apply in_map_iff.
exists (Pos.to_nat pos).
split.
- apply Pos2Nat.id.
- apply ltInRange.
+ apply Pos2Nat.inj_le; auto.
+ pose proof (Pos2Nat.is_succ pos) as Contra; inversion_clear Contra; congruence.
Qed.

(* Specifications: *)
Lemma rangeNatLt : forall n m, In m (rangeNat n) -> lt m (S n) /\ m <> O.
induction n; intros.