# HG changeset patch
# User haftmann
# Date 1222684319 -7200
# Node ID 09e4aa3ddc256a9eea78d2eec3e41dfdf69fc9bf
# Parent  d5f39173444cc54e5c154b09ba84003d597d25e6
clarified dependencies between arith tools

diff -r d5f39173444c -r 09e4aa3ddc25 src/HOL/Arith_Tools.thy
--- a/src/HOL/Arith_Tools.thy	Mon Sep 29 12:31:58 2008 +0200
+++ b/src/HOL/Arith_Tools.thy	Mon Sep 29 12:31:59 2008 +0200
@@ -7,12 +7,13 @@
 header {* Setup of arithmetic tools *}
 
 theory Arith_Tools
-imports Groebner_Basis
+imports NatBin
 uses
   "~~/src/Provers/Arith/cancel_numeral_factor.ML"
   "~~/src/Provers/Arith/extract_common_term.ML"
   "int_factor_simprocs.ML"
   "nat_simprocs.ML"
+  "Tools/Qelim/qelim.ML"
 begin
 
 subsection {* Simprocs for the Naturals *}
@@ -382,219 +383,4 @@
 val minus1_divide = @{thm minus1_divide};
 *}
 
-
-subsection{* Groebner Bases for fields *}
-
-interpretation class_fieldgb:
-  fieldgb["op +" "op *" "op ^" "0::'a::{field,recpower,number_ring}" "1" "op -" "uminus" "op /" "inverse"] apply (unfold_locales) by (simp_all add: divide_inverse)
-
-lemma divide_Numeral1: "(x::'a::{field,number_ring}) / Numeral1 = x" by simp
-lemma divide_Numeral0: "(x::'a::{field,number_ring, division_by_zero}) / Numeral0 = 0"
-  by simp
-lemma mult_frac_frac: "((x::'a::{field,division_by_zero}) / y) * (z / w) = (x*z) / (y*w)"
-  by simp
-lemma mult_frac_num: "((x::'a::{field, division_by_zero}) / y) * z  = (x*z) / y"
-  by simp
-lemma mult_num_frac: "((x::'a::{field, division_by_zero}) / y) * z  = (x*z) / y"
-  by simp
-
-lemma Numeral1_eq1_nat: "(1::nat) = Numeral1" by simp
-
-lemma add_frac_num: "y\<noteq> 0 \<Longrightarrow> (x::'a::{field, division_by_zero}) / y + z = (x + z*y) / y"
-  by (simp add: add_divide_distrib)
-lemma add_num_frac: "y\<noteq> 0 \<Longrightarrow> z + (x::'a::{field, division_by_zero}) / y = (x + z*y) / y"
-  by (simp add: add_divide_distrib)
-
-
-ML{* 
-local
- val zr = @{cpat "0"}
- val zT = ctyp_of_term zr
- val geq = @{cpat "op ="}
- val eqT = Thm.dest_ctyp (ctyp_of_term geq) |> hd
- val add_frac_eq = mk_meta_eq @{thm "add_frac_eq"}
- val add_frac_num = mk_meta_eq @{thm "add_frac_num"}
- val add_num_frac = mk_meta_eq @{thm "add_num_frac"}
-
- fun prove_nz ss T t =
-    let
-      val z = instantiate_cterm ([(zT,T)],[]) zr
-      val eq = instantiate_cterm ([(eqT,T)],[]) geq
-      val th = Simplifier.rewrite (ss addsimps simp_thms)
-           (Thm.capply @{cterm "Trueprop"} (Thm.capply @{cterm "Not"}
-                  (Thm.capply (Thm.capply eq t) z)))
-    in equal_elim (symmetric th) TrueI
-    end
-
- fun proc phi ss ct =
-  let
-    val ((x,y),(w,z)) =
-         (Thm.dest_binop #> (fn (a,b) => (Thm.dest_binop a, Thm.dest_binop b))) ct
-    val _ = map (HOLogic.dest_number o term_of) [x,y,z,w]
-    val T = ctyp_of_term x
-    val [y_nz, z_nz] = map (prove_nz ss T) [y, z]
-    val th = instantiate' [SOME T] (map SOME [y,z,x,w]) add_frac_eq
-  in SOME (implies_elim (implies_elim th y_nz) z_nz)
-  end
-  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
-
- fun proc2 phi ss ct =
-  let
-    val (l,r) = Thm.dest_binop ct
-    val T = ctyp_of_term l
-  in (case (term_of l, term_of r) of
-      (Const(@{const_name "HOL.divide"},_)$_$_, _) =>
-        let val (x,y) = Thm.dest_binop l val z = r
