exists (z2 + z1)%Z; try rewrite Hz1; try rewrite Hz2; ring.
Qed.
Hint Resolve EvenPlus1 EvenPlus2 OddPlus1 OddPlus2: zarith.

(* Specifications: *)
Theorem EvenPlusInv1 :
forall n m : Z, Even (n + m) -> Even n -> Even m.