proposition: Lemma LPO_notforall : forall P : nat -> Prop, (forall n, P n \/ ~P n) -> (~ forall n : nat, ~ P n) -> exists n : nat, P n.
proof: Proof. intros. destruct (LPO P H). destruct s as (n,H1) ; exists n ; apply H1. contradict H0 ; apply n. Qed.
imports: Coq(RIneq Lia) Rcomplements