Theorem. (MetaCat_struct_u)

MetaCat struct_u Hom_struct_u struct_id struct_comp

In Proofgold the corresponding term root is 5de126... and proposition id is 73eabf...

Proof:

An exact proof term for the current goal is MetaCat_struct_u_gen struct_u (λX H ⇒ H).

∎

Theorem. (MetaCat_struct_u_Forgetful)

MetaFunctor struct_u Hom_struct_u 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 b3eb4d... and proposition id is 0032df...

Proof:

An exact proof term for the current goal is MetaCat_struct_u_Forgetful_gen struct_u (λX H ⇒ H).

∎

Proposition. (MetaCat_struct_u_initial)

∃Y : set, ∃uniqa : set → set, initial_p struct_u Hom_struct_u struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is a50b15... and proposition id is 1e2ae3...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_terminal)

∃Y : set, ∃uniqa : set → set, terminal_p struct_u Hom_struct_u struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 48aa9d... and proposition id is 75feaa...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_coproduct_constr)

∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p struct_u Hom_struct_u struct_id struct_comp coprod i0 i1 copair

In Proofgold the corresponding term root is 8a51f5... and proposition id is 83a644...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_product_constr)

∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p struct_u Hom_struct_u struct_id struct_comp prod pi0 pi1 pair

In Proofgold the corresponding term root is 1c55d4... and proposition id is a90797...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is 5a672b... and proposition id is 5e64c8...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is a41118... and proposition id is ee44bb...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp po i0 i1 copair

In Proofgold the corresponding term root is 027a4b... and proposition id is 322ee4...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp pb pi0 pi1 pair

In Proofgold the corresponding term root is a46f9c... and proposition id is 75a416...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp prod pi0 pi1 pair exp a lm

In Proofgold the corresponding term root is e31eac... and proposition id is 17553d...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp one uniqa Omega tru ch constr

In Proofgold the corresponding term root is f68686... and proposition id is 927359...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_nno)

∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p struct_u Hom_struct_u struct_id struct_comp one uniqa N zer suc rec

In Proofgold the corresponding term root is d545a7... and proposition id is 12c76a...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_u_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_u Hom_struct_u struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps

In Proofgold the corresponding term root is 8dacc4... and proposition id is ed3d2e...

Proof:

The rest of the proof is missing.