proposition: Lemma not_all_ex_not : forall P:U -> Prop, ~ (forall n:U, P n) -> exists n : U, ~ P n.
proof: Proof. intros P notall. apply not_all_not_ex with (P:=fun x => ~ P x). intro all; apply notall. intro n; apply NNPP. apply all. Qed.
imports: Classical_Prop