Proposition runitor_v_comp_square'' {B : verity_double_bicat} {w x y z : B} {h₁ : w --> x} {h₂ : y --> z} {v₁ : w -|-> y} {v₂ : x -|-> z} (s : square_double_bicat h₁ h₂ v₁ v₂) : runitor v₂ ▹s (rinvunitor v₁ ◃s s ⋆v id_v_square_bicat h₂) = s. Proof. rewrite runitor_v_comp_square'. rewrite !rwhisker_lwhisker_square. rewrite <- lwhisker_square_comp. rewrite <- rwhisker_square_comp. rewrite !rinvunitor_runitor. rewrite lwhisker_square_id. rewrite rwhisker_square_id. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat.