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Thomas Baruchel 2023-02-11 11:14:49 +01:00
parent 8c7bd4940a
commit 6a9c177d2f
1 changed files with 16 additions and 28 deletions
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src/thue_morse3.v
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@ -507,19 +507,16 @@ Proof.
(* un sous-cas
(T F) | F T T F || F T T F | (F T) cube
*)
assert (b4 = b). destruct b4; destruct b1; destruct b.
reflexivity. contradiction n3. reflexivity. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
reflexivity. contradiction n3. reflexivity. reflexivity. rewrite H1 in H.
assert (b4 = b). destruct b4; destruct b1; destruct b;
reflexivity || contradiction n3 || contradiction n1; reflexivity.
rewrite H1 in H.
assert (b2 = b). destruct b2; destruct b1; destruct b.
reflexivity. contradiction n0. reflexivity. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
reflexivity. contradiction n0. reflexivity. reflexivity. rewrite H2 in H.
assert (last (b3::hd) false = b).
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.
destruct (last (b3::hd) false); destruct b1; destruct b;
reflexivity || contradiction n2 || contradiction n1; reflexivity.
(* élargir hd et tl à l'aide des booléens b5 (gauche) et b6 (droite) *)
destruct hd. inversion Q. destruct tl.
@ -562,10 +559,9 @@ Proof.
++ [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.
assert (b6 = b1). destruct (b6); destruct b1; destruct b;
reflexivity || contradiction n5 || contradiction n1; reflexivity.
rewrite H5 in H.
(* contradiction *)
replace (
@ -642,10 +638,8 @@ reflexivity. contradiction n0. reflexivity. reflexivity. rewrite H1 in H.
destruct M. left. assumption. (* ici on postule le modulo = 2 *)
assert (last (b3::hd) false = b1).
destruct (last (b3::hd) false); destruct b1; destruct b0.
reflexivity. reflexivity. contradiction n2. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
contradiction n2. reflexivity. reflexivity. reflexivity.
destruct (last (b3::hd) false); destruct b1; destruct b0;
reflexivity || contradiction n2 || contradiction n1; reflexivity.
assert ({b4=b0} + {~ b4=b0}). apply bool_dec. destruct H3. rewrite e0 in H.
assert (exists x, skipn 2 [b1;b0;b1;b0] = [x;x]).
@ -664,10 +658,8 @@ reflexivity. contradiction n0. reflexivity. reflexivity. rewrite H1 in H.
destruct H3. inversion H3. rewrite <- H6 in H5. rewrite H5 in n1.
contradiction n1. reflexivity.
assert (b4 = b1). destruct b4; destruct b1; destruct b0.
reflexivity. reflexivity. contradiction n3. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
contradiction n3. reflexivity. reflexivity. reflexivity.
assert (b4 = b1). destruct b4; destruct b1; destruct b0;
reflexivity || contradiction n3 || contradiction n1; reflexivity.
rewrite H3 in H. rewrite H2 in H.
assert (b2 = b0). destruct b2; destruct b1; destruct b0.
@ -751,17 +743,13 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
rewrite <- app_assoc. reflexivity.
(* on assigne les valeurs correctes aux deux extrémités *)
assert (b6 = b0). destruct b6; destruct b1; destruct b0.
reflexivity. contradiction n5. reflexivity. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
reflexivity. contradiction n5. reflexivity. reflexivity.
assert (b6 = b0). destruct b6; destruct b1; destruct b0;
reflexivity || contradiction n5 || contradiction n1; reflexivity.
rewrite H5 in H.
assert (last (removelast (b3 :: b5 :: hd)) false = b0).
destruct (last (removelast (b3 :: b5 :: hd)) false);
destruct b1; destruct b0.
reflexivity. contradiction n4. reflexivity. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
reflexivity. contradiction n4. reflexivity. reflexivity.
destruct b1; destruct b0;
reflexivity || contradiction n4 || contradiction n1; reflexivity.
rewrite H6 in H.
(* on étend hd *)