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This commit is contained in:
Thomas Baruchel 2023-02-13 06:18:37 +01:00
parent 42ae58755d
commit 8f1fd646db
1 changed files with 15 additions and 1 deletions
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16
src/thue_morse4.v
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@ -1559,7 +1559,7 @@ Proof.
apply tm_step_square_rev_even.
Qed.
Lemma tm_step_square2_even_pos :
Lemma tm_step_square2_rev_even' :
forall (m n : nat) (hd a tl : list bool),
tm_step n = hd ++ a ++ a ++ tl
-> length a = 2^m
@ -1756,3 +1756,17 @@ Proof.
rewrite <- Nat.add_sub_assoc. rewrite <- Nat.mul_sub_distr_r.
apply Nat.le_add_r. apply Nat.mul_le_mono_r. lia. lia.
Qed.
Lemma tm_step_square3_rev_even' :
forall (m n : nat) (hd a tl : list bool),
tm_step n = hd ++ a ++ a ++ tl
-> length a = 3 * 2^m
-> even m = true
-> length (hd ++ a) mod 2^(S m) = 0.
Proof.
intros m n hd a tl. intros H I J.
assert (a = rev a).
rewrite tm_step_square3_rev_even_swap
with (n := n) (hd := hd) (a := a) (tl := tl) (m := m) in J; assumption.
generalize H0. generalize I. generalize H. apply tm_step_square3_rev_even.
Qed.