proposition: Lemma teqi'''_to_id_to_teqi''' {C : bicat_of_univ_cats} {TC TD : bidisp_tensor_disp_bicat C} (p : tensor_eqi''' TC TD) : id_tensor_eqi''' TC TD (tensor_eqi'''_to_eq TC TD p) = p.
proof: Proof. use total2_paths_f. - apply funextsec ; intro x ; apply funextsec ; intro y. etrans. { apply pr_id_tensor_eqi'''_funextsec. } etrans. { apply distributer_funext. } unfold id_tensor_eqi'''_2. unfold tensor_eqi'''_to_eq1. rewrite toforallpaths_funextsec. rewrite toforallpaths_funextsec. apply idpath. - repeat (apply funextsec ; intro). 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