Proposition composition_preserves_hor_comp_data {C₁ C₂ C₃ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {D₃ : twosided_disp_cat C₃ C₃} {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} {Cm₃ : hor_comp D₃} {F : C₁ ⟶ C₂} {G : C₂ ⟶ C₃} {FF : twosided_disp_functor F F D₁ D₂} (FFc : preserves_hor_comp Cm₁ Cm₂ FF) {GG : twosided_disp_functor G G D₂ D₃} (GGc : preserves_hor_comp Cm₂ Cm₃ GG) : preserves_hor_comp_data Cm₁ Cm₃ (comp_twosided_disp_functor FF GG). Proof. intros x y z f g ; cbn. etrans. { apply maponpaths. exact (FFc x y z f g). } exact (GGc (F x) (F y) (F z) (FF x y f) (FF y z g)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.