(** 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] *)

Lemma ltb_nlt x y : x <? y = false <-> ~ (x < y).