Theorem. (MetaCat_struct_b)

MetaCat struct_b Hom_struct_b struct_id struct_comp

In Proofgold the corresponding term root is cb8d37... and proposition id is c55c1b...

Proof:

An exact proof term for the current goal is MetaCat_struct_b_gen struct_b (λX H ⇒ H).

∎

Theorem. (MetaCat_struct_b_Forgetful)

MetaFunctor struct_b Hom_struct_b 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 5098f3... and proposition id is dda03f...

Proof:

An exact proof term for the current goal is MetaCat_struct_b_Forgetful_gen struct_b (λX H ⇒ H).

∎

Proposition. (MetaCat_struct_b_initial)

∃Y : set, ∃uniqa : set → set, initial_p struct_b Hom_struct_b struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 9513dd... and proposition id is e97858...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_terminal)

∃Y : set, ∃uniqa : set → set, terminal_p struct_b Hom_struct_b struct_id struct_comp Y uniqa

In Proofgold the corresponding term root is 20fce0... and proposition id is 021fde...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_coproduct_constr)

∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p struct_b Hom_struct_b struct_id struct_comp coprod i0 i1 copair

In Proofgold the corresponding term root is 667057... and proposition id is 9ba760...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_product_constr)

∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p struct_b Hom_struct_b struct_id struct_comp prod pi0 pi1 pair

In Proofgold the corresponding term root is d64c39... and proposition id is 150e37...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is 5a8409... and proposition id is e3aadc...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp quot canonmap fac

In Proofgold the corresponding term root is 9ae50e... and proposition id is c368b9...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp po i0 i1 copair

In Proofgold the corresponding term root is cb5883... and proposition id is b9bb0b...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp pb pi0 pi1 pair

In Proofgold the corresponding term root is 7fc78e... and proposition id is a238ad...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp prod pi0 pi1 pair exp a lm

In Proofgold the corresponding term root is 252214... and proposition id is d53a27...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp one uniqa Omega tru ch constr

In Proofgold the corresponding term root is bf74fa... and proposition id is d4af08...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_nno)

∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p struct_b Hom_struct_b struct_id struct_comp one uniqa N zer suc rec

In Proofgold the corresponding term root is 0ff695... and proposition id is ee0c26...

Proof:

The rest of the proof is missing.

Proposition. (MetaCat_struct_b_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_b Hom_struct_b struct_id struct_comp F0 F1 (λX ⇒ X 0) (λX Y f ⇒ f) eta eps

In Proofgold the corresponding term root is c08b58... and proposition id is 19cf32...

Proof:

The rest of the proof is missing.