Definition preserves_hor_comp_to_double_functor {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} {F : C₁ ⟶ C₂} {FF : twosided_disp_functor F F D₁ D₂} (HFF : preserves_hor_comp Cm₁ Cm₂ FF) : double_functor_hor_comp FF Cm₁ Cm₂. Proof. use make_double_functor_hor_comp. - exact (λ x y z f g, idtoiso_twosided_disp (idpath _) (idpath _) (!(HFF x y z f g))). - abstract (intros x₁ x₂ y₁ y₂ z₁ z₂ v₁ v₂ v₃ h₁ h₂ k₁ k₂ s₁ s₂ ; cbn -[idtoiso_twosided_disp] ; refine (!(is_natural_preserves_hor_comp_alt' HFF s₁ s₂) @ _) ; use transportf_disp_mor2_eq ; apply idpath). 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.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.StrictTwoSidedDispCat. 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. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.CatOfStrictDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor.