Module Type IsNZOrd (Import NZ : NZOrd').
Declare Instance lt_wd : Proper (eq ==> eq ==> iff) lt.

Axiom lt_eq_cases : forall n m, n <= m <-> n < m \/ n == m.
Axiom lt_irrefl : forall n, ~ (n < n).
Axiom lt_succ_r : forall n m, n < S m <-> n <= m.