Section Partition.
Variable f : key -> elt -> bool.
Hypothesis Hf : Proper (E.eq==>eq==>eq) f.
End Partition.

Lemma update_mapsto_iff : forall m m' k e,
MapsTo k e (update m m') <->
(MapsTo k e m' \/ (MapsTo k e m /\ ~In k m')).