Definition ltF : list Tree -> list Tree -> Prop := fun f' => fun f => exists w, exists a,
is_insert_forest f w a f'  /\ (forall t, tree_in_forest t f' -> bad_seq_in_lbl t) /\ f<>f'.
Fact acc_ltF_nil : Acc ltF nil.
constructor; intros f Hf.
elim Hf; clear Hf; intros w H; elim H; clear H; intros a H;
elim H; clear H; intros H1 H; elim H; clear H; intros H2 H3.
inversion H1; subst.
elim H3; trivial.
Qed.
Fact acc_ltF_cons : forall f t, Acc ltF f -> Acc ltF (t::nil) -> Acc ltF (t::f).

Lemma is_forest_roots_labels : forall ws f, is_forest ws f ->
roots_labels f = Some (bad_subsequence leA leA_dec (firsts ws)).