Proposition lax_double_functor_lassociator_h' {C₁ C₂ : univalent_double_cat} (F : lax_double_functor C₁ C₂) {w x y z : C₁} (f : w -->h x) (g : x -->h y) (h : y -->h z) : (id_v_square _ ⋆h lax_double_functor_comp_h F g h) ⋆v lax_double_functor_comp_h F f (g ·h h) ⋆v #s F (lassociator_h f g h) = transportb_square (maponpaths _ (lax_double_functor_id_v _ _)) (maponpaths _ (lax_double_functor_id_v _ _)) (lassociator_h (#h F f) (#h F g) (#h F h) ⋆v (lax_double_functor_comp_h F f g ⋆h id_v_square _) ⋆v lax_double_functor_comp_h F (f ·h g) h). Proof. rewrite lax_double_functor_lassociator_h. rewrite transportbf_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.