Proposition double_hor_comp_mor_id {C : category} {D : twosided_disp_cat C C} (Cm : hor_comp D) {x y z : C} (h₁ : D x y) (h₂ : D y z) : double_hor_comp_mor Cm (id_two_disp h₁) (id_two_disp h₂) = id_two_disp (double_hor_comp Cm h₁ h₂). Proof. exact (pr12 Cm x y z h₁ h₂). 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.