Lemma horcomp_id_left (C D : category) (X : functor C C) (Z Z' : functor C D)(f : nat_trans Z Z') : ∏ c : C, horcomp (nat_trans_id X) f c = f (X c). Proof. intro c; simpl. unfold horcomp_data; simpl. now rewrite functor_id, id_right. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors.