proposition: Lemma full_and_faithful_implies_fully_faithful (C D : precategory_data) (F : functor C D) : full_and_faithful F -> fully_faithful F.
proof: Proof. intros [Hfull Hfaith]. intros a b. simpl in *. apply isweqinclandsurj. - apply Hfaith. - apply Hfull. 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