Proposition isaprop_double_nat_trans_hor_comp {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {F G : C₁ ⟶ C₂} {FF : twosided_disp_functor F F D₁ D₂} {GG : twosided_disp_functor G G D₁ D₂} {τ : F ⟹ G} (ττ : twosided_disp_nat_trans τ τ FF GG) {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} (FC : double_functor_hor_comp FF Cm₁ Cm₂) (GC : double_functor_hor_comp GG Cm₁ Cm₂) : isaprop (double_nat_trans_hor_comp ττ FC GC). Proof. repeat (use impred ; intro). apply isaset_disp_mor. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor.