proposition: Lemma not_ex_all_func (A : Type) (P Q : A -> Prop) : (forall x, ~P x -> Q x) -> (~exists x, P x) -> (forall x, Q x).
proof: Proof. intros allx_notPx_to_Qx notsomex_Px. intuition. apply allx_notPx_to_Qx. intros Px. apply notsomex_Px. exists x. assumption. Qed.
imports: Classical_Prop Classical_Pred_Type