proposition: Proposition double_transformation_comp_h {C₁ C₂ : univalent_double_cat} {F G : lax_double_functor C₁ C₂} (τ : double_transformation F G) {x y z : C₁} (h : x -->h y) (k : y -->h z) : lax_double_functor_comp_h F h k ⋆v double_transformation_hor_mor τ (h ·h k) = transportb_square (id_v_left _ @ !(id_v_right _)) (id_v_left _ @ !(id_v_right _)) ((double_transformation_hor_mor τ h ⋆h double_transformation_hor_mor τ k) ⋆v lax_double_functor_comp_h G h k).
proof: Proof. exact (pr2 (pr211 τ) x y z h k). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfTwoSidedDispCat UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor UniMath.Bicategories.DoubleCategories.Core.DoubleTransformation UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats UniMath.Bicategories.DoubleCategories.Core.DoubleCats