Set Implicit Arguments.
Fixpoint nats (b: nat) (w: nat) {struct w}: list nat :=
match w with
| 0 => nil
| S w' => b :: nats (S b) w'
end.
Proof with auto.
induction w in b |- * ...
simpl.
intros.
rewrite IHw...
Qed.

Lemma In_nats (w x b: nat): b <= x -> x < b + w -> In x (nats b w).