diff --git a/src/HOL/arith_data.ML b/src/HOL/arith_data.ML
--- a/src/HOL/arith_data.ML
+++ b/src/HOL/arith_data.ML
@@ -1,547 +1,547 @@
 (*  Title:      HOL/arith_data.ML
     ID:         $Id$
     Author:     Markus Wenzel, Stefan Berghofer and Tobias Nipkow
 
 Various arithmetic proof procedures.
 *)
 
 (*---------------------------------------------------------------------------*)
 (* 1. Cancellation of common terms                                           *)
 (*---------------------------------------------------------------------------*)
 
 structure NatArithUtils =
 struct
 
 (** abstract syntax of structure nat: 0, Suc, + **)
 
 (* mk_sum, mk_norm_sum *)
 
 val one = HOLogic.mk_nat 1;
 val mk_plus = HOLogic.mk_binop "op +";
 
 fun mk_sum [] = HOLogic.zero
   | mk_sum [t] = t
   | mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
 (*normal form of sums: Suc (... (Suc (a + (b + ...))))*)
 fun mk_norm_sum ts =
   let val (ones, sums) = List.partition (equal one) ts in
     funpow (length ones) HOLogic.mk_Suc (mk_sum sums)
   end;
 
 
 (* dest_sum *)
 
 val dest_plus = HOLogic.dest_bin "op +" HOLogic.natT;
 
 fun dest_sum tm =
   if HOLogic.is_zero tm then []
   else
     (case try HOLogic.dest_Suc tm of
       SOME t => one :: dest_sum t
     | NONE =>
         (case try dest_plus tm of
           SOME (t, u) => dest_sum t @ dest_sum u
         | NONE => [tm]));
 
 
 (** generic proof tools **)
 
 (* prove conversions *)
 
 val mk_eqv = HOLogic.mk_Trueprop o HOLogic.mk_eq;
 
 fun prove_conv expand_tac norm_tac sg tu =
   mk_meta_eq (prove_goalw_cterm_nocheck [] (cterm_of sg (mk_eqv tu))
     (K [expand_tac, norm_tac]))
   handle ERROR => error ("The error(s) above occurred while trying to prove " ^
     (string_of_cterm (cterm_of sg (mk_eqv tu))));
 
 val subst_equals = prove_goal HOL.thy "[| t = s; u = t |] ==> u = s"
   (fn prems => [cut_facts_tac prems 1, SIMPSET' asm_simp_tac 1]);
 
 
 (* rewriting *)
 
 fun simp_all rules = ALLGOALS (simp_tac (HOL_ss addsimps rules));
 
 val add_rules = [add_Suc, add_Suc_right, add_0, add_0_right];
 val mult_rules = [mult_Suc, mult_Suc_right, mult_0, mult_0_right];
 
 fun prep_simproc (name, pats, proc) =
   Simplifier.simproc (Theory.sign_of (the_context ())) name pats proc;
 
 end;
 
 signature ARITH_DATA =
 sig
   val nat_cancel_sums_add: simproc list
   val nat_cancel_sums: simproc list
 end;
 
 structure ArithData: ARITH_DATA =
 struct
 
 open NatArithUtils;
 
 
 (** cancel common summands **)
 
 structure Sum =
 struct
   val mk_sum = mk_norm_sum;
   val dest_sum = dest_sum;
   val prove_conv = prove_conv;
   val norm_tac = simp_all add_rules THEN simp_all add_ac;
 end;
 
 fun gen_uncancel_tac rule ct =
   rtac (instantiate' [] [NONE, SOME ct] (rule RS subst_equals)) 1;
 
 
 (* nat eq *)
 
 structure EqCancelSums = CancelSumsFun
 (struct
   open Sum;
   val mk_bal = HOLogic.mk_eq;
   val dest_bal = HOLogic.dest_bin "op =" HOLogic.natT;
   val uncancel_tac = gen_uncancel_tac nat_add_left_cancel;
 end);
 
