Update

src/thue_morse3.v

@@ -522,7 +522,68 @@ Proof.
   destruct (last (b3::hd) false); destruct b1; destruct b.
   reflexivity. contradiction n2. reflexivity. reflexivity.
   contradiction n1. reflexivity. contradiction n1. reflexivity.
-  reflexivity. contradiction n2. reflexivity. reflexivity. rewrite H3 in H.
+  reflexivity. contradiction n2. reflexivity. reflexivity.
+
+       (* élargir hd et tl à l'aide des booléens b5 (gauche) et b6 (droite) *)
+  destruct hd. inversion Q. destruct tl.
+  assert (0 < n). assert (0 < 2). apply Nat.lt_0_2. generalize H0.
+  generalize H4. apply Nat.lt_trans. apply tm_step_length_even in H4.
+  rewrite H in H4.
+  rewrite app_assoc in H4. rewrite <- app_removelast_last in H4.
+  rewrite app_length in H4. rewrite Nat.even_add in H4.
+  rewrite Q in H4. inversion H4. easy. rewrite H3 in H.
+  rewrite app_removelast_last
+         with (l := removelast (b3::b5::hd)) (d := false) in H.
+  rewrite <- app_assoc in H.
+
+  (* assigner
+       last (removelast (b3 :: b5 :: hd)) false = b1
+       b6 = b1
+   *)
+  assert ({last (removelast (b3 :: b5 :: hd)) false=b}
+            + {~ last (removelast (b3 :: b5 :: hd)) false=b}). apply bool_dec.
+  destruct H4. rewrite e0 in H.
+  replace (
+    removelast (removelast (b3 :: b5 :: hd)) ++ [b] ++ [b]
+      ++ b :: b1 :: b1 :: b :: b :: b1 :: b1 :: b :: b :: b6 :: tl)
+    with (
+    removelast (removelast (b3 :: b5 :: hd)) ++ [b] ++ [b] ++ [b]
+      ++ b1 :: b1 :: b :: b :: b1 :: b1 :: b :: b :: b6 :: tl) in H.
+  apply tm_step_cubefree in H. contradiction H. reflexivity.
+  apply Nat.lt_0_1. reflexivity.
+  assert (last (removelast (b3 :: b5 :: hd)) false = b1).
+  destruct (last (removelast (b3 :: b5 :: hd)) false); destruct b1; destruct b.
+  reflexivity. reflexivity. contradiction n4. reflexivity.
+  contradiction n1. reflexivity. contradiction n1. reflexivity.
+  contradiction n4. reflexivity. reflexivity. reflexivity. rewrite H4 in H.
+  assert ({b6=b} + {~ b6=b}). apply bool_dec. destruct H5. rewrite e0 in H.
+  replace (
+    removelast (removelast (b3 :: b5 :: hd)) ++ [b1] ++ [b]
+      ++ b :: b1 :: b1 :: b :: b :: b1 :: b1 :: b :: b :: b :: tl)
+    with (
+    (removelast (removelast (b3 :: b5 :: hd)) ++ [b1] ++ [b]
+      ++ b :: b1 :: b1 :: b :: b :: b1 :: b1 :: nil)
+      ++ [b] ++ [b] ++ [b] ++ tl) in H.
+  apply tm_step_cubefree in H. contradiction H. reflexivity.
+  apply Nat.lt_0_1. rewrite <- app_assoc. reflexivity.
+  assert (b6 = b1). destruct (b6); destruct b1; destruct b.
+  reflexivity. reflexivity. contradiction n5. reflexivity.
+  contradiction n1. reflexivity. contradiction n1. reflexivity.
+  contradiction n5. reflexivity. reflexivity. reflexivity. rewrite H5 in H.
+
+  (* contradiction *)
+  replace (
+    removelast (removelast (b3 :: b5 :: hd)) ++
+    [b1] ++ [b] ++ b :: b1 :: b1 :: b :: b :: b1 :: b1 :: b :: b :: b1 :: tl)
+    with (removelast (removelast (b3 :: b5 :: hd)) ++
+    [b1;b;b;b1] ++ [b1;b;b;b1] ++ [b1;b;b;b1] ++ tl) in H.
+  apply tm_step_cubefree in H. contradiction H. reflexivity.
+  apply Nat.lt_0_succ. reflexivity. easy. easy.
+
+
+
+
+