(************* Informative definitions of Even and Or ********************)

Inductive Even (n : nat) : Set :=
    Even_intro : forall q : nat, n = 2 * q -> Even n.(************* Informative definitions of Even and Or ********************)

Inductive Even (n : nat) : Set :=
    Even_intro : forall q : nat, n = 2 * q -> Even n.Inductive Odd (n : nat) : Set :=
    Odd_intro : forall q : nat, n = 2 * q + 1 -> Odd n.Inductive Odd (n : nat) : Set :=
    Odd_intro : forall q : nat, n = 2 * q + 1 -> Odd n.

(* Specifications: *)
Lemma Even_or_Odd : forall n : nat, Even n + Odd n.
Lemma Odd_odd : forall n : nat, Odd n -> odd n.