Definition Equivb m m' :=
  (forall k, In k m <-> In k m') /\
  (forall k e e', MapsTo k e m -> MapsTo k e' m' -> cmp e e' = true).

Lemma equal_Equivb : forall (s s': t elt), bst s -> bst s' -> (equal cmp s s' = true <-> Equivb s s').