proposition: Lemma maponpaths_isotoid (a b : C) (i : z_iso a b) : maponpaths (functor_on_objects F) (isotoid _ HC i) = isotoid _ HD (functor_on_z_iso F i).
proof: Proof. apply (invmaponpathsweq (make_weq (idtoiso) (HD _ _ ))). simpl. rewrite maponpaths_idtoiso. repeat rewrite idtoiso_isotoid. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Univalence UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.TransportMorphisms UniMath.CategoryTheory.Core.Univalence