Proposition double_cat_runitor_two_cat_arrow_twosided_disp_cat_laws : double_runitor_laws double_cat_runitor_two_cat_arrow_twosided_disp_cat_data. Proof. intro ; intros ; cbn. rewrite transportb_disp_mor2_two_cat_arrow. unfold two_cat_lassociator, two_cat_rassociator. unfold two_cat_lunitor, two_cat_linvunitor. unfold two_cat_runitor, two_cat_rinvunitor. rewrite <- !lwhisker_vcomp. rewrite <- !rwhisker_vcomp. rewrite !vassocl. rewrite !idto2mor_lwhisker. rewrite !idto2mor_rwhisker. rewrite !idto2mor_comp. rewrite !vassocr. rewrite !idto2mor_comp. etrans. { apply maponpaths_2. apply maponpaths. apply id1_lwhisker. } unfold two_cat_lunitor, two_cat_linvunitor. rewrite !vassocl. rewrite !idto2mor_comp. rewrite !vassocr. rewrite !idto2mor_comp. refine (!_). etrans. { apply maponpaths_2. apply maponpaths. apply rwhisker_id1. } unfold two_cat_runitor, two_cat_rinvunitor. rewrite !vassocl. rewrite !idto2mor_comp. rewrite !vassocr. rewrite !idto2mor_comp. etrans. { apply maponpaths_2. apply maponpaths. apply rwhisker_id1. } unfold two_cat_runitor, two_cat_rinvunitor. rewrite !vassocl. rewrite !idto2mor_comp. rewrite !vassocr. rewrite !idto2mor_comp. use arr_idto2mor_eq. apply idpath. 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.