proposition: Lemma BZ_order_aux: order (opp_order (induced_order Nat_order Nats)) /\ order Nat_order.
proof: Proof. move: Nat_order_wor => [[or _] _]; move: BZ_order_aux1 => h. move: (proj1 (iorder_osr or h)) => h1; move: (proj1 (opp_osr h1)) => h2. split;fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)