Definition embeds : list A -> list A -> Prop := (higman_aux.embeds leA).Definition sublist : list (list A) -> list (list A) -> Prop := (higman_aux.sublist (A:=A)).Definition Tree := (higman_aux.Tree A).Definition is_forest := (higman_aux.is_forest leA leA_dec).Definition is_insert_forest := (higman_aux.is_insert_forest leA).Definition is_insert_tree := (higman_aux.is_insert_tree leA).Definition sub_seq_in_lbl (ws : list (list A)) (t : Tree) : Prop := 
forall vs l ts, t = node (vs,l) ts -> sublist (merge_label vs l) ws.

Lemma sub_seq_in_forest : forall ws f, is_forest ws f -> P_on_forest sub_seq_in_lbl ws f.