proposition: Lemma horizontal_comp_id {C : prebicategory_id_comp} {a b c : C} {f : a -1-> b} {g : b -1-> c} : identity f ;h; identity g = identity (f ;1; g).
proof: Proof. unfold compose2h. intermediate_path (functor_on_morphisms (compose_functor a b c) (identity (make_catbinprod f g))). reflexivity. apply functor_id. Defined.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Categories.StandardCategories UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.Equivalences.Core