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 mapi_1 : forall (m: tree elt)(x:key)(e:elt), MapsTo x e m -> exists y, X.eq y x /\ MapsTo x (f y e) (mapi f m).