proposition: Lemma eq_in_sub_precategory (C : category)(C':sub_precategories C) (a b : sub_ob C') (f g : sub_precategory_morphisms C' a b) : pr1 f = pr1 g -> f = g.
proof: Proof. intro H. apply (total2_paths_f H). apply proofirrelevance. apply pr2. Qed.
imports: UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos