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This commit is contained in:
Thomas Baruchel 2023-01-28 12:10:42 +01:00
parent bba694fa47
commit e274d2789b
1 changed files with 25 additions and 5 deletions
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30
src/thue_morse3.v
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@ -1888,13 +1888,33 @@ Proof.
assert (V: 3 < n). generalize I. generalize H.
apply tm_step_palindromic_length_12_n.
destruct n. inversion V. destruct n. inversion V. inversion H1.
rewrite K in H. rewrite L in H. rewrite M in H.
rewrite tm_morphism_twice_rev in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_step_lemma in H. rewrite <- tm_step_lemma in H.
rewrite <- tm_morphism_eq in H. rewrite <- tm_morphism_eq in H.
rewrite Nat.pred_succ in H. rewrite Nat.pred_succ in H.
pose (hd' := (firstn (length hd / 4) (tm_step n))).
pose (a' := (firstn (length a / 4) (skipn (length hd / 4) (tm_step n)))).
pose (tl' := (skipn (length hd / 4 + Nat.div2 (length a)) (tm_step n))).
fold hd' in H. fold a' in H. fold tl' in H.
rewrite Nat.pred_succ in L. rewrite Nat.pred_succ in L.
assert (N: length a = length a). reflexivity.
rewrite L in N at 2. fold a' in N.
rewrite tm_morphism_length in N. rewrite tm_morphism_length in N.
rewrite Nat.mul_assoc in N. replace (2*2) with 4 in N.
induction m.
- rewrite K in H. rewrite L in H. rewrite M in H.
rewrite tm_morphism_twice_rev in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
- assert (even (length (hd' ++ a')) = true).