apply le_trans with (cPair (cPairPi1 a) (cPairPi2 a)).
apply cPairLe2.
rewrite cPairProjections.
apply le_n.
Qed.

(* Specifications: *)
Lemma cPairLe3 :
forall a b c d : nat, a <= b -> c <= d -> cPair a c <= cPair b d.
Lemma cPairLt1 : forall a b : nat, a < cPair a (S b).
Lemma cPairLt2 : forall a b : nat, b < cPair (S a) b.
End CPair_Order.