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 "<< x , y >>" := (exist Descl x y) (at level 0, x, y at level 100).
(* Hint Resolve d_one d_nil t_step. *)

Lemma desc_end :
forall (a b : A) (x : List),
Descl (x ++ [a]) /\ ltl (x ++ [a]) [b] -> clos_trans A leA a b.