Proposition runitor_h_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) : s ⋆h id_h_square_bicat v₂ = rinvunitor h₂ ▿s (runitor h₁ ▵s s). Proof. rewrite <- runitor_h_comp_square. rewrite <- dwhisker_square_comp. rewrite runitor_rinvunitor. rewrite dwhisker_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.