(** [Equivb] and [Equiv] and equivalent when [eq_elt] and [cmp] are related. *)
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'.

(* Specifications: *)
Lemma Equiv_Equivb : compat_cmp ->
forall m m', Equiv eq_elt m m' <-> Equivb cmp m m'.