 
 (* nat less *)
 
 structure LessCancelSums = CancelSumsFun
 (struct
   open Sum;
   val mk_bal = HOLogic.mk_binrel "op <";
   val dest_bal = HOLogic.dest_bin "op <" HOLogic.natT;
   val uncancel_tac = gen_uncancel_tac nat_add_left_cancel_less;
 end);
 
 
 (* nat le *)
 
 structure LeCancelSums = CancelSumsFun
 (struct
   open Sum;
   val mk_bal = HOLogic.mk_binrel "op <=";
   val dest_bal = HOLogic.dest_bin "op <=" HOLogic.natT;
   val uncancel_tac = gen_uncancel_tac nat_add_left_cancel_le;
 end);
 
 
 (* nat diff *)
 
 structure DiffCancelSums = CancelSumsFun
 (struct
   open Sum;
   val mk_bal = HOLogic.mk_binop "op -";
   val dest_bal = HOLogic.dest_bin "op -" HOLogic.natT;
   val uncancel_tac = gen_uncancel_tac diff_cancel;
 end);
 
 
 
 (** prepare nat_cancel simprocs **)
 
 val nat_cancel_sums_add = map prep_simproc
   [("nateq_cancel_sums",
      ["(l::nat) + m = n", "(l::nat) = m + n", "Suc m = n", "m = Suc n"], EqCancelSums.proc),
    ("natless_cancel_sums",
      ["(l::nat) + m < n", "(l::nat) < m + n", "Suc m < n", "m < Suc n"], LessCancelSums.proc),
    ("natle_cancel_sums",
      ["(l::nat) + m <= n", "(l::nat) <= m + n", "Suc m <= n", "m <= Suc n"], LeCancelSums.proc)];
 
 val nat_cancel_sums = nat_cancel_sums_add @
   [prep_simproc ("natdiff_cancel_sums",
     ["((l::nat) + m) - n", "(l::nat) - (m + n)", "Suc m - n", "m - Suc n"], DiffCancelSums.proc)];
 
 end;
 
 open ArithData;
 
 
 (*---------------------------------------------------------------------------*)
 (* 2. Linear arithmetic                                                      *)
 (*---------------------------------------------------------------------------*)
 
 (* Parameters data for general linear arithmetic functor *)
 
 structure LA_Logic: LIN_ARITH_LOGIC =
 struct
 val ccontr = ccontr;
 val conjI = conjI;
 val notI = notI;
 val sym = sym;
 val not_lessD = linorder_not_less RS iffD1;
 val not_leD = linorder_not_le RS iffD1;
 
 
 fun mk_Eq thm = (thm RS Eq_FalseI) handle THM _ => (thm RS Eq_TrueI);
 
 val mk_Trueprop = HOLogic.mk_Trueprop;
 
 fun neg_prop(TP$(Const("Not",_)$t)) = TP$t
   | neg_prop(TP$t) = TP $ (Const("Not",HOLogic.boolT-->HOLogic.boolT)$t);
 
 fun is_False thm =
   let val _ $ t = #prop(rep_thm thm)
   in t = Const("False",HOLogic.boolT) end;
 
 fun is_nat(t) = fastype_of1 t = HOLogic.natT;
 
 fun mk_nat_thm sg t =
   let val ct = cterm_of sg t  and cn = cterm_of sg (Var(("n",0),HOLogic.natT))
   in instantiate ([],[(cn,ct)]) le0 end;
 
 end;
 
 
 (* arith theory data *)
 
 structure ArithTheoryDataArgs =
 struct
   val name = "HOL/arith";
   type T = {splits: thm list, inj_consts: (string * typ)list, discrete: string  list, presburger: (int -> tactic) option};
 
   val empty = {splits = [], inj_consts = [], discrete = [], presburger = NONE};
   val copy = I;
   val prep_ext = I;
   fun merge ({splits= splits1, inj_consts= inj_consts1, discrete= discrete1, presburger= presburger1},
              {splits= splits2, inj_consts= inj_consts2, discrete= discrete2, presburger= presburger2}) =
    {splits = Drule.merge_rules (splits1, splits2),
     inj_consts = merge_lists inj_consts1 inj_consts2,
     discrete = merge_lists discrete1 discrete2,
     presburger = (case presburger1 of NONE => presburger2 | p => p)};
   fun print _ _ = ();
 end;
 
