Theorem. (MetaCat_struct_b_group)
MetaCat Group Hom_struct_b struct_id struct_comp
In Proofgold the corresponding term root is 7f680c... and proposition id is d87b91...
Proof:
We prove the intermediate claim L1: ∀X, Group X → struct_b 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_gen Group L1.
∎
Theorem. (MetaCat_struct_b_group_Forgetful)
MetaFunctor Group 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 04fc33... and proposition id is e09773...
Proof:
We prove the intermediate claim L1: ∀X, Group X → struct_b 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_Forgetful_gen Group L1.
∎
Proposition. (MetaCat_struct_b_group_initial)
∃Y : set, ∃uniqa : set → set, initial_p Group Hom_struct_b struct_id struct_comp Y uniqa
In Proofgold the corresponding term root is 6b9f58... and proposition id is 8e7ab8...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_terminal)
∃Y : set, ∃uniqa : set → set, terminal_p Group Hom_struct_b struct_id struct_comp Y uniqa
In Proofgold the corresponding term root is f08232... and proposition id is 4ce241...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_coproduct_constr)
∃coprod : set → set → set, ∃i0 i1 : set → set → set, ∃copair : set → set → set → set → set → set, coproduct_constr_p Group Hom_struct_b struct_id struct_comp coprod i0 i1 copair
In Proofgold the corresponding term root is fe7952... and proposition id is 7abd1a...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_product_constr)
∃prod : set → set → set, ∃pi0 pi1 : set → set → set, ∃pair : set → set → set → set → set → set, product_constr_p Group Hom_struct_b struct_id struct_comp prod pi0 pi1 pair
In Proofgold the corresponding term root is 5c6bb5... and proposition id is 05bdfc...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp quot canonmap fac
In Proofgold the corresponding term root is ed858f... and proposition id is 236d23...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp quot canonmap fac
In Proofgold the corresponding term root is c5cb8c... and proposition id is e6d9eb...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp po i0 i1 copair
In Proofgold the corresponding term root is a0f538... and proposition id is 9f70c2...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp pb pi0 pi1 pair
In Proofgold the corresponding term root is 8129e3... and proposition id is 428633...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp prod pi0 pi1 pair exp a lm
In Proofgold the corresponding term root is 89ad61... and proposition id is 01a47d...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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 Group Hom_struct_b struct_id struct_comp one uniqa Omega tru ch constr
In Proofgold the corresponding term root is 4c2e73... and proposition id is 6810bf...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_nno)
∃one : set, ∃uniqa : set → set, ∃N : set, ∃zer suc : set, ∃rec : set → set → set → set, nno_p Group Hom_struct_b struct_id struct_comp one uniqa N zer suc rec
In Proofgold the corresponding term root is 0367a3... and proposition id is b8f7d6...
Proof:
The rest of the proof is missing.

Proposition. (MetaCat_struct_b_group_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)) Group 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 892837... and proposition id is 2570d7...
Proof:
The rest of the proof is missing.