proposition: Lemma fully_faithful_implies_full_and_faithful (C D : precategory_data) (F : functor C D) : fully_faithful F -> full_and_faithful F.
proof: Proof. intro H. split; simpl. unfold full. intros a b. apply issurjectiveweq. apply H. intros a b. apply isinclweq. apply H. 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