 structure ArithTheoryData = TheoryDataFun(ArithTheoryDataArgs);
 
 fun arith_split_add (thy, thm) = (ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
   {splits= thm::splits, inj_consts= inj_consts, discrete= discrete, presburger= presburger}) thy, thm);
 
 fun arith_discrete d = ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
   {splits = splits, inj_consts = inj_consts, discrete = d :: discrete, presburger= presburger});
 
 fun arith_inj_const c = ArithTheoryData.map (fn {splits,inj_consts,discrete,presburger} =>
   {splits = splits, inj_consts = c :: inj_consts, discrete = discrete, presburger = presburger});
 
 
 structure LA_Data_Ref: LIN_ARITH_DATA =
 struct
 
 (* Decomposition of terms *)
 
 fun nT (Type("fun",[N,_])) = N = HOLogic.natT
   | nT _ = false;
 
 fun add_atom(t,m,(p,i)) = (case assoc(p,t) of NONE => ((t,m)::p,i)
                            | SOME n => (overwrite(p,(t,ratadd(n,m))), i));
 
 exception Zero;
 
 fun rat_of_term(numt,dent) =
   let val num = HOLogic.dest_binum numt and den = HOLogic.dest_binum dent
   in if den = 0 then raise Zero else int_ratdiv(num,den) end;
 
 (* Warning: in rare cases number_of encloses a non-numeral,
    in which case dest_binum raises TERM; hence all the handles below.
    Same for Suc-terms that turn out not to be numerals -
    although the simplifier should eliminate those anyway...
 *)
 
 fun number_of_Sucs (Const("Suc",_) $ n) = number_of_Sucs n + 1
   | number_of_Sucs t = if HOLogic.is_zero t then 0
                        else raise TERM("number_of_Sucs",[])
 
 (* decompose nested multiplications, bracketing them to the right and combining all
    their coefficients
 *)
 
 fun demult inj_consts =
 let
 fun demult((mC as Const("op *",_)) $ s $ t,m) = ((case s of
         Const("Numeral.number_of",_)$n
         => demult(t,ratmul(m,rat_of_int(HOLogic.dest_binum n)))
       | Const("uminus",_)$(Const("Numeral.number_of",_)$n)
         => demult(t,ratmul(m,rat_of_int(~(HOLogic.dest_binum n))))
       | Const("Suc",_) $ _
         => demult(t,ratmul(m,rat_of_int(number_of_Sucs s)))
       | Const("op *",_) $ s1 $ s2 => demult(mC $ s1 $ (mC $ s2 $ t),m)
       | Const("HOL.divide",_) $ numt $ (Const("Numeral.number_of",_)$dent) =>
           let val den = HOLogic.dest_binum dent
           in if den = 0 then raise Zero
              else demult(mC $ numt $ t,ratmul(m, ratinv(rat_of_int den)))
           end
       | _ => atomult(mC,s,t,m)
       ) handle TERM _ => atomult(mC,s,t,m))
   | demult(atom as Const("HOL.divide",_) $ t $ (Const("Numeral.number_of",_)$dent), m) =
       (let val den = HOLogic.dest_binum dent
        in if den = 0 then raise Zero else demult(t,ratmul(m, ratinv(rat_of_int den))) end
        handle TERM _ => (SOME atom,m))
   | demult(Const("0",_),m) = (NONE, rat_of_int 0)
   | demult(Const("1",_),m) = (NONE, m)
   | demult(t as Const("Numeral.number_of",_)$n,m) =
       ((NONE,ratmul(m,rat_of_int(HOLogic.dest_binum n)))
        handle TERM _ => (SOME t,m))
   | demult(Const("uminus",_)$t, m) = demult(t,ratmul(m,rat_of_int(~1)))
   | demult(t as Const f $ x, m) =
       (if f mem inj_consts then SOME x else SOME t,m)
   | demult(atom,m) = (SOME atom,m)
 
