Proposition runitor_square {C : double_cat} {x₁ x₂ y₁ y₂ : C} {v₁ : x₁ -->v x₂} {v₂ : y₁ -->v y₂} {h₁ : x₁ -->h y₁} {h₂ : x₂ -->h y₂} (s : square v₁ v₂ h₁ h₂) : (s ⋆h id_h_square _) ⋆v runitor_h h₂ = transportb_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (runitor_h h₁ ⋆v s). Proof. exact (!(double_runitor_nat (double_cat_double_runitor C) s)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.