Section NatOrd.

Lemma irr_ltn_nat : irreflexive ltn. Proof. by move=>x; rewrite /= ltnn. Qed.
Lemma trans_ltn_nat : transitive ltn. Proof. by apply: ltn_trans. Qed.
Lemma total_ltn_nat x y : [|| x < y, x == y | y < x].