Section Even_Odd.
(** Zeven, used for rounding to nearest, ties to even *)
Definition Zeven (n : Z) :=
match n with
| Zpos (xO _) => true
| Zneg (xO _) => true
| Z0 => true
| _ => false
end.

Theorem Zeven_plus :
forall x y, Zeven (x + y) = Bool.eqb (Zeven x) (Zeven y).