 and atomult(mC,atom,t,m) = (case demult(t,m) of (NONE,m') => (SOME atom,m')
                             | (SOME t',m') => (SOME(mC $ atom $ t'),m'))
 in demult end;
 
 fun decomp2 inj_consts (rel,lhs,rhs) =
 let
 (* Turn term into list of summand * multiplicity plus a constant *)
 fun poly(Const("op +",_) $ s $ t, m, pi) = poly(s,m,poly(t,m,pi))
   | poly(all as Const("op -",T) $ s $ t, m, pi) =
-      if nT T then add_atom(all,m,pi)
-      else poly(s,m,poly(t,ratneg m,pi))
-  | poly(Const("uminus",_) $ t, m, pi) = poly(t,ratneg m,pi)
+      if nT T then add_atom(all,m,pi) else poly(s,m,poly(t,ratneg m,pi))
+  | poly(all as Const("uminus",T) $ t, m, pi) =
+      if nT T then add_atom(all,m,pi) else poly(t,ratneg m,pi)
   | poly(Const("0",_), _, pi) = pi
   | poly(Const("1",_), m, (p,i)) = (p,ratadd(i,m))
   | poly(Const("Suc",_)$t, m, (p,i)) = poly(t, m, (p,ratadd(i,m)))
   | poly(t as Const("op *",_) $ _ $ _, m, pi as (p,i)) =
       (case demult inj_consts (t,m) of
          (NONE,m') => (p,ratadd(i,m))
        | (SOME u,m') => add_atom(u,m',pi))
   | poly(t as Const("HOL.divide",_) $ _ $ _, m, pi as (p,i)) =
       (case demult inj_consts (t,m) of
          (NONE,m') => (p,ratadd(i,m'))
        | (SOME u,m') => add_atom(u,m',pi))
   | poly(all as (Const("Numeral.number_of",_)$t,m,(p,i))) =
       ((p,ratadd(i,ratmul(m,rat_of_int(HOLogic.dest_binum t))))
        handle TERM _ => add_atom all)
   | poly(all as Const f $ x, m, pi) =
       if f mem inj_consts then poly(x,m,pi) else add_atom(all,m,pi)
   | poly x  = add_atom x;
 
 val (p,i) = poly(lhs,rat_of_int 1,([],rat_of_int 0))
 and (q,j) = poly(rhs,rat_of_int 1,([],rat_of_int 0))
 
   in case rel of
        "op <"  => SOME(p,i,"<",q,j)
      | "op <=" => SOME(p,i,"<=",q,j)
      | "op ="  => SOME(p,i,"=",q,j)
      | _       => NONE
   end handle Zero => NONE;
 
 fun negate(SOME(x,i,rel,y,j,d)) = SOME(x,i,"~"^rel,y,j,d)
   | negate NONE = NONE;
 
 fun of_lin_arith_sort sg U =
   Type.of_sort (Sign.tsig_of sg) (U,["Ring_and_Field.ordered_idom"])
 
 fun allows_lin_arith sg discrete (U as Type(D,[])) =
       if of_lin_arith_sort sg U
       then (true, D mem discrete)
       else (* special cases *)
            if D mem discrete then (true,true) else (false,false)
   | allows_lin_arith sg discrete U = (of_lin_arith_sort sg U, false);
 
 fun decomp1 (sg,discrete,inj_consts) (T,xxx) =
   (case T of
      Type("fun",[U,_]) =>
        (case allows_lin_arith sg discrete U of
           (true,d) => (case decomp2 inj_consts xxx of NONE => NONE
                        | SOME(p,i,rel,q,j) => SOME(p,i,rel,q,j,d))
         | (false,_) => NONE)
    | _ => NONE);
 
 fun decomp2 data (_$(Const(rel,T)$lhs$rhs)) = decomp1 data (T,(rel,lhs,rhs))
   | decomp2 data (_$(Const("Not",_)$(Const(rel,T)$lhs$rhs))) =
       negate(decomp1 data (T,(rel,lhs,rhs)))
   | decomp2 data _ = NONE
 
