proposition: Proposition isaprop_preserves_hor_id {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : strict_twosided_disp_cat C₂ C₂} (I₁ : hor_id D₁) (I₂ : hor_id D₂) {F : C₁ ⟶ C₂} (FF : twosided_disp_functor F F D₁ D₂) : isaprop (preserves_hor_id I₁ I₂ FF).
proof: Proof. use isaproptotal2. - intro. apply isaprop_preserves_hor_id_laws. - intros. use funextsec ; intro. apply is_strict_strict_twosided_disp_cat. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics