Definition comp_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} {FF : twosided_disp_functor F F D₁ D₂} {G : C₂ ⟶ C₃} {GG : twosided_disp_functor G G D₂ D₃} (HFF : double_functor_hor_id FF I₁ I₂) (HGG : double_functor_hor_id GG I₂ I₃) : double_functor_hor_id_data (comp_twosided_disp_functor FF GG) I₁ I₃ := λ x, transportf_disp_mor2 (id_left _ @ functor_id _ _) (id_left _ @ functor_id _ _) (functor_double_id_cell HGG (F x) ;;2 #2 GG (functor_double_id_cell HFF x)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. 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.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.