Module Type NZParityProp
(Import A : NZOrdAxiomsSig')
(Import B : NZParity A)
(Import C : NZMulOrderProp A).
(** Morphisms *)
#[global]
Instance Even_wd : Proper (eq==>iff) Even.
#[global]
Instance odd_wd : Proper (eq==>Logic.eq) odd.
(** Evenness and oddity are dual notions *)

(** Parity of [2 * n] and [2 * n + 1] *)
Lemma even_even : forall n, even (2 * n) = true.