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(**                     Even                         *)

Definition even (x : N.t) := recursion true (fun _ p => negb p) x.#[global]
Instance even_wd : Proper (N.eq==>Logic.eq) even.

(* Specifications: *)
Theorem even_0 : even 0 = true.
Theorem even_succ : forall x, even (S x) = negb (even x).