Lemma is_nat_trans_horcomp : is_nat_trans _ _ horcomp_data. Proof. intros c d f; unfold horcomp_data; simpl. rewrite assoc, nat_trans_ax, <- !assoc; apply maponpaths. now rewrite <- !functor_comp, nat_trans_ax. 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.