Update

src/thue_morse3.v

@@ -402,6 +402,41 @@ Proof.
     generalize K. generalize N. apply tm_morphism_app3.
     symmetry in P.
 
+    assert (even (length (rev a)) = true). rewrite rev_length. assumption.
+
+    assert (R: tl = tm_morphism (skipn (Nat.div2 (length (rev a)))
+              (skipn (Nat.div2 (length a))
+                 (skipn (Nat.div2 (length hd)) (tm_step n))))).
+    generalize H0. generalize P. apply tm_morphism_app3.
+
+    rewrite M in H. rewrite O in H. rewrite R in H.
+    rewrite tm_morphism_rev in H. rewrite <- tm_morphism_app in H.
+    rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
+    rewrite <- tm_morphism_eq in H.
+    pose (hd' := firstn (Nat.div2 (length hd)) (tm_step n)).
+    pose (a' := firstn (Nat.div2 (length a))
+               (skipn (Nat.div2 (length hd)) (tm_step n))).
+    pose (tl' := skipn (Nat.div2 (length (rev a)))
+                    (skipn (Nat.div2 (length a))
+                          (skipn (Nat.div2 (length hd)) (tm_step n)))).
+    fold hd' in H. fold a' in H. fold tl' in H.
+
+    assert (length a' = 2^S (Nat.double m)). unfold a'.
+    rewrite firstn_length_le. rewrite I. rewrite Nat.double_S.
+    rewrite Nat.pow_succ_r. rewrite Nat.div2_double. reflexivity.
+    apply le_0_n. rewrite skipn_length.
+    rewrite Nat.mul_le_mono_pos_r with (p := 2).
+    rewrite Nat.mul_comm. rewrite <- Nat.add_0_r at 1.
+    replace 0 with (Nat.b2n (Nat.odd (length a))) at 2.
+    rewrite <- Nat.div2_odd. rewrite Nat.mul_sub_distr_r.
+
+
+    re
+
+
+
+
+
 
     (* réduire par la réciproque du morphisme *)