Proposition bicat_to_triangle_law : triangle_law bicat_to_lunitor bicat_to_runitor bicat_to_associator. Proof. intros x y z f g ; cbn. rewrite <- !rwhisker_vcomp. rewrite !vassocr. do 3 apply maponpaths_2. rewrite !vassocl. etrans. { do 2 apply maponpaths. rewrite !vassocr. rewrite linvunitor_lunitor. rewrite id2_left. rewrite !vassocl. rewrite <- rinvunitor_triangle. rewrite !vassocl. etrans. { apply maponpaths. rewrite !vassocr. rewrite lassociator_rassociator. rewrite id2_left. apply idpath. } rewrite !vassocr. rewrite lwhisker_vcomp. rewrite !vassocr. rewrite rinvunitor_runitor. rewrite id2_left. rewrite !vassocl. apply idpath. } rewrite runitor_rwhisker. rewrite lwhisker_vcomp. rewrite linvunitor_lunitor. rewrite lwhisker_id2. rewrite id2_right. rewrite !vassocr. apply maponpaths_2. rewrite runitor_triangle. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Groupoids. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Strictness. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats.