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Thomas Baruchel 2023-01-22 21:29:01 +01:00
parent 458f9aa148
commit a304f0a9a8
1 changed files with 24 additions and 1 deletions
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src/thue_morse3.v
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@ -908,7 +908,30 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
rewrite H9.
apply eq_S in H9. rewrite <- Nat.add_1_r in H9.
rewrite <- Nat.add_assoc in H9. rewrite Nat.add_1_r in H9.
rewrite H9. unfold lh.
rewrite H9. unfold lh. unfold hd'.
rewrite nth_error_app2. symmetry. rewrite nth_error_app2. rewrite Y''.
rewrite app_length.
replace (length (b3::b5::b7::hd)) with (S (S (S (length hd)))).
rewrite Nat.add_succ_comm. rewrite Nat.add_succ_comm.
rewrite Nat.add_succ_comm. rewrite <- Nat.sub_succ_l.
rewrite <- Nat.add_succ_r. rewrite Nat.add_sub.
rewrite Nat.sub_succ_l. rewrite Nat.sub_diag. reflexivity.
apply Nat.le_refl. unfold lh in T.
rewrite <- Nat.add_succ_comm. rewrite <- Nat.add_succ_comm.
rewrite <- Nat.add_succ_comm. rewrite app_length in T.
assumption. reflexivity. rewrite Y''.
rewrite app_length.
replace (length (b3::b5::b7::hd)) with (S (S (S (length hd)))).
rewrite Nat.add_succ_comm. rewrite Nat.add_succ_comm.
rewrite Nat.add_succ_comm. rewrite <- Nat.sub_succ_l.
rewrite <- Nat.add_succ_r. rewrite Nat.add_sub.
apply Nat.le_succ_diag_r. rewrite Nat.add_succ_r.
rewrite Nat.add_succ_r. rewrite Nat.add_succ_r.
rewrite <- Nat.succ_le_mono. rewrite <- Nat.succ_le_mono.
rewrite <- Nat.succ_le_mono. replace 5 with (1 + 4).
rewrite <- Nat.add_le_mono_r.
(* TODO: montrer l'absurdité avec le cas réel de tm_step_repeating_patterns *)