proposition: Lemma is_functor_homSet_functor_type : is_functor homSet_functor_data.
proof: Proof. use make_dirprod. - intro; cbn. apply funextsec; intro. refine (id_right _ @ _). apply id_left. - repeat intro. apply funextsec; intro; cbn. do 3 rewrite assoc. reflexivity. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Foundations.NaturalNumbers UniMath.Foundations.HLevels UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.PrecategoryBinProduct