Theorem. (MetaCat_struct_b_b_e_e_field)
MetaCat Field Hom_struct_b_b_e_e struct_id struct_comp
In Proofgold the corresponding term root is 8f936a... and proposition id is 6f0349...
Proof:
We prove the intermediate claim L1: ∀X, Field X → struct_b_b_e_e X.
Let X be given.
Assume HX.
Apply HX to the current goal.
Assume H _.
An exact proof term for the current goal is H.
An exact proof term for the current goal is MetaCat_struct_b_b_e_e_gen Field L1.
∎
Theorem. (MetaCat_struct_b_b_e_e_field_Forgetful)
MetaFunctor Field Hom_struct_b_b_e_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)
In Proofgold the corresponding term root is e1dddc... and proposition id is 0a2f59...
Proof:
We prove the intermediate claim L1: ∀X, Field X → struct_b_b_e_e X.
Let X be given.
Assume HX.
Apply HX to the current goal.
Assume H _.
An exact proof term for the current goal is H.
An exact proof term for the current goal is MetaCat_struct_b_b_e_e_Forgetful_gen Field L1.
∎
Proposition. (MetaCat_struct_b_b_e_e_field_initial)
∃Y : set, ∃uniqa : set → set, initial_p Field Hom_struct_b_b_e_e struct_id struct_comp Y uniqa
In Proofgold the corresponding term root is d8cc08... and proposition id is 088b78...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_terminal)
∃Y : set, ∃uniqa : set → set, terminal_p Field Hom_struct_b_b_e_e struct_id struct_comp Y uniqa
In Proofgold the corresponding term root is ecb48b... and proposition id is c07a0e...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_coproduct_constr)
∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp coprod i0 i1 copair
In Proofgold the corresponding term root is 8c431f... and proposition id is ad01d0...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_product_constr)
∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp prod pi0 pi1 pair
In Proofgold the corresponding term root is b8d036... and proposition id is 80dffe...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_coequalizer_constr)
∃quot : set → set → set → set → set, ∃canonmap : set → set → set → set → set, ∃fac : set → set → set → set → set → set → set, coequalizer_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp quot canonmap fac
In Proofgold the corresponding term root is ed2931... and proposition id is 27d536...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_equalizer_constr)
∃quot : set → set → set → set → set, ∃canonmap : set → set → set → set → set, ∃fac : set → set → set → set → set → set → set, equalizer_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp quot canonmap fac
In Proofgold the corresponding term root is e1942d... and proposition id is 3c3a59...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_pushout_constr)
∃po : set → set → set → set → set → set, ∃i0 : set → set → set → set → set → set, ∃i1 : set → set → set → set → set → set, ∃copair : set → set → set → set → set → set → set → set → set, pushout_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp po i0 i1 copair
In Proofgold the corresponding term root is f2ab61... and proposition id is 364053...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_pullback_constr)
∃pb : set → set → set → set → set → set, ∃pi0 : set → set → set → set → set → set, ∃pi1 : set → set → set → set → set → set, ∃pair : set → set → set → set → set → set → set → set → set, pullback_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp pb pi0 pi1 pair
In Proofgold the corresponding term root is 10d27a... and proposition id is 87fc11...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_product_exponent)
∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, ∃exp : set → set → set, ∃a : set → set → set, ∃lm : set → set → set → set → set, product_exponent_constr_p Field Hom_struct_b_b_e_e struct_id struct_comp prod pi0 pi1 pair exp a lm
In Proofgold the corresponding term root is 480f39... and proposition id is 65da8d...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_subobject_classifier)
∃one : set, ∃uniqa : set → set, ∃Omega : set, ∃tru : set, ∃ch : set → set → set → set, ∃constr : set → set → set → set → set → set → set, subobject_classifier_p Field Hom_struct_b_b_e_e struct_id struct_comp one uniqa Omega tru ch constr
In Proofgold the corresponding term root is dce3a4... and proposition id is e3586c...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_nno)
∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p Field Hom_struct_b_b_e_e struct_id struct_comp one uniqa N zer suc rec
In Proofgold the corresponding term root is 5baf68... and proposition id is 38f472...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_b_e_e_field_left_adjoint_forgetful)
∃F0 : set → set, ∃F1 : set → set → set → set, ∃eta eps : set → set, MetaAdjunction_strict (λ_ ⇒ True) SetHom (λX ⇒ (lam_id X)) (λX Y Z f g ⇒ (lam_comp X f g)) Field Hom_struct_b_b_e_e struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps
In Proofgold the corresponding term root is 610698... and proposition id is 1ef6ee...
Proof:
The rest of the proof is missing.