 fun decomp sg =
   let val {discrete, inj_consts, ...} = ArithTheoryData.get_sg sg
   in decomp2 (sg,discrete,inj_consts) end
 
 fun number_of(n,T) = HOLogic.number_of_const T $ (HOLogic.mk_bin n)
 
 end;
 
 
 structure Fast_Arith =
   Fast_Lin_Arith(structure LA_Logic=LA_Logic and LA_Data=LA_Data_Ref);
 
 val fast_arith_tac    = Fast_Arith.lin_arith_tac false
 and fast_ex_arith_tac = Fast_Arith.lin_arith_tac
 and trace_arith    = Fast_Arith.trace
 and fast_arith_neq_limit = Fast_Arith.fast_arith_neq_limit;
 
 local
 
 val isolateSuc =
   let val thy = theory "Nat"
   in prove_goal thy "Suc(i+j) = i+j + Suc 0"
      (fn _ => [simp_tac (simpset_of thy) 1])
   end;
 
 (* reduce contradictory <= to False.
    Most of the work is done by the cancel tactics.
 *)
 val add_rules =
  [add_zero_left,add_zero_right,Zero_not_Suc,Suc_not_Zero,le_0_eq,
   One_nat_def,isolateSuc,
   order_less_irrefl];
 
 val add_mono_thms_ordered_semiring = map (fn s => prove_goal (the_context ()) s
  (fn prems => [cut_facts_tac prems 1,
                blast_tac (claset() addIs [add_mono]) 1]))
 ["(i <= j) & (k <= l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
  "(i  = j) & (k <= l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
  "(i <= j) & (k  = l) ==> i + k <= j + (l::'a::pordered_ab_semigroup_add)",
  "(i  = j) & (k  = l) ==> i + k  = j + (l::'a::pordered_ab_semigroup_add)"
 ];
 
 val mono_ss = simpset() addsimps
                 [add_mono,add_strict_mono,add_less_le_mono,add_le_less_mono];
 
 val add_mono_thms_ordered_field =
   map (fn s => prove_goal (the_context ()) s
                  (fn prems => [cut_facts_tac prems 1, asm_simp_tac mono_ss 1]))
     ["(i<j) & (k=l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
      "(i=j) & (k<l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
      "(i<j) & (k<=l)  ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
      "(i<=j) & (k<l)  ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)",
      "(i<j) & (k<l)   ==> i+k < j+(l::'a::pordered_cancel_ab_semigroup_add)"];
 
 in
 
 val init_lin_arith_data =
  Fast_Arith.setup @
  [Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, ...} =>
    {add_mono_thms = add_mono_thms @
     add_mono_thms_ordered_semiring @ add_mono_thms_ordered_field,
     mult_mono_thms = mult_mono_thms,
     inj_thms = inj_thms,
     lessD = lessD @ [Suc_leI],
     neqE = [linorder_neqE_nat,
       Goals.get_thm (theory "Ring_and_Field") "linorder_neqE_ordered_idom"],
     simpset = HOL_basic_ss addsimps add_rules
                    addsimprocs [ab_group_add_cancel.sum_conv, 
                                 ab_group_add_cancel.rel_conv]
                    (*abel_cancel helps it work in abstract algebraic domains*)
                    addsimprocs nat_cancel_sums_add}),
   ArithTheoryData.init, arith_discrete "nat"];
 
 end;
 
 val fast_nat_arith_simproc =
   Simplifier.simproc (Theory.sign_of (the_context ())) "fast_nat_arith"
     ["(m::nat) < n","(m::nat) <= n", "(m::nat) = n"] Fast_Arith.lin_arith_prover;
 
 
 (* Because of fast_nat_arith_simproc, the arithmetic solver is really only
 useful to detect inconsistencies among the premises for subgoals which are
 *not* themselves (in)equalities, because the latter activate
 fast_nat_arith_simproc anyway. However, it seems cheaper to activate the
 solver all the time rather than add the additional check. *)
 
