Proposition lax_double_functor_comp_v_square {C₁ C₂ : strict_double_cat} (F : strict_double_functor C₁ C₂) {x₁ x₂ y₁ y₂ z₁ z₂ : C₁} {v₁ : x₁ -->v y₁} {v₁' : y₁ --> z₁} {v₂ : x₂ -->v y₂} {v₂' : y₂ --> z₂} {h₁ : x₁ -->h x₂} {h₂ : y₁ -->h y₂} {h₃ : z₁ -->h z₂} (s₁ : s_square v₁ v₂ h₁ h₂) (s₂ : s_square v₁' v₂' h₂ h₃) : #s F (s₁ ⋆v s₂) = transportb_s_square (strict_double_functor_comp_v _ _ _) (strict_double_functor_comp_v _ _ _) (idpath _) (idpath _) (#s F s₁ ⋆v #s F s₂). Proof. apply (twosided_disp_functor_comp _ _ _ _ (strict_double_functor_hor_mor F)). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.StrictTwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.CatOfStrictDoubleCats.