proposition: Lemma ideal_intersection_is_product (I J : Ideal R) : Coprime I J -> I ∩ J ↔ I ⋅ J.
proof: Proof. intros p. apply ideal_subset_antisymm. - apply ideal_intersection_subset_product. unfold Coprime in p. apply symmetry in p. rapply p. - apply ideal_product_subset_intersection. Defined.
imports: Basics Types Spaces.Finite.Fin Classes.interfaces.abstract_algebra Algebra.Rings.CRing Algebra.AbGroups