Proposition lassociator_square {C : double_cat} {w₁ w₂ x₁ x₂ y₁ y₂ z₁ z₂ : C} {vw : w₁ -->v w₂} {vx : x₁ -->v x₂} {vy : y₁ -->v y₂} {vz : z₁ -->v z₂} {h₁ : w₁ -->h x₁} {h₂ : w₂ -->h x₂} {j₁ : x₁ -->h y₁} {j₂ : x₂ -->h y₂} {k₁ : y₁ -->h z₁} {k₂ : y₂ -->h z₂} (s₁ : square vw vx h₁ h₂) (s₂ : square vx vy j₁ j₂) (s₃ : square vy vz k₁ k₂) : (s₁ ⋆h (s₂ ⋆h s₃)) ⋆v lassociator_h h₂ j₂ k₂ = transportb_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (lassociator_h h₁ j₁ k₁ ⋆v ((s₁ ⋆h s₂) ⋆h s₃)). Proof. exact (!(double_associator_nat (double_cat_double_associator C) s₁ s₂ s₃)). 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.