Module Type NSubProp (Import N : NAxiomsMiniSig').
Include NMulOrderProp N.
(* This could be proved by adding m to both sides. Then the proof would use add_sub_assoc and sub_0_le, which is proven below. *)

Theorem add_sub_eq_nz : forall n m p, p ~= 0 -> n - m == p -> m + p == n.