proposition: 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: Proof. intro c; 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