Section Cmp.
Variable eq_elt : elt->elt->Prop.
Variable cmp : elt->elt->bool.
Definition compat_cmp :=
forall e e', cmp e e' = true <-> eq_elt e e'.
End Cmp.
(** Composition of the two last results: relation between [Equal] and [Equivb]. *)

Lemma Equal_Equivb : forall cmp,
(forall e e', cmp e e' = true <-> e = e') ->
forall (m m':t elt), Equal m m' <-> Equivb cmp m m'.