Theorem. (MetaCat_struct_e)
MetaCat struct_e Hom_struct_e struct_id struct_comp
Proof:
An exact proof term for the current goal is MetaCat_struct_e_gen struct_e (λX H ⇒ H).
Theorem. (MetaCat_struct_e_Forgetful)
MetaFunctor struct_e Hom_struct_e struct_id struct_comp (λ_ ⇒ True) SetHom (λX ⇒ lam_id X) (λX Y Z f g ⇒ (lam_comp X f g)) (λX ⇒ X 0) (λX Y f ⇒ f)
Proof:
An exact proof term for the current goal is MetaCat_struct_e_Forgetful_gen struct_e (λX H ⇒ H).
Proposition. (MetaCat_struct_e_initial)
∃Y : set, ∃uniqa : setset, initial_p struct_e Hom_struct_e struct_id struct_comp Y uniqa
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_terminal)
∃Y : set, ∃uniqa : setset, terminal_p struct_e Hom_struct_e struct_id struct_comp Y uniqa
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_coproduct_constr)
∃coprod : setsetset, ∃i0 i1 : setsetset, ∃copair : setsetsetsetsetset, coproduct_constr_p struct_e Hom_struct_e struct_id struct_comp coprod i0 i1 copair
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_product_constr)
∃prod : setsetset, ∃pi0 pi1 : setsetset, ∃pair : setsetsetsetsetset, product_constr_p struct_e Hom_struct_e struct_id struct_comp prod pi0 pi1 pair
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_coequalizer_constr)
∃quot : setsetsetsetset, ∃canonmap : setsetsetsetset, ∃fac : setsetsetsetsetsetset, coequalizer_constr_p struct_e Hom_struct_e struct_id struct_comp quot canonmap fac
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_equalizer_constr)
∃quot : setsetsetsetset, ∃canonmap : setsetsetsetset, ∃fac : setsetsetsetsetsetset, equalizer_constr_p struct_e Hom_struct_e struct_id struct_comp quot canonmap fac
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_pushout_constr)
∃po : setsetsetsetsetset, ∃i0 : setsetsetsetsetset, ∃i1 : setsetsetsetsetset, ∃copair : setsetsetsetsetsetsetsetset, pushout_constr_p struct_e Hom_struct_e struct_id struct_comp po i0 i1 copair
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_pullback_constr)
∃pb : setsetsetsetsetset, ∃pi0 : setsetsetsetsetset, ∃pi1 : setsetsetsetsetset, ∃pair : setsetsetsetsetsetsetsetset, pullback_constr_p struct_e Hom_struct_e struct_id struct_comp pb pi0 pi1 pair
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_product_exponent)
∃prod : setsetset, ∃pi0 pi1 : setsetset, ∃pair : setsetsetsetsetset, ∃exp : setsetset, ∃a : setsetset, ∃lm : setsetsetsetset, product_exponent_constr_p struct_e Hom_struct_e struct_id struct_comp prod pi0 pi1 pair exp a lm
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_subobject_classifier)
∃one : set, ∃uniqa : setset, ∃Omega : set, ∃tru : set, ∃ch : setsetsetset, ∃constr : setsetsetsetsetsetset, subobject_classifier_p struct_e Hom_struct_e struct_id struct_comp one uniqa Omega tru ch constr
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_nno)
∃one : set, ∃uniqa : setset, ∃N : set, ∃zer suc : set, ∃rec : setsetsetset, nno_p struct_e Hom_struct_e struct_id struct_comp one uniqa N zer suc rec
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_e_left_adjoint_forgetful)
∃F0 : setset, ∃F1 : setsetsetset, ∃eta eps : setset, MetaAdjunction_strict (λ_ ⇒ True) SetHom (λX ⇒ (lam_id X)) (λX Y Z f g ⇒ (lam_comp X f g)) struct_e Hom_struct_e struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps
Proof:
The rest of the proof is missing.