proposition: Lemma mem_filter_inv : forall x P l, mem x (filter P l) -> mem x l /\ P x.
proof: Proof. Proof using. introv E. rewrite* mem_filter_eq in E. Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)