proposition: Lemma functor_on_iso_iso_from_fully_faithful_reflection (C : precategory)(D : category) (F : functor C D) (HF : fully_faithful F) (a b : ob C) (f : z_iso (F a) (F b)) : functor_on_z_iso F (iso_from_fully_faithful_reflection HF f) = f.
proof: Proof. apply z_iso_eq. simpl; apply (homotweqinvweq (weq_from_fully_faithful HF a b)). 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