(** ** 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_neq_in_iff : forall m x y,
~ E.eq x y -> (In y (remove x m)  <-> In y m).