proposition: Lemma functor_eq (C C' : precategory_data) (hs: has_homsets C') (F F': functor C C'): pr1 F = pr1 F' -> F = F'.
proof: Proof. intro H. apply (total2_paths_f H). apply proofirrelevance. apply isaprop_is_functor. apply hs. 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