Module ZAddOrderProp (Import Z : ZAxiomsMiniSig').
Include ZOrderProp Z.
(** Theorems that are either not valid on N or have different proofs on N and Z *)
(** Sub and order *)
Notation sub_pos := lt_0_sub (only parsing).
Notation sub_nonneg := le_0_sub (only parsing).
Notation sub_neg := lt_sub_0 (only parsing).
Notation sub_nonpos := le_sub_0 (only parsing).

Theorem sub_nonpos_cases : forall n m, n - m <= 0 -> n <= 0 \/ 0 <= m.