proposition: Lemma ideal_sum_subset_pres_l (I J K : Ideal R) : I ⊆ J -> (I + K) ⊆ (J + K).
proof: Proof. intros p. apply ideal_sum_smallest. { transitivity J. 1: exact p. apply ideal_sum_subset_l. } apply ideal_sum_subset_r. Defined.
imports: Basics Types Spaces.Finite.Fin Classes.interfaces.abstract_algebra Algebra.Rings.CRing Algebra.AbGroups