Proposition comp_h_square_comp {C : double_cat} {x₁ x₂ x₃ y₁ y₂ y₃ z₁ z₂ z₃ : C} {v₁ : x₁ -->v x₂} {v₁' : x₂ -->v x₃} {v₂ : y₁ -->v y₂} {v₂' : y₂ -->v y₃} {v₃ : z₁ -->v z₂} {v₃' : z₂ -->v z₃} {h₁ : x₁ -->h y₁} {h₂ : y₁ -->h z₁} {k₁ : x₂ -->h y₂} {k₂ : y₂ -->h z₂} {l₁ : x₃ -->h y₃} {l₂ : y₃ -->h z₃} (s₁ : square v₁ v₂ h₁ k₁) (s₁' : square v₁' v₂' k₁ l₁) (s₂ : square v₂ v₃ h₂ k₂) (s₂' : square v₂' v₃' k₂ l₂) : (s₁ ⋆v s₁') ⋆h (s₂ ⋆v s₂') = (s₁ ⋆h s₂) ⋆v (s₁' ⋆h s₂'). Proof. apply double_hor_comp_mor_comp. 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.