Definition double_id_mor {C : category} {D : twosided_disp_cat C C} (I : hor_id_data D) {x y : C} (f : x --> y) : double_id I x -->[ f ][ f ] double_id I y := pr2 I x y f.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos.