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'.