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_eqdec :
forall eq_elt_dec : (forall e e', { e = e' } + { e <> e' }),
let cmp := fun e e' => if eq_elt_dec e e' then true else false in
forall (m m':t elt), Equal m m' <-> Equivb cmp m m'.