proposition: 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 s₂) = transportb_square (lax_double_functor_comp_v _ _ _) (lax_double_functor_comp_v _ _ _) (#s F s₁ ⋆v #s F s₂).
proof: Proof. apply (twosided_disp_functor_comp _ _ _ _ (lax_double_functor_hor_mor F)). 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