Lemma assoc_step_4 : linvunitor_h _ ⋆h id_v_square _ ⋆v ((s₁ ⋆h s₂) ⋆h s₃ ⋆v lunitor_h _ ⋆h id_v_square _) = (linvunitor_h (identity_h x) ⋆v ((s₁ ⋆h s₂) ⋆v lunitor_h (identity_h y))) ⋆h (id_v_square _ ⋆v (s₃ ⋆v id_v_square _)). Proof. rewrite <- !comp_h_square_comp. 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. Require Import UniMath.CategoryTheory.Monads.Monads. 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.Comma. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. 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.DerivedLaws. Import TransportSquare.