 
 (* arith proof method *)
 
 (* FIXME: K true should be replaced by a sensible test to speed things up
    in case there are lots of irrelevant terms involved;
    elimination of min/max can be optimized:
    (max m n + k <= r) = (m+k <= r & n+k <= r)
    (l <= min m n + k) = (l <= m+k & l <= n+k)
 *)
 local
 
 fun raw_arith_tac ex i st =
   refute_tac (K true)
    (REPEAT o split_tac (#splits (ArithTheoryData.get_sg (Thm.sign_of_thm st))))
    ((REPEAT_DETERM o etac linorder_neqE) THEN' fast_ex_arith_tac ex)
    i st;
 
 fun presburger_tac i st =
   (case ArithTheoryData.get_sg (sign_of_thm st) of
      {presburger = SOME tac, ...} =>
        (tracing "Simple arithmetic decision procedure failed.\nNow trying full Presburger arithmetic..."; tac i st)
    | _ => no_tac st);
 
 in
 
 val simple_arith_tac = FIRST' [fast_arith_tac,
   ObjectLogic.atomize_tac THEN' raw_arith_tac true];
 
 val arith_tac = FIRST' [fast_arith_tac,
   ObjectLogic.atomize_tac THEN' raw_arith_tac true,
   presburger_tac];
 
 val silent_arith_tac = FIRST' [fast_arith_tac,
   ObjectLogic.atomize_tac THEN' raw_arith_tac false,
   presburger_tac];
 
 fun arith_method prems =
   Method.METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ facts) THEN' arith_tac));
 
 end;
 
 (* antisymmetry:
    combines x <= y (or ~(y < x)) and y <= x (or ~(x < y)) into x = y
 
 local
 val antisym = mk_meta_eq order_antisym
 val not_lessD = linorder_not_less RS iffD1
 fun prp t thm = (#prop(rep_thm thm) = t)
 in
 fun antisym_eq prems thm =
   let
     val r = #prop(rep_thm thm);
   in
     case r of
       Tr $ ((c as Const("op <=",T)) $ s $ t) =>
         let val r' = Tr $ (c $ t $ s)
         in
           case Library.find_first (prp r') prems of
             NONE =>
               let val r' = Tr $ (HOLogic.not_const $ (Const("op <",T) $ s $ t))
               in case Library.find_first (prp r') prems of
                    NONE => []
                  | SOME thm' => [(thm' RS not_lessD) RS (thm RS antisym)]
               end
           | SOME thm' => [thm' RS (thm RS antisym)]
         end
     | Tr $ (Const("Not",_) $ (Const("op <",T) $ s $ t)) =>
         let val r' = Tr $ (Const("op <=",T) $ s $ t)
         in
           case Library.find_first (prp r') prems of
             NONE =>
               let val r' = Tr $ (HOLogic.not_const $ (Const("op <",T) $ t $ s))
               in case Library.find_first (prp r') prems of
                    NONE => []
                  | SOME thm' =>
                      [(thm' RS not_lessD) RS ((thm RS not_lessD) RS antisym)]
               end
           | SOME thm' => [thm' RS ((thm RS not_lessD) RS antisym)]
         end
     | _ => []
   end
   handle THM _ => []
 end;
 *)
 
 (* theory setup *)
 
 val arith_setup =
  [Simplifier.change_simpset_of (op addsimprocs) nat_cancel_sums] @
   init_lin_arith_data @
   [Simplifier.change_simpset_of (op addSolver)
    (mk_solver "lin. arith." Fast_Arith.cut_lin_arith_tac),
   Simplifier.change_simpset_of (op addsimprocs) [fast_nat_arith_simproc],
   Method.add_methods
       [("arith", (arith_method o #2) oo Method.syntax Args.bang_facts,
 	"decide linear arithmethic")],
   Attrib.add_attributes [("arith_split",
     (Attrib.no_args arith_split_add, 
      Attrib.no_args Attrib.undef_local_attribute),
     "declaration of split rules for arithmetic procedure")]];