-            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
-            val ynz = prove_nz ss T y
-        in SOME (implies_elim (instantiate' [SOME T] (map SOME [y,x,z]) add_frac_num) ynz)
-        end
-     | (_, Const (@{const_name "HOL.divide"},_)$_$_) =>
-        let val (x,y) = Thm.dest_binop r val z = l
-            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
-            val ynz = prove_nz ss T y
-        in SOME (implies_elim (instantiate' [SOME T] (map SOME [y,z,x]) add_num_frac) ynz)
-        end
-     | _ => NONE)
-  end
-  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
-
- fun is_number (Const(@{const_name "HOL.divide"},_)$a$b) = is_number a andalso is_number b
-   | is_number t = can HOLogic.dest_number t
-
- val is_number = is_number o term_of
-
- fun proc3 phi ss ct =
-  (case term_of ct of
-    Const(@{const_name HOL.less},_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
-      let
-        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_less_eq"}
-      in SOME (mk_meta_eq th) end
-  | Const(@{const_name HOL.less_eq},_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
-      let
-        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_le_eq"}
-      in SOME (mk_meta_eq th) end
-  | Const("op =",_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
-      let
-        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_eq_eq"}
-      in SOME (mk_meta_eq th) end
-  | Const(@{const_name HOL.less},_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
-    let
-      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "less_divide_eq"}
-      in SOME (mk_meta_eq th) end
-  | Const(@{const_name HOL.less_eq},_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
-    let
-      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "le_divide_eq"}
-      in SOME (mk_meta_eq th) end
-  | Const("op =",_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
-    let
-      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
-        val _ = map is_number [a,b,c]
-        val T = ctyp_of_term c
-        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "eq_divide_eq"}
-      in SOME (mk_meta_eq th) end
-  | _ => NONE)
-  handle TERM _ => NONE | CTERM _ => NONE | THM _ => NONE
-
-val add_frac_frac_simproc =
-       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + (?w::?'a::field)/?z"}],
-                     name = "add_frac_frac_simproc",
-                     proc = proc, identifier = []}
-
-val add_frac_num_simproc =
-       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + ?z"}, @{cpat "?z + (?x::?'a::field)/?y"}],
-                     name = "add_frac_num_simproc",
-                     proc = proc2, identifier = []}
-
-val ord_frac_simproc =
-  make_simproc
-    {lhss = [@{cpat "(?a::(?'a::{field, ord}))/?b < ?c"},
-             @{cpat "(?a::(?'a::{field, ord}))/?b \<le> ?c"},
-             @{cpat "?c < (?a::(?'a::{field, ord}))/?b"},
-             @{cpat "?c \<le> (?a::(?'a::{field, ord}))/?b"},
-             @{cpat "?c = ((?a::(?'a::{field, ord}))/?b)"},
-             @{cpat "((?a::(?'a::{field, ord}))/ ?b) = ?c"}],
-             name = "ord_frac_simproc", proc = proc3, identifier = []}
-
-val nat_arith = map thm ["add_nat_number_of", "diff_nat_number_of",
