proposition: Lemma two_cat_is_strict_bicat (C : two_cat) : is_strict_bicat (two_cat_to_bicat C).
proof: Proof. use make_is_strict_bicat. - apply (homset_property C). - use tpair. + repeat split. * intros a b f. exact (id_left (f : pr1 C ⟦ _ , _ ⟧)). * intros a b f. exact (id_right (f : pr1 C ⟦ _ , _ ⟧)). * intros a b c d f g h. exact (assoc (f : pr1 C ⟦ _ , _ ⟧) g h). + simpl. repeat split ; intros ; apply idto2mor_idtoiso_two_cat. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.TwoCategories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.HSET.All UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.TransportLaws