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This commit is contained in:
Thomas Baruchel 2022-12-10 22:32:51 +01:00
parent de7cc14376
commit dd2bd9d4f5
1 changed files with 4 additions and 2 deletions
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6
thue-morse.v
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@ -1190,6 +1190,9 @@ Proof.
generalize H2. generalize J. apply Nat.le_trans.
Qed.
(* Note: a first version included the 0 < k hypothesis but in the very
unorthodox case where k=0 it happens to be true anyway, and the hypothesis
was removed in order to make the theorem more general *)
Theorem tm_step_flip_low_bit :
forall (n m k j : nat),
j < m -> k * 2^m < 2^n
@ -1212,8 +1215,7 @@ Proof.
rewrite <- Nat.neq_0_lt_0. apply Nat.pow_nonzero. easy.
apply Nat.le_0_l. assumption.
assert (G: k = 0 \/ 0 < k). apply Nat.eq_0_gt_0_cases.
destruct G.
assert (G: k = 0 \/ 0 < k). apply Nat.eq_0_gt_0_cases. destruct G.
(* k = 0 *)
rewrite H0. rewrite Nat.mul_0_l. rewrite Nat.add_0_l.