intros n m H H0; replace m with (n + m + - n)%Z; auto with zarith.
Qed.

(* Specifications: *)
Theorem EvenPlusInv2 : forall n m : Z, Even (n + m) -> Odd n -> Odd m.
intros n m H H0; replace m with (n + m + - n)%Z; auto with zarith.