Section Wf_Lexicographic_Exponentiation.
Variable A : Set.
Variable leA : A -> A -> Prop.
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 Nil := (nil (A:=A)).
(* useless but symmetric *)
Notation Cons := (cons (A:=A)).
Notation "<< x , y >>" := (exist Descl x y) (at level 0, x, y at level 100).
(* Hint Resolve d_one d_nil t_step. *)

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 >>.