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21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
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33 (*i $Id: Lexicographic_Exponentiation.v,v 1.10.2.1 2004/07/16 19:31:19 herbelin Exp $ i*)
35 (*#* Author: Cristina Cornes
37 From : Constructing Recursion Operators in Type Theory
38 L. Paulson JSC (1986) 2, 325-355 *)
40 include "Logic/Eqdep.ma".
42 include "Lists/List.ma".
44 include "Relations/Relation_Operators.ma".
46 include "Wellfounded/Transitive_Closure.ma".
49 Section Wf_Lexicographic_Exponentiation
53 cic:/Coq/Wellfounded/Lexicographic_Exponentiation/Wf_Lexicographic_Exponentiation/A.var
57 cic:/Coq/Wellfounded/Lexicographic_Exponentiation/Wf_Lexicographic_Exponentiation/leA.var
61 Notation Power := (Pow A leA).
65 Notation Lex_Exp := (lex_exp A leA).
69 Notation ltl := (Ltl A leA).
73 Notation Descl := (Desc A leA).
77 Notation List := (list A).
81 Notation Nil := (nil (A:=A)).
84 (* useless but symmetric *)
87 Notation Cons := (cons (A:=A)).
91 Notation "<< x , y >>" := (exist Descl x y) (at level 0, x, y at level 100).
95 Hint Resolve d_one d_nil t_step.
98 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/left_prefix.con" as lemma.
100 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/right_prefix.con" as lemma.
102 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/desc_prefix.con" as lemma.
104 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/desc_tail.con" as lemma.
106 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/dist_aux.con" as lemma.
108 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/dist_Desc_concat.con" as lemma.
110 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/desc_end.con" as lemma.
112 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/ltl_unit.con" as lemma.
114 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/acc_app.con" as lemma.
116 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Exponentiation/wf_lex_exp.con" as theorem.
119 End Wf_Lexicographic_Exponentiation