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Thomas Baruchel 2023-01-21 19:38:07 +01:00
parent a21f147de0
commit 03aa9cd43f
1 changed files with 62 additions and 1 deletions
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63
src/thue_morse3.v
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@ -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.