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