1 (setsum ∅ (setsum X9 ∅ ) (setsum (Inj1 (setsum (Inj1 ∅ (Inj1 ∅ (X6 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ ∅ ) X7 (λX8 : set ⇒ ∅ ) (X4 (λX8 : set ⇒ ∅ ) (setsum ∅ ∅ (λX8 : set ⇒ ∅ ) X5 X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set X8 ) (Inj0 (Inj1 X5 (setsum ∅ (Inj1 (setsum (Inj1 ∅ (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : ((set → set → set → set → set → set → set → (set → set → set ∀X6 : (set → set → set → set ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set → set λX11 : set → set setsum (X10 ∅ (Inj0 ∅ ) (Inj0 (Inj0 (Inj0 X7 (X6 (λX8 : set ⇒ ∅ ) ∅ False ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMQMEpeaqDZQfKrSosV1W7Z4snbV5vuUYux )
∀X0 : (set → set → set → set → set → prop ∀X1 : (set → set → set → set → prop ∀X2 : (set → set → set → prop ∀X3 : (set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set → set X3 (λX8 : set ⇒ ∅ ) X4 (Inj0 (setsum (Inj1 (Inj0 ∅ (setsum X4 ∅ ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set ∀X7 : set → set X3 (λX8 : set ⇒ ∅ ) (Inj1 (X6 (λX8 : set ⇒ setsum X5 (Inj0 ∅ ) ∅ False ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set → set ∀X7 : set → set (Inj0 X5 ∈ setsum (Inj0 (setsum X5 (Inj1 ∅ ∅ → X2 (λX8 : set ⇒ Inj1 (setsum (setsum ∅ (Inj0 ∅ X8 ) X4 ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : (((set → set → set → set → set → set → set X2 (λX8 : set ⇒ X5 ) (Inj0 X4 False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set , ∀X7 : set , (Inj1 X4 ∈ Inj0 X5 → X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ X8 ) (setsum X6 ∅ X1 (λX8 : set ⇒ setsum ∅ ∅ ) (setsum ∅ (setsum (setsum (setsum ∅ ∅ X6 ∅ (Inj1 X6 ) → (∀X4 : (set → set → set → set → set → set ∀X5 : (((set → set → set → (set → set → set → set → (set → set → set → set ∀X6 : set → (set → set → set → set ∀X7 : set , X1 (λX8 : set ⇒ ∅ ) (Inj0 (setsum (X6 (X5 (λX8 : (set → set → set λX9 : set → set ∅ ) ∅ (λX8 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ λX9 : set ⇒ Inj1 ∅ ) (X5 (λX8 : (set → set → set λX9 : set → set X9 ∅ ) (Inj1 ∅ (λX8 : set ⇒ ∅ ) ∅ X7 False ) → (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set ∀X7 : set , (Inj0 (setsum (setsum (setsum ∅ ∅ (setsum ∅ ∅ (setsum X5 (setsum ∅ ∅ ∈ X6 X5 X4 → X1 (λX8 : set ⇒ setsum ∅ (setsum (setsum (Inj0 ∅ X5 (setsum ∅ (Inj0 ∅ ) (X6 (setsum X4 ∅ ∅ (setsum (setsum (setsum (Inj0 ∅ (Inj0 ∅ ∅ ∅ X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X9 (Inj0 (setsum X10 X7 ) (setsum ∅ (setsum ∅ X7 ) → (∀X4 : (set → (set → set → set → set → set → set ∀X5 : (set → set → set ∀X6 : set , ∀X7 : set , X0 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum ∅ (Inj1 (setsum (Inj1 ∅ ∅ ) (setsum (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ X10 ) ∅ (setsum ∅ (X4 (λX8 : set ⇒ λX9 : set → set λX10 : set ⇒ Inj0 ∅ ) ∅ X2 (λX8 : set ⇒ ∅ ) (Inj1 ∅ ) → False Proof: The rest of this subproof is missing.
