proposition: Lemma ff_reflects_is_iso (C D : precategory) (F : functor C D) (HF : fully_faithful F) : reflects_isos F.
proof: Proof. intros a b f H. set (X:= fully_faithful_reflects_iso_proof _ _ F HF _ _ (_,,H)). simpl in X. set (T:= homotinvweqweq (weq_from_fully_faithful HF a b ) ). simpl in T. unfold fully_faithful_inv_hom in X. simpl in X. rewrite T in X. apply X. 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