Definition identity_hor_comp {C : category} {D : twosided_disp_cat C C} (Cm : hor_comp D) : double_functor_hor_comp (twosided_disp_functor_identity D) Cm Cm. Proof. use make_double_functor_hor_comp. - exact (identity_hor_comp_data Cm). - exact (identity_hor_comp_laws Cm). Defined.
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.