-               "mult_nat_number_of", "eq_nat_number_of", "less_nat_number_of"]
-
-val comp_arith = (map thm ["Let_def", "if_False", "if_True", "add_0",
-                 "add_Suc", "add_number_of_left", "mult_number_of_left",
-                 "Suc_eq_add_numeral_1"])@
-                 (map (fn s => thm s RS sym) ["numeral_1_eq_1", "numeral_0_eq_0"])
-                 @ @{thms arith_simps} @ nat_arith @ @{thms rel_simps}
-val ths = [@{thm "mult_numeral_1"}, @{thm "mult_numeral_1_right"},
-           @{thm "divide_Numeral1"},
-           @{thm "Ring_and_Field.divide_zero"}, @{thm "divide_Numeral0"},
-           @{thm "divide_divide_eq_left"}, @{thm "mult_frac_frac"},
-           @{thm "mult_num_frac"}, @{thm "mult_frac_num"},
-           @{thm "mult_frac_frac"}, @{thm "times_divide_eq_right"},
-           @{thm "times_divide_eq_left"}, @{thm "divide_divide_eq_right"},
-           @{thm "diff_def"}, @{thm "minus_divide_left"},
-           @{thm "Numeral1_eq1_nat"}, @{thm "add_divide_distrib"} RS sym]
-
-local
-open Conv
-in
-val comp_conv = (Simplifier.rewrite
-(HOL_basic_ss addsimps @{thms "Groebner_Basis.comp_arith"}
-              addsimps ths addsimps comp_arith addsimps simp_thms
-              addsimprocs field_cancel_numeral_factors
-               addsimprocs [add_frac_frac_simproc, add_frac_num_simproc,
-                            ord_frac_simproc]
-                addcongs [@{thm "if_weak_cong"}]))
-then_conv (Simplifier.rewrite (HOL_basic_ss addsimps
-  [@{thm numeral_1_eq_1},@{thm numeral_0_eq_0}] @ @{thms numerals(1-2)}))
 end
-
-fun numeral_is_const ct =
-  case term_of ct of
-   Const (@{const_name "HOL.divide"},_) $ a $ b =>
-     numeral_is_const (Thm.dest_arg1 ct) andalso numeral_is_const (Thm.dest_arg ct)
- | Const (@{const_name "HOL.uminus"},_)$t => numeral_is_const (Thm.dest_arg ct)
- | t => can HOLogic.dest_number t
-
-fun dest_const ct = ((case term_of ct of
-   Const (@{const_name "HOL.divide"},_) $ a $ b=>
-    Rat.rat_of_quotient (snd (HOLogic.dest_number a), snd (HOLogic.dest_number b))
- | t => Rat.rat_of_int (snd (HOLogic.dest_number t))) 
-   handle TERM _ => error "ring_dest_const")
-
-fun mk_const phi cT x =
- let val (a, b) = Rat.quotient_of_rat x
- in if b = 1 then Numeral.mk_cnumber cT a
-    else Thm.capply
-         (Thm.capply (Drule.cterm_rule (instantiate' [SOME cT] []) @{cpat "op /"})
-                     (Numeral.mk_cnumber cT a))
-         (Numeral.mk_cnumber cT b)
-  end
-
-in
- val field_comp_conv = comp_conv;
- val fieldgb_declaration = 
-  NormalizerData.funs @{thm class_fieldgb.fieldgb_axioms'}
-   {is_const = K numeral_is_const,
-    dest_const = K dest_const,
-    mk_const = mk_const,
-    conv = K (K comp_conv)}
-end;
-*}
-
-declaration{* fieldgb_declaration *}
-end
diff -r d5f39173444c -r 09e4aa3ddc25 src/HOL/Groebner_Basis.thy
--- a/src/HOL/Groebner_Basis.thy	Mon Sep 29 12:31:58 2008 +0200
+++ b/src/HOL/Groebner_Basis.thy	Mon Sep 29 12:31:59 2008 +0200
@@ -4,8 +4,9 @@
 *)
 
 header {* Semiring normalization and Groebner Bases *}
+
 theory Groebner_Basis
-imports NatBin
+imports Arith_Tools
 uses
   "Tools/Groebner_Basis/misc.ML"
   "Tools/Groebner_Basis/normalizer_data.ML"
@@ -461,4 +462,220 @@
 declare zmod_eq_dvd_iff[algebra]
 declare nat_mod_eq_iff[algebra]
 
+
+subsection{* Groebner Bases for fields *}
