Lemma is_functor_hcomp : is_functor hcomp_functor_data. Proof. split; red; cbn. - intros (f1, f2). cbn. apply hcomp_identity. - intros (f1, f2) (g1, g2) (h1, h2). unfold precategory_binproduct_mor. cbn. intros (x1, x2) (y1, y2). cbn. apply hcomp_vcomp. Qed.
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.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.