Theorem. (MetaCat_struct_c)

MetaCat struct_c Hom_struct_c struct_id struct_comp

In Proofgold the corresponding term root is 4f44ef... and proposition id is ed6b54...

Proof:

An exact proof term for the current goal is MetaCat_struct_c_gen struct_c (λX H ⇒ H).

∎

Theorem. (MetaCat_struct_c_Forgetful)

MetaFunctor struct_c Hom_struct_c 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 f3e562... and proposition id is 803c1d...

Proof:

An exact proof term for the current goal is MetaCat_struct_c_Forgetful_gen struct_c (λX H ⇒ H).

∎

Proposition. (MetaCat_struct_c_initial)

∃Y : set, ∃uniqa : set → set, initial_p struct_c Hom_struct_c struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 1cdb7b... and proposition id is 05e4be...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_terminal)

∃Y : set, ∃uniqa : set → set, terminal_p struct_c Hom_struct_c struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is bbf6e8... and proposition id is 40a5e2...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_coproduct_constr)

∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p struct_c Hom_struct_c struct_id struct_comp coprod i0 i1 copair

In Proofgold the corresponding term root is 96920f... and proposition id is e99602...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_product_constr)

∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p struct_c Hom_struct_c struct_id struct_comp prod pi0 pi1 pair

In Proofgold the corresponding term root is c8c33a... and proposition id is 3a1251...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is 07129f... and proposition id is 4a5472...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is e1028a... and proposition id is 64a619...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp po i0 i1 copair

In Proofgold the corresponding term root is 1c96f2... and proposition id is 7ebca2...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp pb pi0 pi1 pair

In Proofgold the corresponding term root is a7c26a... and proposition id is f7c1a7...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp prod pi0 pi1 pair exp a lm

In Proofgold the corresponding term root is 430703... and proposition id is dda510...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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 struct_c Hom_struct_c struct_id struct_comp one uniqa Omega tru ch constr

In Proofgold the corresponding term root is ae0977... and proposition id is 411fc7...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_nno)

∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p struct_c Hom_struct_c struct_id struct_comp one uniqa N zer suc rec

In Proofgold the corresponding term root is 9b6a61... and proposition id is ea0ba4...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_c_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)) struct_c Hom_struct_c struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps

In Proofgold the corresponding term root is 07cb72... and proposition id is 5da2f8...

Proof:

The rest of the proof is missing.