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thue-morse.v
20
thue-morse.v
@ -628,10 +628,10 @@ Qed.
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Lemma tm_step_pred : forall (n k m : nat),
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Lemma tm_step_pred : forall (n k m : nat),
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S (2*k) * 2^m < 2^n -> (
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S (2*k) * 2^m < 2^n ->
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nth_error (tm_step n) (S (2*k) * 2^m)
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nth_error (tm_step n) (S (2*k) * 2^m)
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= nth_error (tm_step n) (S (2*k) * 2^m - 1)
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= nth_error (tm_step n) (S (2*k) * 2^m - 1)
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<-> odd m = true).
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<-> odd m = true.
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Proof.
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Proof.
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intros n k m.
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intros n k m.
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@ -730,26 +730,20 @@ Proof.
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reflexivity.
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reflexivity.
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simpl; split; reflexivity.
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simpl; split; reflexivity.
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assumption.
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assumption. rewrite tm_size_power2. assumption. assumption.
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rewrite tm_size_power2. assumption.
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rewrite tm_size_power2. generalize I. generalize L. apply Nat.lt_trans.
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assumption.
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rewrite tm_size_power2. generalize I. generalize L. apply Nat.lt_trans.
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rewrite tm_size_power2. generalize I. generalize L.
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apply Nat.lt_trans.
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rewrite tm_size_power2. generalize I. generalize L.
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apply Nat.lt_trans.
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rewrite tm_size_power2. assumption.
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rewrite tm_size_power2. assumption.
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rewrite Nat.mul_sub_distr_l. rewrite Nat.mul_1_r.
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rewrite Nat.mul_sub_distr_l. rewrite Nat.mul_1_r.
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rewrite <- Nat.sub_succ_l.
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rewrite <- Nat.sub_succ_l. rewrite Nat.sub_succ. reflexivity.
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rewrite Nat.sub_succ. reflexivity.
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replace (2) with (2*1) at 1.
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replace (2) with (2*1) at 1.
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apply Nat.mul_le_mono_pos_l. apply Nat.lt_0_2.
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apply Nat.mul_le_mono_pos_l. apply Nat.lt_0_2.
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apply Nat.le_succ_l. apply Nat.mul_pos_pos.
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apply Nat.le_succ_l. apply Nat.mul_pos_pos.
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apply Nat.lt_0_succ. assumption. apply Nat.mul_1_r.
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apply Nat.lt_0_succ. assumption. apply Nat.mul_1_r.
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apply Nat.lt_0_2.
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apply Nat.lt_0_2.
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apply Nat.mul_comm.
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apply Nat.mul_comm. apply Nat.mul_comm.
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apply Nat.mul_comm.
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Qed.
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Qed.
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