Module Type NZParityProp
(Import A : NZOrdAxiomsSig')
(Import B : NZParity A)
(Import C : NZMulOrderProp A).
(** Morphisms *)
Instance Even_wd : Proper (eq==>iff) Even.
Instance odd_wd : Proper (eq==>Logic.eq) odd.
(** Evenness and oddity are dual notions *)
(** Constants *)
(** Parity and successor *)
(** Parity and successor of successor *)
(** Parity and addition *)
(** Parity and multiplication *)
(** A particular case : adding by an even number *)

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