Lemma horizontal_comp_id {C : prebicategory_id_comp} {a b c : C} {f : a -1-> b} {g : b -1-> c} : identity f ;h; identity g = identity (f ;1; g). Proof. unfold compose2h. intermediate_path (functor_on_morphisms (compose_functor a b c) (identity (make_catbinprod f g))). reflexivity. apply functor_id. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.Equivalences.Core.