Section NatOrd.

(* Specifications: *)
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 : forall x y, [|| x < y, x == y | y < x].
Lemma total_lex : forall x y, [|| lex x y, x == y | lex y x].
Definition prod_ordMixin := OrdMixin irr_lex trans_lex total_lex.