Definition stable P := ~~ P -> P.Definition MP := forall f : nat -> bool, stable (exists n, f n = true).Definition mu (p : nat -> Prop) :
  (forall x, dec (p x)) -> ex p -> sig p.Local Notation R p :=
  (fun x y : nat => x = S y /\ ~ p y).

(* Specifications: *)
Lemma Acc_ind_dep (A : Type) (R : A -> A -> Prop) (P : forall a, Acc R a -> Prop) : (forall x (F : (forall y, R y x -> Acc R y)), (forall y (Hy : R y x), P y (F y Hy)) -> P x (Acc_intro x F)) -> forall x (h : Acc R x), P x h.