Coercion seq_In T : seq T -> set T := fun s x => List.In x s.Coercion list_In T : list T -> set T := fun s x => List.In x s.

Lemma setU_subset_l {U} (s1 s2 s3 : set U) : s1 \subset s2 -> s1 \subset (s2 :|: s3).