Update
This commit is contained in:
parent
8e2b9958e5
commit
af637eaae3
26
thue-morse.v
26
thue-morse.v
|
@ -773,7 +773,7 @@ Proof.
|
||||||
reflexivity.
|
reflexivity.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Theorem tm_size_expo : forall n : nat, length (tm_step n) = 2^n.
|
Theorem tm_size_power2 : forall n : nat, length (tm_step n) = 2^n.
|
||||||
Proof.
|
Proof.
|
||||||
intros n.
|
intros n.
|
||||||
induction n.
|
induction n.
|
||||||
|
@ -794,16 +794,8 @@ Proof.
|
||||||
simpl. reflexivity.
|
simpl. reflexivity.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma tm_step_head_1 : forall (n : nat),
|
|
||||||
tm_step n = false :: tl (tm_step n).
|
|
||||||
Proof.
|
|
||||||
intros n. destruct n.
|
|
||||||
- reflexivity.
|
|
||||||
- rewrite tm_step_head_2. reflexivity.
|
|
||||||
Qed.
|
|
||||||
|
|
||||||
Lemma tm_step_end_2 : forall (n : nat),
|
Lemma tm_step_end_2 : forall (n : nat),
|
||||||
rev (tm_step (S n)) = (even n) :: (odd n) :: tl (tl (rev (tm_step (S n)))).
|
rev (tm_step (S n)) = even n :: odd n :: tl (tl (rev (tm_step (S n)))).
|
||||||
Proof.
|
Proof.
|
||||||
intros n. induction n.
|
intros n. induction n.
|
||||||
- reflexivity.
|
- reflexivity.
|
||||||
|
@ -813,12 +805,19 @@ Proof.
|
||||||
rewrite PeanoNat.Nat.even_succ.
|
rewrite PeanoNat.Nat.even_succ.
|
||||||
rewrite PeanoNat.Nat.odd_succ.
|
rewrite PeanoNat.Nat.odd_succ.
|
||||||
rewrite Bool.negb_involutive.
|
rewrite Bool.negb_involutive.
|
||||||
reflexivity.
|
reflexivity. reflexivity.
|
||||||
reflexivity.
|
Qed.
|
||||||
|
|
||||||
|
Lemma tm_step_head_1 : forall (n : nat),
|
||||||
|
tm_step n = false :: tl (tm_step n).
|
||||||
|
Proof.
|
||||||
|
intros n. destruct n.
|
||||||
|
- reflexivity.
|
||||||
|
- rewrite tm_step_head_2. reflexivity.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
Lemma tm_step_end_1 : forall (n : nat),
|
Lemma tm_step_end_1 : forall (n : nat),
|
||||||
rev (tm_step n) = (odd n) :: tl (rev (tm_step n)).
|
rev (tm_step n) = odd n :: tl (rev (tm_step n)).
|
||||||
Proof.
|
Proof.
|
||||||
intros n.
|
intros n.
|
||||||
destruct n.
|
destruct n.
|
||||||
|
@ -827,3 +826,4 @@ Proof.
|
||||||
rewrite PeanoNat.Nat.odd_succ.
|
rewrite PeanoNat.Nat.odd_succ.
|
||||||
reflexivity.
|
reflexivity.
|
||||||
Qed.
|
Qed.
|
||||||
|
|
||||||
|
|
Loading…
Reference in New Issue
Block a user