+
+interpretation class_fieldgb:
+  fieldgb["op +" "op *" "op ^" "0::'a::{field,recpower,number_ring}" "1" "op -" "uminus" "op /" "inverse"] apply (unfold_locales) by (simp_all add: divide_inverse)
+
+lemma divide_Numeral1: "(x::'a::{field,number_ring}) / Numeral1 = x" by simp
+lemma divide_Numeral0: "(x::'a::{field,number_ring, division_by_zero}) / Numeral0 = 0"
+  by simp
+lemma mult_frac_frac: "((x::'a::{field,division_by_zero}) / y) * (z / w) = (x*z) / (y*w)"
+  by simp
+lemma mult_frac_num: "((x::'a::{field, division_by_zero}) / y) * z  = (x*z) / y"
+  by simp
+lemma mult_num_frac: "((x::'a::{field, division_by_zero}) / y) * z  = (x*z) / y"
+  by simp
+
+lemma Numeral1_eq1_nat: "(1::nat) = Numeral1" by simp
+
+lemma add_frac_num: "y\<noteq> 0 \<Longrightarrow> (x::'a::{field, division_by_zero}) / y + z = (x + z*y) / y"
+  by (simp add: add_divide_distrib)
+lemma add_num_frac: "y\<noteq> 0 \<Longrightarrow> z + (x::'a::{field, division_by_zero}) / y = (x + z*y) / y"
+  by (simp add: add_divide_distrib)
+
+
+ML{* 
+local
+ val zr = @{cpat "0"}
+ val zT = ctyp_of_term zr
+ val geq = @{cpat "op ="}
+ val eqT = Thm.dest_ctyp (ctyp_of_term geq) |> hd
+ val add_frac_eq = mk_meta_eq @{thm "add_frac_eq"}
+ val add_frac_num = mk_meta_eq @{thm "add_frac_num"}
+ val add_num_frac = mk_meta_eq @{thm "add_num_frac"}
+
+ fun prove_nz ss T t =
+    let
+      val z = instantiate_cterm ([(zT,T)],[]) zr
+      val eq = instantiate_cterm ([(eqT,T)],[]) geq
+      val th = Simplifier.rewrite (ss addsimps simp_thms)
+           (Thm.capply @{cterm "Trueprop"} (Thm.capply @{cterm "Not"}
+                  (Thm.capply (Thm.capply eq t) z)))
+    in equal_elim (symmetric th) TrueI
+    end
+
+ fun proc phi ss ct =
+  let
+    val ((x,y),(w,z)) =
+         (Thm.dest_binop #> (fn (a,b) => (Thm.dest_binop a, Thm.dest_binop b))) ct
+    val _ = map (HOLogic.dest_number o term_of) [x,y,z,w]
+    val T = ctyp_of_term x
+    val [y_nz, z_nz] = map (prove_nz ss T) [y, z]
+    val th = instantiate' [SOME T] (map SOME [y,z,x,w]) add_frac_eq
+  in SOME (implies_elim (implies_elim th y_nz) z_nz)
+  end
+  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
+
+ fun proc2 phi ss ct =
+  let
+    val (l,r) = Thm.dest_binop ct
+    val T = ctyp_of_term l
+  in (case (term_of l, term_of r) of
+      (Const(@{const_name "HOL.divide"},_)$_$_, _) =>
+        let val (x,y) = Thm.dest_binop l val z = r
+            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
+            val ynz = prove_nz ss T y
+        in SOME (implies_elim (instantiate' [SOME T] (map SOME [y,x,z]) add_frac_num) ynz)
+        end
+     | (_, Const (@{const_name "HOL.divide"},_)$_$_) =>
+        let val (x,y) = Thm.dest_binop r val z = l
+            val _ = map (HOLogic.dest_number o term_of) [x,y,z]
+            val ynz = prove_nz ss T y
+        in SOME (implies_elim (instantiate' [SOME T] (map SOME [y,z,x]) add_num_frac) ynz)
+        end
+     | _ => NONE)
+  end
+  handle CTERM _ => NONE | TERM _ => NONE | THM _ => NONE
+
+ fun is_number (Const(@{const_name "HOL.divide"},_)$a$b) = is_number a andalso is_number b
+   | is_number t = can HOLogic.dest_number t
+
+ val is_number = is_number o term_of
+
+ fun proc3 phi ss ct =
+  (case term_of ct of
