Definition ldecidable X (p : X -> Prop) :=
  forall x, p x \/ ~ p x.

(* Specifications: *)
Lemma weakPost X (p : X -> Prop) : discrete X -> ldecidable p -> enumerable p -> enumerable (compl p) -> decidable p.
Lemma MP_to_decMP : MP -> (forall p : nat -> Prop, decidable p -> stable (exists n, p n)).
Lemma decMP_to_eMP : (forall p : nat -> Prop, decidable p -> stable (exists n, p n)) -> (forall X (p : X -> Prop), enumerable p -> stable (exists n, p n)).
Lemma eMP_to_MP : (forall X (p : X -> Prop), enumerable p -> stable (exists n, p n)) -> MP.
Lemma MP_enum_stable X (p : X -> Prop) : MP -> enumerable p -> discrete X -> forall x, stable (p x).