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@ -1088,9 +1088,42 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
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rewrite app_length in Q. rewrite Nat.even_add in Q. rewrite H9 in Q.
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inversion Q. reflexivity. rewrite Y''. apply Nat.le_pred_l.
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(* proof ath b11 = b0 *)
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assert (b11 = b0). destruct b11; destruct b1; destruct b0.
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reflexivity. contradiction n7. reflexivity. reflexivity.
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contradiction n1. reflexivity. contradiction n1. reflexivity.
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reflexivity. contradiction n7. reflexivity. reflexivity.
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rewrite H9 in H.
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(* on élargit tl (adding b12 in front of tl) *)
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destruct tl.
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assert (tm_step n = rev (tm_step n)
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\/ tm_step n = map negb (rev (tm_step n))).
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apply tm_step_rev. destruct H10; rewrite H in H10 at 2;
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rewrite rev_app_distr in H10;
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assert (odd 1 = true). reflexivity.
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rewrite <- tm_step_pred with (n := n) (k := 0) in H11.
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rewrite H10 in H11. simpl in H11. inversion H11. rewrite H13 in n1.
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contradiction n1. reflexivity. simpl.
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replace 2 with (2^1). rewrite <- Nat.pow_lt_mono_r_iff.
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apply Nat.lt_succ_l in R. apply Nat.lt_succ_l in R. assumption.
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apply Nat.lt_1_2. reflexivity.
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reflexivity.
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rewrite <- tm_step_pred with (n := n) (k := 0) in H11.
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rewrite H10 in H11. simpl in H11. inversion H11.
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destruct b0; destruct b1. contradiction n1. reflexivity.
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inversion H13. inversion H13. contradiction n1. reflexivity. simpl.
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replace 2 with (2^1). rewrite <- Nat.pow_lt_mono_r_iff.
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apply Nat.lt_succ_l in R. apply Nat.lt_succ_l in R. assumption.
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apply Nat.lt_1_2. reflexivity.
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(* now we have added b12 in front of tl *)
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False, True, True, False, True, False, False, True, True, False, False, True, False, True, True, False]'
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