(* Make [lia] work for [N] *)
Local Open Scope N_scope.
Hint Rewrite Nplus_0_r nat_of_Nsucc nat_of_Nplus nat_of_Nminus
N_of_nat_of_N nat_of_N_of_nat
nat_of_P_o_P_of_succ_nat_eq_succ nat_of_P_succ_morphism : N.
intros ? ? H; apply (f_equal N_of_nat) in H;
autorewrite with N in *; assumption.
Qed.

Theorem Nneq_in : forall n m,
nat_of_N n <> nat_of_N m
-> n <> m.