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).