exists (z2 + z1 + 1)%Z; try rewrite Hz1; try rewrite Hz2; ring.
Qed.

(* Specifications: *)
Theorem OddPlus1 : forall n m : Z, Odd n -> Even m -> Odd (n + m).
intros n m H H0; case H; case H0; intros z1 Hz1 z2 Hz2.