(** ** Corollaries *)

(* Specifications: *)
Lemma LPO_notforall : forall P : nat -> Prop, (forall n, P n \/ ~P n) ->
(~ forall n : nat, ~ P n) -> exists n : nat, P n.
Lemma LPO_notnotexists : forall P : nat -> Prop, (forall n, P n \/ ~P n) ->
~~ (exists n : nat, P n) -> exists n : nat, P n.
Lemma LPO_ub_dec : forall (u : nat -> R),
{M : R | forall n, u n <= M} + {forall M : R, exists n, M < u n}.