intros p q; case (Pcompare p q Datatypes.Eq); auto; right; red in |- *;
intros; discriminate.
Qed.
Hint Resolve lt_O_nat_of_P: arith.

Theorem odd_even_lem : forall p q, 2 * p + 1 <> 2 * q.
intros p; elim p; auto.