Proposition lax_double_functor_id_h_mor' {C₁ C₂ : univalent_double_cat} (F : lax_double_functor C₁ C₂) {x y : C₁} (f : x -->v y) : lax_double_functor_id_h F x ⋆v #s F (id_h_square f) = transportf_square (id_v_right _ @ !(id_v_left _)) (id_v_right _ @ !(id_v_left _)) (id_h_square (#v F f) ⋆v lax_double_functor_id_h F y). Proof. refine (!(transportfb_square _ _ _) @ maponpaths _ _). exact (!(lax_double_functor_id_h_mor F f)). 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.