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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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(** Author: Cristina Cornes  From : Constructing Recursion Operators in Type Theory L. Paulson  JSC (1986) 2, 325-355  *)
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.