(** ** 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 elements_in_iff : forall m x,
In x m <-> exists e, InA (@eq_key_elt _) (x,e) (elements m).