Notation Power := (Pow A leA).Notation Lex_Exp := (lex_exp A leA).Notation ltl := (Ltl A leA).Notation Descl := (Desc A leA).Notation List := (list A).Notation "<< x , y >>" := (exist Descl x y) (at level 0, x, y at level 100).

Lemma acc_app : forall (x1 x2 : List) (y1 : Descl (x1 ++ x2)), Acc Lex_Exp << x1 ++ x2, y1 >> -> forall (x : List) (y : Descl x), ltl x (x1 ++ x2) -> Acc Lex_Exp << x, y >>.