proposition: Lemma two_cat_to_strict_bicat_to_two_cat (C : two_cat) : strict_bicat_to_two_cat (two_cat_to_strict_bicat C) = C.
proof: Proof. use subtypePath. { intro. do 4 (use impred ; intro). apply isapropisaset. } use total2_paths2_f. - use total2_paths2_f. + apply idpath. + apply isapropdirprod. * apply isaprop_is_precategory. intros x y. apply (pr22 (pr11 C)). * apply isaprop_has_homsets. - apply isaprop_two_cat_laws. 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