proposition: Lemma Forall_filter_same : forall P l, Forall P (filter P l).
proof: Proof. Proof using. introv. induction l. { rewrite filter_nil. constructors~. } { rewrite filter_cons. cases_if~. } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)