Canonical nat_eqType := Eval hnf in EqType nat nat_eqMixin.
Arguments eqn !m !n.
Arguments eqnP {x y}.

Lemma leq_sub m1 m2 n1 n2 : m1 <= m2 -> n2 <= n1 -> m1 - n1 <= m2 - n2.
Definition maxn m n := if m < n then n else m.