proposition: Lemma is_precategory_setwith2binop_precategory_data : is_precategory setwith2binop_precategory_data.
proof: Proof. use make_is_precategory. - intros a b f. use setwith2binop_id_left. - intros a b f. use setwith2binop_id_right. - intros a b c d f g h. use setwith2binop_assoc. - intros a b c d f g h. apply pathsinv0, setwith2binop_assoc. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.Algebra.BinaryOperations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence