proposition: Proposition composition_preserves_hor_id_data {C₁ C₂ C₃ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {D₃ : twosided_disp_cat C₃ C₃} {I₁ : hor_id D₁} {I₂ : hor_id D₂} {I₃ : hor_id D₃} {F : C₁ ⟶ C₂} {G : C₂ ⟶ C₃} {FF : twosided_disp_functor F F D₁ D₂} (FFI : preserves_hor_id I₁ I₂ FF) {GG : twosided_disp_functor G G D₂ D₃} (GGI : preserves_hor_id I₂ I₃ GG) : preserves_hor_id_data I₁ I₃ (comp_twosided_disp_functor FF GG).
proof: Proof. intro x ; cbn. refine (_ @ GGI (F x)). apply maponpaths. apply (FFI x). Defined.
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