proposition: Lemma is_precategory_monoid_precategory_data : is_precategory monoid_precategory_data.
proof: Proof. use make_is_precategory_one_assoc. - intros a b f. use monoid_id_left. - intros a b f. use monoid_id_right. - intros a b c d f g h. use monoid_assoc. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Free_Monoids_and_Groups UniMath.Combinatorics.Lists UniMath.Algebra.IteratedBinaryOperations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Adjunctions.Core