proposition: Lemma ptd_composite_compose (Z Z' : ptd_obj C): ptd_composite Z Z' = ptd_compose Z Z'.
proof: Proof. use total2_paths_f. - apply idpath. - cbn. rewrite (@horcomp_post_pre _ _ C). apply (nat_trans_eq (homset_property C)). intro c. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.HorizontalComposition