Definition double_id_mor_id_comp {C : category} {D : twosided_disp_cat C C} (I : hor_id D) {x y z : C} (f : x --> y) (g : y --> z) : double_id_mor I (f · g) = double_id_mor I f ;;2 double_id_mor I g. Proof. exact (pr22 I x y z f g). Defined.
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.