Proposition lax_double_functor_comp_v_square' {C₁ C₂ : univalent_double_cat} (F : lax_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 : square v₁ v₂ h₁ h₂) (s₂ : square v₁' v₂' h₂ h₃) : #s F s₁ ⋆v #s F s₂ = transportf_square (lax_double_functor_comp_v _ _ _) (lax_double_functor_comp_v _ _ _) (#s F (s₁ ⋆v s₂)). Proof. rewrite lax_double_functor_comp_v_square. rewrite transportfb_square. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.DerivedLaws.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats.