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This commit is contained in:
Thomas Baruchel 2022-11-25 11:54:08 +01:00
parent ef846b4fdc
commit 29890ef332
1 changed files with 1 additions and 35 deletions
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36
thue-morse.v
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@ -1068,15 +1068,6 @@ Proof.
rewrite <- Nat.add_succ_l. rewrite <- Nat.add_lt_mono_r. apply H.
assert (J := K). rewrite Nat.add_succ_l in J. apply Nat.lt_succ_l in J.
(*
Lemma tm_step_next_range2_neighbor' : forall (n k : nat),
S k < 2^n ->
nth_error (tm_step n) k = nth_error (tm_step n) (S k)
<->
nth_error (tm_step (S n)) (k + 2^n)
= nth_error (tm_step (S n)) (S k + 2^n).
*)
split.
- induction m.
+ intros L. rewrite Nat.add_0_r. rewrite Nat.add_0_r.
@ -1136,37 +1127,12 @@ Lemma tm_step_next_range2_neighbor' : forall (n k : nat),
Qed.
Lemma tm_step_next_range2_neighbor : forall (n k : nat),
S k < 2^n ->
eqb (nth k (tm_step n) false) (nth (S k) (tm_step n) false)
= eqb
(nth (k + 2^n) (tm_step (S n)) false) (nth (S k + 2^n) (tm_step (S n)) false).
- intros H1. induction m.
+ rewrite Nat.add_0_r. rewrite Nat.add_0_r.
nth_error_nth:
forall [A : Type] (l : list A) (n : nat) [x : A] (d : A),
nth_error l n = Some x -> nth n l d = x
nth_error_nth':
forall [A : Type] (l : list A) [n : nat] (d : A),
n < length l -> nth_error l n = Some (nth n l d)
Lemma tm_step_next_range2' :
forall (n k : nat) (b : bool),
nth_error (tm_step n) k = Some b
-> nth_error (tm_step (S n)) (k + 2^n) = Some (negb b).
Lemma tm_step_add_range2_neighbor : forall (n m k : nat),
Lemma tm_step_add_range2_neighbor0 : forall (n m k : nat),
S k < 2^n ->
eqb (nth k (tm_step n) false)
(nth (S k) (tm_step n) false)