(I J : Ideal R) : I ⋅ J ⊆ I ∩ J. Proof. apply ideal_intersection_subset. + apply ideal_product_subset_l. + apply ideal_product_subset_r. Defined.
Require Import Basics Types. Require Import Spaces.Finite.Fin. Require Import Classes.interfaces.canonical_names. Require Import Algebra.Rings.Ring. Require Import Algebra.Groups.Subgroup. Require Import Algebra.AbGroups. Require Import WildCat.Core. Module Import Notation.