Proposition lax_double_functor_comp_h_mor' {C₁ C₂ : univalent_double_cat} (F : lax_double_functor C₁ C₂) {x₁ x₂ y₁ y₂ z₁ z₂ : C₁} {vx : x₁ -->v x₂} {vy : y₁ -->v y₂} {vz : z₁ -->v z₂} {h₁ : x₁ -->h y₁} {h₂ : x₂ -->h y₂} {k₁ : y₁ -->h z₁} {k₂ : y₂ -->h z₂} (sh : square vx vy h₁ h₂) (sk : square vy vz k₁ k₂) : lax_double_functor_comp_h F h₁ k₁ ⋆v #s F (sh ⋆h sk) = transportf_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) ((#s F sh ⋆h #s F sk) ⋆v lax_double_functor_comp_h F h₂ k₂). Proof. refine (!(transportfb_square _ _ _) @ maponpaths _ _). exact (!(lax_double_functor_comp_h_mor F sh sk)). 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.