proposition: Corollary functorial_composition_legacy_ok {A B C : category} : functorial_composition_legacy A B C = functorial_composition _ _ _.
proof: Proof. apply functor_eq. - apply homset_property. - cbn. use functor_data_eq. + intro FG. apply idpath. + intros FG1 FG2 αβ. cbn. apply (horcomp_post_pre _ _ C). 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