proposition: Lemma horcomp_id_prewhisker {C D E : category} (X : functor C D) (Z Z' : functor D E) (f : nat_trans Z Z') : horcomp (nat_trans_id X) f = pre_whisker _ f.
proof: Proof. apply (nat_trans_eq E); intro x; simpl; unfold horcomp_data; simpl. now rewrite functor_id, id_right. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors