(** ** Specifications written using equivalences *)
Section IffSpec.
Variable elt elt' elt'': Type.
Implicit Type m: t elt.
Implicit Type x y z: key.
Implicit Type e: elt.

Lemma remove_mapsto_iff : forall m x y e,
MapsTo y e (remove x m) <-> ~E.eq x y /\ MapsTo y e m.