Require Export VST.msl.eq_dec.
Hint Rewrite andb_true_iff: align.
Hint Rewrite <- Zle_is_le_bool: align.
Hint Rewrite Z.eqb_eq: align.
Hint Rewrite power_nat_divide_le using (auto with align): align.
Hint Rewrite Z.mod_divide using (apply two_power_nat_0; auto with align): align.
Hint Rewrite two_p_max_divide using (auto with align): align.
Hint Rewrite two_p_max_1 using (auto with align): align.
Hint Resolve Z_max_two_p: align.
Inductive sublist {A} : list A -> list A -> Prop :=
| sublist_nil : sublist nil nil
| sublist_cons a l1 l2 : sublist l1 l2 -> sublist (a :: l1) (a :: l2)
| sublist_drop a l1 l2 : sublist l1 l2 -> sublist l1 (a :: l2).
Definition Ensemble_join {A} (X Y Z: Ensemble A): Prop :=
(forall a, Z a <-> X a \/ Y a) /\ (forall a, X a -> Y a -> False).
Require Coq.Logic.ConstructiveEpsilon.

Lemma decidable_countable_ex_sig {A} (f : nat -> A)
(Hf : forall a, exists n, a = f n)
(P : A -> Prop)
(Pdec : forall x, {P x} + {~ P x}) :
(exists x : A, P x) -> {x : A | P x}.