+    Const(@{const_name HOL.less},_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
+      let
+        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_less_eq"}
+      in SOME (mk_meta_eq th) end
+  | Const(@{const_name HOL.less_eq},_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
+      let
+        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_le_eq"}
+      in SOME (mk_meta_eq th) end
+  | Const("op =",_)$(Const(@{const_name "HOL.divide"},_)$_$_)$_ =>
+      let
+        val ((a,b),c) = Thm.dest_binop ct |>> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "divide_eq_eq"}
+      in SOME (mk_meta_eq th) end
+  | Const(@{const_name HOL.less},_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
+    let
+      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "less_divide_eq"}
+      in SOME (mk_meta_eq th) end
+  | Const(@{const_name HOL.less_eq},_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
+    let
+      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "le_divide_eq"}
+      in SOME (mk_meta_eq th) end
+  | Const("op =",_)$_$(Const(@{const_name "HOL.divide"},_)$_$_) =>
+    let
+      val (a,(b,c)) = Thm.dest_binop ct ||> Thm.dest_binop
+        val _ = map is_number [a,b,c]
+        val T = ctyp_of_term c
+        val th = instantiate' [SOME T] (map SOME [a,b,c]) @{thm "eq_divide_eq"}
+      in SOME (mk_meta_eq th) end
+  | _ => NONE)
+  handle TERM _ => NONE | CTERM _ => NONE | THM _ => NONE
+
+val add_frac_frac_simproc =
+       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + (?w::?'a::field)/?z"}],
+                     name = "add_frac_frac_simproc",
+                     proc = proc, identifier = []}
+
+val add_frac_num_simproc =
+       make_simproc {lhss = [@{cpat "(?x::?'a::field)/?y + ?z"}, @{cpat "?z + (?x::?'a::field)/?y"}],
+                     name = "add_frac_num_simproc",
+                     proc = proc2, identifier = []}
+
+val ord_frac_simproc =
+  make_simproc
+    {lhss = [@{cpat "(?a::(?'a::{field, ord}))/?b < ?c"},
+             @{cpat "(?a::(?'a::{field, ord}))/?b \<le> ?c"},
+             @{cpat "?c < (?a::(?'a::{field, ord}))/?b"},
+             @{cpat "?c \<le> (?a::(?'a::{field, ord}))/?b"},
+             @{cpat "?c = ((?a::(?'a::{field, ord}))/?b)"},
+             @{cpat "((?a::(?'a::{field, ord}))/ ?b) = ?c"}],
+             name = "ord_frac_simproc", proc = proc3, identifier = []}
+
+val nat_arith = map thm ["add_nat_number_of", "diff_nat_number_of",
+               "mult_nat_number_of", "eq_nat_number_of", "less_nat_number_of"]
+
+val comp_arith = (map thm ["Let_def", "if_False", "if_True", "add_0",
+                 "add_Suc", "add_number_of_left", "mult_number_of_left",
+                 "Suc_eq_add_numeral_1"])@
+                 (map (fn s => thm s RS sym) ["numeral_1_eq_1", "numeral_0_eq_0"])
+                 @ @{thms arith_simps} @ nat_arith @ @{thms rel_simps}
+val ths = [@{thm "mult_numeral_1"}, @{thm "mult_numeral_1_right"},
+           @{thm "divide_Numeral1"},
+           @{thm "Ring_and_Field.divide_zero"}, @{thm "divide_Numeral0"},
+           @{thm "divide_divide_eq_left"}, @{thm "mult_frac_frac"},
+           @{thm "mult_num_frac"}, @{thm "mult_frac_num"},
+           @{thm "mult_frac_frac"}, @{thm "times_divide_eq_right"},
