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Thomas Baruchel 2023-02-02 18:44:05 +01:00
parent 7b5ca73448
commit 09b3f8f05c
1 changed files with 64 additions and 0 deletions
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64
src/thue_morse3.v
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@ -2108,6 +2108,9 @@ Proof.
assert (K := J).
rewrite tm_step_palindromic_length_12_prefix
with (n := n) (hd := hd) (tl := tl) in K.
assert (L: even (length hd) = true).
rewrite <- Nat.div_exact in K. rewrite K.
rewrite Nat.even_mul. reflexivity. easy.
destruct a. inversion I. destruct a. inversion I.
destruct a. inversion I. destruct a. inversion I.
@ -2133,6 +2136,15 @@ Proof.
reflexivity. destruct H1. inversion H1. reflexivity.
rewrite <- app_assoc. reflexivity. rewrite H0 in H.
assert (b5 <> b6).
replace (hd ++ [b; b0; b1; b2; b3; b5; b5; b6]
++ [b6; b5; b5; b3; b2; b1; b0; b] ++ tl)
with ((hd ++ [b; b0; b1; b2; b3]) ++ [b5] ++ [b5] ++ [b6]
++ [b6; b5; b5; b3; b2;b1;b0;b] ++ tl) in H.
apply tm_step_cubefree in H. destruct b5; destruct b6.
contradiction H. reflexivity. easy. easy. contradiction H. reflexivity.
apply Nat.lt_0_1. rewrite <- app_assoc. reflexivity.
assert (b5 <> b3).
replace (hd ++ [b; b0; b1; b2; b3; b5; b5; b6]
++ [b6; b5; b5; b3; b2; b1; b0; b] ++ tl)
@ -2142,8 +2154,60 @@ Proof.
contradiction H. reflexivity. easy. easy. contradiction H. reflexivity.
apply Nat.lt_0_1. rewrite <- app_assoc. reflexivity.
assert (b3 = b6). destruct b3; destruct b5; destruct b6.
contradiction H1. reflexivity. contradiction H2. reflexivity.
reflexivity. contradiction H1. reflexivity.
contradiction H1. reflexivity. reflexivity.
contradiction H2. reflexivity. contradiction H1. reflexivity.
rewrite H3 in H.
assert (b0 = b1).
replace (hd ++ [b; b0; b1; b2; b6; b5; b5; b6]
++ [b6; b5; b5; b6; b2; b1; b0; b] ++ tl)
with ((hd ++ [b]) ++ [b0; b1; b2; b6]
++ [b5; b5; b6; b6; b5; b5; b6; b2; b1; b0; b] ++ tl) in H.
assert (length (hd ++ [b]) mod 4 = 1).
rewrite app_length. rewrite <- Nat.add_mod_idemp_l. rewrite K.
reflexivity. easy.
assert (exists x, firstn 2 [b0; b1; b2; b6] = [x; x]).
generalize H4.
apply tm_step_factor4_1mod4 with (n' := n)
(y := [b5; b5; b6; b6; b5; b5; b6; b2; b1; b0; b] ++ tl). assumption.
reflexivity. destruct H5. inversion H5. reflexivity.
rewrite <- app_assoc. reflexivity. rewrite H4 in H.
assert ({b2=b6} + {~ b2=b6}). apply bool_dec. destruct H5. rewrite e in H.
replace (hd ++ [b; b1; b1; b6; b6; b5; b5; b6]
++ [b6; b5; b5; b6; b6; b1; b1; b] ++ tl)
with ((hd ++ [b; b1; b1]) ++ [b6; b6; b5; b5]
++ [b6; b6; b5; b5] ++ [b6; b6; b1; b1; b] ++ tl) in H.
assert (even (length ((hd ++ [b; b1; b1]) ++ [b6; b6; b5; b5])) = true).
assert (0 < length ([b6; b6; b5; b5])). apply Nat.lt_0_succ.
generalize H5. generalize H. apply tm_step_square_pos.
rewrite app_length in H5. rewrite app_length in H5.
rewrite <- Nat.add_assoc in H5. rewrite Nat.even_add in H5.
rewrite L in H5. inversion H5. rewrite <- app_assoc. reflexivity.
assert (b2 = b5). destruct b2; destruct b6; destruct b5.
reflexivity. contradiction n0. reflexivity. reflexivity.
contradiction H1. reflexivity. contradiction H1. reflexivity.
reflexivity. contradiction n0. reflexivity. reflexivity.
rewrite H5 in H.
assert (b1 <> b5).
replace (hd ++ [b; b1; b1; b5; b6; b5; b5; b6]
++ [b6; b5; b5; b6; b5; b1; b1; b] ++ tl)
with ((hd ++ [b]) ++ [b1] ++ [b1] ++ [b5]
++ [b6;b5;b5;b6;b6; b5; b5; b6; b5; b1; b1; b] ++ tl) in H.
apply tm_step_cubefree in H. destruct b1; destruct b5.
contradiction H. reflexivity. easy. easy. contradiction H. reflexivity.
apply Nat.lt_0_1. rewrite <- app_assoc. reflexivity.
assert (b1 = b6). destruct b1; destruct b5; destruct b6.
reflexivity. contradiction H6. reflexivity. reflexivity.
contradiction H1. reflexivity. contradiction H1. reflexivity.
reflexivity. contradiction H6. reflexivity. reflexivity.
rewrite H7 in H.
(*
Lemma tm_step_proper_palindrome_center :