absurd (n = n); auto.
pattern n at 1 in |- *; rewrite Hz1; rewrite Hz2;
repeat rewrite (fun x => Zplus_comm x 1).
case z1; case z2; simpl in |- *;
try (intros; red in |- *; intros; discriminate).
intros p p0; case p; simpl in |- *;
try (intros; red in |- *; intros; discriminate).
Qed.

Theorem EvenNOdd : forall n : Z, Even n -> ~ Odd n.
intros n H1; red in |- *; intros H2; case H1; case H2; intros z1 Hz1 z2 Hz2.