proposition: Lemma id_to_teqi'''_to_id {C : bicat_of_univ_cats} {TC TD : bidisp_tensor_disp_bicat C} (p : TC = TD) : tensor_eqi'''_to_eq TC TD (id_tensor_eqi''' TC TD p) = p.
proof: Proof. unfold tensor_eqi'''_to_eq. unfold id_tensor_eqi'''. induction p. use pathscomp0. 3: apply total2_paths_idpath. apply maponpaths_total. - use pathscomp0. 3: apply total2_paths_idpath. apply maponpaths_total. + apply funextsec_id. + intro T. repeat (apply impred_isaset ; intro). apply homset_property. - intro T. apply isaset_dirprod; repeat (apply impred_isaset ; intro) ; apply isasetaprop ; apply homset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.Core.Univalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories