diff --git a/thue-morse.v b/thue-morse.v
index 10b31c2..6060bb1 100644
--- a/thue-morse.v
+++ b/thue-morse.v
@@ -1110,7 +1110,10 @@ Lemma tm_step_next_range2_neighbor' : forall (n k : nat),
       rewrite <- H2. rewrite <- H3. apply L.
 
       apply H0.
-  -
+  - induction m.
+    + intros L. rewrite Nat.add_0_r in L. rewrite Nat.add_0_r in L.
+      apply tm_step_next_range2_neighbor'. apply H. apply L.
+    +