Module Type NZDivProp
(Import A : NZOrdAxiomsSig')
(Import B : NZDiv' A)
(Import C : NZMulOrderProp A).
(** Uniqueness theorems *)
(** A division by itself returns 1 *)
(** A division of a small number by a bigger one yields zero. *)
(** Same situation, in term of modulo: *)
(** * Basic values of divisions and modulo. *)

Lemma mod_1_l: forall a, 1<a -> 1 mod a == 1.