+           @{thm "times_divide_eq_left"}, @{thm "divide_divide_eq_right"},
+           @{thm "diff_def"}, @{thm "minus_divide_left"},
+           @{thm "Numeral1_eq1_nat"}, @{thm "add_divide_distrib"} RS sym]
+
+local
+open Conv
+in
+val comp_conv = (Simplifier.rewrite
+(HOL_basic_ss addsimps @{thms "Groebner_Basis.comp_arith"}
+              addsimps ths addsimps comp_arith addsimps simp_thms
+              addsimprocs field_cancel_numeral_factors
+               addsimprocs [add_frac_frac_simproc, add_frac_num_simproc,
+                            ord_frac_simproc]
+                addcongs [@{thm "if_weak_cong"}]))
+then_conv (Simplifier.rewrite (HOL_basic_ss addsimps
+  [@{thm numeral_1_eq_1},@{thm numeral_0_eq_0}] @ @{thms numerals(1-2)}))
 end
+
+fun numeral_is_const ct =
+  case term_of ct of
+   Const (@{const_name "HOL.divide"},_) $ a $ b =>
+     numeral_is_const (Thm.dest_arg1 ct) andalso numeral_is_const (Thm.dest_arg ct)
+ | Const (@{const_name "HOL.uminus"},_)$t => numeral_is_const (Thm.dest_arg ct)
+ | t => can HOLogic.dest_number t
+
+fun dest_const ct = ((case term_of ct of
+   Const (@{const_name "HOL.divide"},_) $ a $ b=>
+    Rat.rat_of_quotient (snd (HOLogic.dest_number a), snd (HOLogic.dest_number b))
+ | t => Rat.rat_of_int (snd (HOLogic.dest_number t))) 
+   handle TERM _ => error "ring_dest_const")
+
+fun mk_const phi cT x =
+ let val (a, b) = Rat.quotient_of_rat x
+ in if b = 1 then Numeral.mk_cnumber cT a
+    else Thm.capply
+         (Thm.capply (Drule.cterm_rule (instantiate' [SOME cT] []) @{cpat "op /"})
+                     (Numeral.mk_cnumber cT a))
+         (Numeral.mk_cnumber cT b)
+  end
+
+in
+ val field_comp_conv = comp_conv;
+ val fieldgb_declaration = 
+  NormalizerData.funs @{thm class_fieldgb.fieldgb_axioms'}
+   {is_const = K numeral_is_const,
+    dest_const = K dest_const,
+    mk_const = mk_const,
+    conv = K (K comp_conv)}
+end;
+*}
+
+declaration fieldgb_declaration
+
+end
diff -r d5f39173444c -r 09e4aa3ddc25 src/HOL/Library/Dense_Linear_Order.thy
--- a/src/HOL/Library/Dense_Linear_Order.thy	Mon Sep 29 12:31:58 2008 +0200
+++ b/src/HOL/Library/Dense_Linear_Order.thy	Mon Sep 29 12:31:59 2008 +0200
@@ -7,17 +7,15 @@
   and a quantifier elimination procedure in Ferrante and Rackoff style *}
 
 theory Dense_Linear_Order
-imports Plain "~~/src/HOL/Presburger"
+imports Plain "~~/src/HOL/Groebner_Basis"
 uses
-  "~~/src/HOL/Tools/Qelim/qelim.ML"
   "~~/src/HOL/Tools/Qelim/langford_data.ML"
   "~~/src/HOL/Tools/Qelim/ferrante_rackoff_data.ML"
   ("~~/src/HOL/Tools/Qelim/langford.ML")
   ("~~/src/HOL/Tools/Qelim/ferrante_rackoff.ML")
 begin
 
-setup Langford_Data.setup
-setup Ferrante_Rackoff_Data.setup
+setup {* Langford_Data.setup #> Ferrante_Rackoff_Data.setup *}
 
 context linorder
 begin
diff -r d5f39173444c -r 09e4aa3ddc25 src/HOL/Presburger.thy
--- a/src/HOL/Presburger.thy	Mon Sep 29 12:31:58 2008 +0200
+++ b/src/HOL/Presburger.thy	Mon Sep 29 12:31:59 2008 +0200
@@ -6,11 +6,10 @@
 header {* Decision Procedure for Presburger Arithmetic *}
 
 theory Presburger
-imports Arith_Tools SetInterval
+imports Groebner_Basis SetInterval
 uses
   "Tools/Qelim/cooper_data.ML"
   "Tools/Qelim/generated_cooper.ML"
-  "Tools/Qelim/qelim.ML"
   ("Tools/Qelim/cooper.ML")
   ("Tools/Qelim/presburger.ML")
 begin