(** A null [ldiff] implies being smaller *)

(* Specifications: *)
Lemma ldiff_le : forall a b, ldiff a b == 0 -> a <= b.
(** Subtraction can be a ldiff when the opposite ldiff is null. *)
Lemma sub_nocarry_ldiff : forall a b, ldiff b a == 0 ->
a-b == ldiff a b.
Lemma ldiff_le : forall a b, 0<=b -> ldiff a b == 0 -> 0 <= a <= b.
(** Subtraction can be a ldiff when the opposite ldiff is null. *)
Lemma sub_nocarry_ldiff : forall a b, ldiff b a == 0 ->
a-b == ldiff a b.