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Thomas Baruchel 2023-02-08 22:02:43 +01:00
parent bc7d6d57b0
commit 77c78b24d5
1 changed files with 9 additions and 2 deletions
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src/thue_morse4.v
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@ -168,7 +168,10 @@ Lemma xxx :
tm_step n = hd ++ a ++ a ++ tl tm_step n = hd ++ a ++ a ++ tl
-> a = rev a -> a = rev a
-> 0 < length a -> 0 < length a
-> length a <= 4 \/ 11 = 42 \/ 17 = 55. -> length a <= 4
\/ (exists m, length a = 2 ^ m /\
length (hd ++ a) mod 2 ^ pred (Nat.double (Nat.div2 (S m))) = 0)
\/ length a = 3 * 2^(pred (Nat.log2 (length a))).
Proof. Proof.
intros n hd a tl. intros H I J. intros n hd a tl. intros H I J.
destruct n. assert (length (tm_step 0) = length (tm_step 0)). reflexivity. destruct n. assert (length (tm_step 0) = length (tm_step 0)). reflexivity.
@ -197,4 +200,8 @@ Proof.
assert (length (hd ++ a) mod 2^(pred (Nat.double (Nat.div2 (S x0)))) = 0). assert (length (hd ++ a) mod 2^(pred (Nat.double (Nat.div2 (S x0)))) = 0).
generalize H3. generalize H0. generalize H. generalize H3. generalize H0. generalize H.
apply tm_step_palindrome_power2. apply tm_step_palindrome_power2.
right. left. exists x0. split; assumption.
- right. right. rewrite H0. rewrite Nat.mul_cancel_l.
rewrite Nat.log2_mul_pow2. rewrite Nat.add_1_r.
rewrite Nat.pred_succ. reflexivity. lia. lia. lia.
Qed.