proposition: Lemma forallb_neg : forall l, forallb f l = false <-> exists x, In x l /\ ~P x.
proof: Proof. intro l. rewrite forallb_false. split; intro. do 2 destruct H. exists x. rewrite <- (ko (@f_ok)). tauto. do 2 destruct H. exists x. rewrite (ko (@f_ok)). tauto. Qed.
imports: CoLoR(LogicUtil EqUtil RelUtil BoolUtil NatUtil) Coq(Setoid SetoidList FunInd)