(* 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 OddPlus1 : forall n m : Z, Odd n -> Even m -> Odd (n + m).