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 setI_subset_compat {U} (s1 s2 s1' s2' : set U) : s1 \subset s1' -> s2 \subset s2' -> (s1 :&: s2) \subset (s1' :&: s2').