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 *)

Lemma odd_add_mul_even : forall n m p, Even m -> odd (n+m*p) = odd n.