proposition: Lemma all_mem xs ys : reflect {subset ys <= xs} (all [mem xs] ys).
proof: Proof. by case: allP=>H; constructor; [move=>x /H | move=>X; apply: H=>x /X]. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat seq path eqtype choice bigop) pcm(options prelude pred)