transcript: we improved the parser/lexer to read the scripts of the standard

[helm.git] / helm / software / matita / contribs / procedural / Coq / Arith / Wf_nat.mma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "Coq.ma".
+
+(*#**********************************************************************)
+
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
+
+(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
+
+(*   \VV/  *************************************************************)
+
+(*    //   *      This file is distributed under the terms of the      *)
+
+(*         *       GNU Lesser General Public License Version 2.1       *)
+
+(*#**********************************************************************)
+
+(*i $Id: Wf_nat.v,v 1.16 2003/12/15 19:48:17 barras Exp $ i*)
+
+(*#* Well-founded relations and natural numbers *)
+
+include "Arith/Lt.ma".
+
+(* UNEXPORTED
+Open Local Scope nat_scope.
+*)
+
+(* UNEXPORTED
+Implicit Types m n p : nat.
+*)
+
+(* UNEXPORTED
+Section Well_founded_Nat
+*)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/Well_founded_Nat/A.var
+*)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/Well_founded_Nat/f.var
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/ltof.con" as definition.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/gtof.con" as definition.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/well_founded_ltof.con" as theorem.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/well_founded_gtof.con" as theorem.
+
+(*#* It is possible to directly prove the induction principle going
+   back to primitive recursion on natural numbers ([induction_ltof1])
+   or to use the previous lemmas to extract a program with a fixpoint
+   ([induction_ltof2]) 
+
+the ML-like program for [induction_ltof1] is : [[
+   let induction_ltof1 F a = indrec ((f a)+1) a 
+   where rec indrec = 
+        function 0    -> (function a -> error)
+               |(S m) -> (function a -> (F a (function y -> indrec y m)));;
+]]
+
+the ML-like program for [induction_ltof2] is : [[
+   let induction_ltof2 F a = indrec a
+   where rec indrec a = F a indrec;;
+]] *)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/induction_ltof1.con" as theorem.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/induction_gtof1.con" as theorem.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/induction_ltof2.con" as theorem.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/induction_gtof2.con" as theorem.
+
+(*#* If a relation [R] is compatible with [lt] i.e. if [x R y => f(x) < f(y)]
+    then [R] is well-founded. *)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/Well_founded_Nat/R.var
+*)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/Well_founded_Nat/H_compat.var
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/well_founded_lt_compat.con" as theorem.
+
+(* UNEXPORTED
+End Well_founded_Nat
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf_rec1.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf_rec.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf_ind.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/gt_wf_rec.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/gt_wf_ind.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf_double_rec.con" as lemma.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/lt_wf_double_ind.con" as lemma.
+
+(* UNEXPORTED
+Hint Resolve lt_wf: arith.
+*)
+
+(* UNEXPORTED
+Hint Resolve well_founded_lt_compat: arith.
+*)
+
+(* UNEXPORTED
+Section LT_WF_REL
+*)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/LT_WF_REL/A.var
+*)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/LT_WF_REL/R.var
+*)
+
+(* Relational form of inversion *)
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/LT_WF_REL/F.var
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/inv_lt_rel.con" as definition.
+
+(* UNEXPORTED
+cic:/Coq/Arith/Wf_nat/LT_WF_REL/F_compat.var
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/acc_lt_rel.con" as remark.
+
+inline procedural "cic:/Coq/Arith/Wf_nat/well_founded_inv_lt_rel_compat.con" as theorem.
+
+(* UNEXPORTED
+End LT_WF_REL
+*)
+
+inline procedural "cic:/Coq/Arith/Wf_nat/well_founded_inv_rel_inv_lt_rel.con" as lemma.
+