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This commit is contained in:
Thomas Baruchel 2022-12-07 21:29:26 +01:00
parent cf667eb25b
commit 8a04d818b7
1 changed files with 8 additions and 1 deletions
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thue-morse.v
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@ -1193,8 +1193,15 @@ Proof.
rewrite <- Nat.pow_add_r. rewrite Nat.sub_add. reflexivity.
apply Nat.lt_le_incl. apply N5.
apply Nat.lt_le_incl. apply I.
- assert ((S k)*2^m + 2^j < 2^(S n)).
- assert ((S k)*2^m + 2^j < 2^(S n)). rewrite Nat.add_comm.
apply Nat.add_lt_mono with (p := 2^m) (q := 2^n) in O.
rewrite <- Nat.add_assoc in O. rewrite Nat.add_shuffle3 in O.
replace (2^m) with (1 * 2^m) in O at 2. rewrite <- Nat.mul_add_distr_r in O.
rewrite Nat.add_1_r in O. rewrite Nat.pow_succ_r'.
replace (2^n) with (1*2^n) in O. rewrite <- Nat.mul_add_distr_r in O.
rewrite Nat.add_1_r in O. apply O.
rewrite Nat.mul_1_l. reflexivity. rewrite Nat.mul_1_l. reflexivity.
apply N0.