proposition: Lemma functor_on_iso_inv (C C' : precategory) (F : functor C C') (a b : ob C) (f : iso a b) : functor_on_iso F (iso_inv_from_iso f) = iso_inv_from_iso (functor_on_iso F f).
proof: Proof. apply eq_iso; simpl. apply inv_iso_unique'; simpl. unfold precomp_with. rewrite <- functor_comp. rewrite iso_inv_after_iso. apply functor_id. Defined.
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