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Thomas Baruchel 2022-11-26 07:51:15 +01:00
parent 0cf8e80ecf
commit 3b91125216
1 changed files with 8 additions and 4 deletions
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12
thue-morse.v
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@ -1091,12 +1091,16 @@ Proof.
intros k b n m. intros H I.
assert (J: nth_error (tm_step (S n)) (2^n-1) = nth_error (tm_step (S n)) (2^n)
<-> odd n = true).
rewrite tm_step_single_bit_index.
assert (nth_error (tm_step n) (2^n - 1) = nth_error (tm_step (S n)) (2^n-1)).
apply tm_step_stable.
assert (2^n - 1 < 2^n).
apply Nat.sub_lt. replace (1) with (2^0) at 1. apply Nat.pow_le_mono_r.
easy. apply le_0_n. simpl. reflexivity. apply Nat.lt_0_1. apply H0.
easy. apply le_0_n. simpl. reflexivity. apply Nat.lt_0_1.
rewrite tm_step_single_bit_index.
assert (nth_error (tm_step n) (2^n - 1) = nth_error (tm_step (S n)) (2^n-1)).
apply tm_step_stable. apply H0.
assert (2^n < 2^(S n)). apply Nat.pow_lt_mono_r. apply Nat.lt_1_2.
apply Nat.lt_succ_diag_r.
generalize H1. generalize H0. apply Nat.lt_trans. rewrite <- H1.
rewrite tm_step_repunit_index.
rewrite Nat.succ_lt_mono. simpl.
(*