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@ -1617,11 +1617,6 @@ Proof.
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rewrite app_length. rewrite Nat.even_add.
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rewrite I'. rewrite J'. reflexivity.
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destruct n. inversion V. inversion H10.
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rewrite app_assoc in H. rewrite <- tm_step_lemma in H.
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@ -1675,6 +1670,40 @@ Proof.
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pose (hd'' := firstn (Nat.div2 (length hd')) (tm_step n)).
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pose (a'' := firstn (Nat.div2 (length a')) (skipn (Nat.div2 (length hd'))
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(tm_step n))).
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pose (tl'' := skipn (Nat.div2 (length hd') + length a') (tm_step n)).
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fold hd'' in H. fold a'' in H. fold tl'' in H.
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assert (length hd'' = Nat.div2 (length hd')). unfold hd''. rewrite H4'.
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rewrite tm_morphism_length_half. rewrite firstn_length. rewrite firstn_length.
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replace (min (Nat.div2 (length hd')) (length (tm_step n)))
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with (min (length (tm_step n)) (Nat.div2 (length hd'))).
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rewrite Nat.min_comm. rewrite Nat.min_assoc. rewrite Nat.min_id.
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reflexivity. rewrite Nat.min_comm. reflexivity.
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assert (length a'' = Nat.div2 (length a')). unfold a''. rewrite H5'.
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rewrite tm_morphism_length_half. rewrite firstn_length. rewrite firstn_length.
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rewrite Nat.min_comm. rewrite <- H9.
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replace
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(min (Nat.div2 (length a')) (length (skipn (length hd'') (tm_step n))))
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with
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(min (length (skipn (length hd'') (tm_step n))) (Nat.div2 (length a'))).
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rewrite Nat.min_assoc. rewrite Nat.min_id. reflexivity.
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rewrite Nat.min_comm. reflexivity.
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assert (length tl'' = Nat.div2 (length tl')). unfold tl''. rewrite H3'.
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rewrite tm_morphism_length_half. rewrite app_length.
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symmetry. rewrite Nat.div2_div.
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rewrite app_length. rewrite map_length. rewrite rev_length.
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replace (length a' + length a') with (length a' * 2).
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rewrite Nat.div_add. rewrite <- Nat.div2_div. reflexivity. easy.
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rewrite Nat.mul_comm. simpl. rewrite Nat.add_0_r. reflexivity.
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Admitted.
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