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Thomas Baruchel 2023-01-22 15:17:52 +01:00
parent 4e36a9abed
commit 4d0d28abae
1 changed files with 20 additions and 1 deletions
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src/thue_morse3.v
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@ -696,9 +696,19 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
--> il y a une contradiction à chaque fois
*)
(* on prouve 3 < n *)
assert (R: 2^3 < length (tm_step n)). rewrite H.
rewrite app_length. rewrite <- Nat.add_0_l at 1.
apply Nat.add_le_lt_mono. apply Nat.le_0_l. simpl.
rewrite <- Nat.succ_lt_mono. rewrite <- Nat.succ_lt_mono.
rewrite <- Nat.succ_lt_mono. rewrite <- Nat.succ_lt_mono.
rewrite <- Nat.succ_lt_mono. rewrite <- Nat.succ_lt_mono.
rewrite <- Nat.succ_lt_mono. rewrite <- Nat.succ_lt_mono.
apply Nat.lt_0_succ. rewrite tm_size_power2 in R.
rewrite <- Nat.pow_lt_mono_r_iff in R.
(* on étend hd *)
destruct hd. inversion Q.
(* TODO : sortir les trucs de removelast *)
rewrite app_removelast_last
with (l := removelast (b3::b5::hd)) (d := false) in H.
assert ({last (removelast (b3 :: b5 :: hd)) false = b1}
@ -763,6 +773,15 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
rewrite <- tm_step_pred with (n := n) (k := 0) in H7.
rewrite H in H7. simpl in H7. inversion H7. rewrite H9 in n1.
contradiction n1. reflexivity. simpl.
replace 8 with (2^3). rewrite <- Nat.pow_lt_mono_r_iff.
assumption. apply Nat.lt_1_2. reflexivity.
rewrite app_removelast_last
with (l := removelast (removelast (b3::b5::b7::hd))) (d := false) in H.
pose (b8 := last (removelast (removelast (b3 :: b5 :: b7 :: hd))) false).
fold b8 in H. rewrite <- app_assoc in H. rewrite <- app_assoc in H.
False, True, True, False, True, False, False, True, True, False, False