(** Basic facts about boolean comparisons *)
Module Type BoolOrderFacts
(Import E:EqLtLe')
(Import C:HasCmp E)
(Import F:HasBoolOrdFuns' E)
(Import O:CompareBasedOrder E C)
(Import S:BoolOrdSpecs E F).
Include CompareBasedOrderFacts E C O.
(** Nota : apart from [eqb_compare] below, facts about [eqb] are in BoolEqualityFacts *)
(** Alternate specifications based on [BoolSpec] and [reflect] *)

(** Relation between [compare] and the boolean comparisons *)
Lemma eqb_compare x y :
(x =? y) = match compare x y with Eq => true | _ => false end.