Definition STadd (x : STelt) (s : STt) := cons x s.Fixpoint STexists_ (f : STelt -> bool) (s : STt) :=
    match s with
      | nil      => false
      | hd :: tl => f hd || STexists_ f tl
    end.Fixpoint STmem elt l :=
    match l with
      | nil      => false
      | hd :: tl => if eqST_dec hd elt then true else STmem elt tl
    end.

Lemma STadd_iff : forall (s : STt) (x y : STelt), STmem y (STadd x s) = true <-> (eqST x y \/ STmem y s = true).