∎
Theorem. (
conj_HOSetConstr_TMcwMWaNaSxr9odQeNqZEZAjyEM3o8rycAK )
∀X0 : (((set → (set → set → set → set → set → set → (set → set → (set → set → set → set → prop ∀X1 : ((set → set → (set → (set → set → set → set → set → set → prop ∀X2 : (set → set → set → (set → set → set → set → ((((set → set → set → set → set → set → set → prop ∀X3 : ((set → set → (set → set → set → set → (((set → set → set → set → set → set → set → set → prop (∀X4 : set , ∀X5 : set , ∀X6 : set → set → set → set → set ∀X7 : set , (Inj1 ∅ ∈ setsum (Inj1 (Inj0 (Inj1 ∅ ∅ → X3 (λX8 : set → set → (set → set → set Inj0 (X6 ∅ (Inj0 ∅ (Inj1 ∅ (Inj0 X7 ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (setsum (Inj0 ∅ ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : set , ∀X7 : (set → set → set → set → (set → set → set X3 (λX8 : set → set → (set → set → set Inj1 (setsum ∅ (X8 X5 (Inj1 ∅ (λX9 : set ⇒ ∅ ) ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ ∅ ) (Inj1 ∅ (X7 (λX8 : set ⇒ λX9 : set ⇒ setsum ∅ X8 ) (setsum (X4 X6 (Inj0 (Inj1 ∅ (λX8 : set ⇒ X8 ) ∈ setsum ∅ (Inj1 ∅ ) → (∀X4 : set → set ∀X5 : set , ∀X6 : (((set → set → set → set → set → set → (set → set → set → set ∀X7 : set → set X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ X7 (X7 ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ setsum (X11 (Inj0 (setsum ∅ ∅ ∅ ) (λX8 : ((set → set → set → set → set → set Inj1 X5 ) ) → (∀X4 : set , ∀X5 : set , ∀X6 : (set → set → set → set → set → set ∀X7 : (set → set → set → (set → set → (set → set → set X2 (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ λX11 : set → set λX12 : set ⇒ ∅ ) (λX8 : ((set → set → set → set → set → set ∅ ) X3 (λX8 : set → set → (set → set → set ∅ ) (λX8 : (set → set → set → set λX9 : set ⇒ λX10 : set ⇒ Inj0 ∅ ) (X7 (λX8 : set ⇒ λX9 : set ⇒ X9 ) (λX8 : set ⇒ X6 (λX9 : set ⇒ λX10 : set ⇒ λX11 : set ⇒ Inj1 ∅ ) (setsum (setsum ∅ ∅ ∅ ) (λX8 : set ⇒ ∅ ) ) → (∀X4 : set , ∀X5 : set → ((set → set → set → set → set → set → set ∀X6 : (set → (set → set → set → set → set ∀X7 : set → set (X7 (X7 (Inj1 X4 ∈ X4 → X1 (λX8 : set → set λX9 : set → (set → set → set ∅ ) (setsum (setsum ∅ (Inj1 (Inj1 ∅ (Inj0 (Inj1 (setsum ∅ ∅ (setsum ∅ (Inj1 (Inj0 ∅ ) → (∀X4 : set → set ∀X5 : (set → set → set → set → (set → set → set ∀X6 : set → set ∀X7 : ((set → set → set → set → set → set → (set → set → set → set → set → set X1 (λX8 : set → set λX9 : set → (set → set → set setsum (Inj0 (Inj0 ∅ (Inj0 (X9 (setsum ∅ ∅ (λX10 : set ⇒ X8 ∅ ) ) (Inj1 (setsum (Inj0 (X6 ∅ (X5 (λX8 : set ⇒ λX9 : set ⇒ ∅ ) ∅ (λX8 : set ⇒ X5 (λX9 : set ⇒ λX10 : set ⇒ ∅ ) ∅ (λX9 : set ⇒ ∅ ) ) (Inj1 ∅ X1 (λX8 : set → set λX9 : set → (set → set → set ∅ ) (X7 (λX8 : set → set → set λX9 : set ⇒ λX10 : set ⇒ setsum (setsum X10 (X8 ∅ ∅ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ X8 ) ∅ ∅ (X4 (setsum ∅ ∅ ) → (∀X4 : set , ∀X5 : set → set ∀X6 : set , ∀X7 : (set → set → set → set (setsum (Inj0 (Inj1 (Inj1 ∅ ∅ ∈ setsum (setsum X6 ∅ (Inj0 (setsum (setsum ∅ ∅ (X5 ∅ → X0 (λX8 : (set → (set → set → set → set → set ∅ ) (λX8 : set ⇒ ∅ ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ ∅ ) ) → (∀X4 : (((set → set → set → set → (set → set → set → set → set ∀X5 : set , ∀X6 : set , ∀X7 : set , X0 (λX8 : (set → (set → set → set → set → set setsum X5 (Inj1 (Inj0 X6 ) (λX8 : set ⇒ Inj0 (Inj1 (setsum X6 X6 ) (λX8 : set ⇒ λX9 : set ⇒ λX10 : set ⇒ setsum X10 ∅ ) False ) → False Proof: The rest of this subproof is missing.
∎
End of Section HOSetConstr