proposition: Theorem disp_lunitor_runitor_identity {C : bicat} {D : disp_bicat C} (a : C) (aa : D a) : disp_lunitor (id_disp aa) = cell_transportb (lunitor_runitor_identity a) (disp_runitor (id_disp aa)).
proof: Proof. set (TT := fiber_paths (lunitor_runitor_identity (C := total_bicat D) (a ,, aa))). cbn in TT. apply cell_transportf_to_b. etrans. 2: now apply TT. unfold cell_transportf. apply maponpaths_2. apply cellset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Univalence