proposition: Lemma length_filter : forall l P, length (filter P l) <= length l.
proof: Proof. Proof using. intros. induction l. { rewrite filter_nil. math. } { rewrite filter_cons. case_if; rew_list; math. } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)