Proposition triangle_law_two_cat_arrow_twosided_disp_cat : triangle_law double_cat_lunitor_two_cat_arrow_twosided_disp_cat double_cat_runitor_two_cat_arrow_twosided_disp_cat double_cat_associator_two_cat_arrow_twosided_disp_cat. Proof. intro ; intros. cbn. rewrite transportb_disp_mor2_two_cat_arrow. unfold two_cat_lassociator, two_cat_rassociator. unfold two_cat_runitor, two_cat_rinvunitor. unfold two_cat_lunitor, two_cat_linvunitor. rewrite <- !lwhisker_vcomp. rewrite <- !rwhisker_vcomp. rewrite <- !lwhisker_vcomp. rewrite !vassocl. rewrite !idto2mor_lwhisker. rewrite !idto2mor_rwhisker. rewrite !idto2mor_lwhisker. rewrite !idto2mor_comp. apply maponpaths. apply (homset_property C). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Import TwoCategories.Notations. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.SquaresTwoCat. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints.