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This commit is contained in:
Thomas Baruchel 2023-01-22 16:33:37 +01:00
parent 7cc18437c9
commit 1aeaa1050f
1 changed files with 13 additions and 0 deletions
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13
src/thue_morse3.v
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@ -803,6 +803,11 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
assumption. apply Nat.lt_1_2. reflexivity.
(* termes à prouver *)
assert (Y: forall (k: bool) (x : list bool),
length (removelast (k::x)) = length x).
intros k x. rewrite removelast_firstn_len. simpl.
rewrite firstn_length_le. reflexivity. simpl.
apply Nat.le_succ_diag_r.
assert (U:
nth_error (b3 :: b5 :: b7 :: hd) (length (b3 :: b5 :: b7 :: hd) - 3)
= Some b8). unfold b8.
@ -812,6 +817,14 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
rewrite app_removelast_last
with (l := (removelast (removelast (b3::b5::b7::hd)))) (d := false) at 1.
rewrite <- app_assoc. rewrite <- app_assoc. rewrite nth_error_app2.
rewrite removelast_firstn_len at 2. rewrite Y.
replace (length (b5::b7::hd)) with (S (S (length hd))).
rewrite <- pred_Sn. rewrite removelast_firstn. rewrite firstn_length_le.
replace (length (b3::b5::b7::hd)) with (S (S (S (length hd)))).
rewrite <- Nat.sub_add_distr. rewrite Nat.sub_diag.
reflexivity. reflexivity.
rewrite Y. simpl.