(* We define the parity predicates*)
 
Definition Even (z : Z) : Prop := exists z1 : _, z = (2 * z1)%Z.Definition Odd (z : Z) : Prop := exists z1 : _, z = (2 * z1 + 1)%Z.

Theorem OddEvenDec : forall n : Z, {Odd n} + {Even n}.