Theorem. (MetaCat_struct_e)

MetaCat struct_e Hom_struct_e struct_id struct_comp

In Proofgold the corresponding term root is 40d0ba... and proposition id is 5aae9b...

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)

In Proofgold the corresponding term root is 4c2b40... and proposition id is a6c491...

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 : set → set, initial_p struct_e Hom_struct_e struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 0c84dd... and proposition id is 11b669...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_terminal)

∃Y : set, ∃uniqa : set → set, terminal_p struct_e Hom_struct_e struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 1e0c73... and proposition id is b54473...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_coproduct_constr)

∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p struct_e Hom_struct_e struct_id struct_comp coprod i0 i1 copair

In Proofgold the corresponding term root is 29ade1... and proposition id is 8da75d...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_product_constr)

∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p struct_e Hom_struct_e struct_id struct_comp prod pi0 pi1 pair

In Proofgold the corresponding term root is bbe71c... and proposition id is 8e8d1b...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is f32eca... and proposition id is 49d002...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is 698c13... and proposition id is 6ae12e...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp po i0 i1 copair

In Proofgold the corresponding term root is 2d56ca... and proposition id is cb8d33...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp pb pi0 pi1 pair

In Proofgold the corresponding term root is 45860a... and proposition id is c5a261...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp prod pi0 pi1 pair exp a lm

In Proofgold the corresponding term root is 83907c... and proposition id is d69772...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp one uniqa Omega tru ch constr

In Proofgold the corresponding term root is 4b715d... and proposition id is 28a72b...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_nno)

∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p struct_e Hom_struct_e struct_id struct_comp one uniqa N zer suc rec

In Proofgold the corresponding term root is 637643... and proposition id is 99f2c5...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_e_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_e Hom_struct_e struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps

In Proofgold the corresponding term root is 1272ed... and proposition id is 1ffb7e...

Proof:

The rest of the proof is missing.