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Thomas Baruchel 2023-01-23 21:56:54 +01:00
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src/thue_morse3.v
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@ -1153,6 +1153,28 @@ Le lemme repeating_patterns se base sur les huit premiers termes de TM :
rewrite firstn_length_le. simpl in Q. rewrite Q. reflexivity.
rewrite Y''. apply Nat.le_succ_diag_r. reflexivity.
(* destructuring n *)
destruct n. inversion H0. rewrite <- tm_step_lemma in H.
(* inverting tm_morphism in tm_step n *)
assert (hd'' = tm_morphism (firstn (Nat.div2 (length hd'')) (tm_step n))).
generalize H11. generalize H. apply tm_morphism_app2.
assert (s ++ tl = tm_morphism (skipn (Nat.div2 (length hd'')) (tm_step n))).
generalize H11. generalize H. apply tm_morphism_app3. symmetry in H13.
assert (even (length s) = true). unfold s. reflexivity.
assert (s = tm_morphism (firstn (Nat.div2 (length s))
(skipn (Nat.div2 (length hd'')) (tm_step n)))).
generalize H14. generalize H13. apply tm_morphism_app2.
assert (tl = tm_morphism (skipn (Nat.div2 (length s))
(skipn (Nat.div2 (length hd'')) (tm_step n)))).
generalize H14. generalize H13. apply tm_morphism_app3.
rewrite H12 in H. rewrite H15 in H. rewrite H16 in H.
rewrite <- tm_morphism_app in H. rewrite <- tm_morphism_app in H.
rewrite <- tm_morphism_eq in H.