proposition: Lemma is_precategory_precategory_monoid_data : is_precategory precategory_monoid_data.
proof: Proof. repeat split; intros; simpl; apply monoid_mor_eq. - apply id_left. - apply id_right. - apply assoc. - apply assoc'. Defined.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored