proposition: Lemma is_precategory_loc_precategory_data : is_precategory loc_precategory_data.
proof: Proof. apply is_precategory_one_assoc_to_two. split. - split. + intros a b f. apply loc_id_left. + intros a b f. apply loc_id_right. - intros a b c d f g h. apply loc_precategory_assoc. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors