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

Lemma Partition_partition : forall m m1 m2, Partition m m1 m2 ->
let f := fun k (_:elt) => mem k m1 in
Equal m1 (fst (partition f m)) /\ Equal m2 (snd (partition f m)).