(** * [equal] *)
Fixpoint equal (cmp:elt->elt->bool)(m m' : t elt) {struct m} : bool :=
match m, m' with
| nil, nil => true
| (x,e)::l, (x',e')::l' =>
match X.compare x x' with
| EQ _ => cmp e e' && equal cmp l l'
| _    => false
end
| _, _ => false
end.
Definition Equivb cmp m m' :=
(forall k, In k m <-> In k m') /\
(forall k e e', MapsTo k e m -> MapsTo k e' m' -> cmp e e' = true).

(* Specifications: *)
Lemma equal_1 : forall m (Hm:Sort m) m' (Hm': Sort m') cmp,
Equivb cmp m m' -> equal cmp m m' = true.
Lemma equal_2 : forall m (Hm:Sort m) m' (Hm:Sort m') cmp,
equal cmp m m' = true -> Equivb cmp m m'.