Proposition identity_hor_id_laws {C : category} {D : twosided_disp_cat C C} (I : hor_id D) : double_functor_hor_id_laws (identity_hor_id_data I). Proof. intros x y f ; cbn. rewrite id_two_disp_left, id_two_disp_right. rewrite transport_b_b_disp_mor2. use transportb_disp_mor2_eq. apply idpath. Qed.
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.