(** [exists_] **)
Definition exists_ {A : Type} (f : key -> A -> bool) dom (m : t A dom) :=
fold (fun x v b => b || f x v) m false.

Lemma exists_spec : forall A f, Proper (X.eq ==> Logic.eq ==> Logic.eq) f -> forall dom (m : t A dom),
exists_ f m = true <-> exists x v, find x m = Some v ∧ f x v = true.