diff --git a/src/Provers/splitter.ML b/src/Provers/splitter.ML
--- a/src/Provers/splitter.ML
+++ b/src/Provers/splitter.ML
@@ -1,489 +1,489 @@
 (*  Title:      Provers/splitter.ML
     Author:     Tobias Nipkow
     Copyright   1995  TU Munich
 
 Generic case-splitter, suitable for most logics.
 Deals with equalities of the form ?P(f args) = ...
 where "f args" must be a first-order term without duplicate variables.
 *)
 
 signature SPLITTER_DATA =
 sig
   val context       : Proof.context
   val mk_eq         : thm -> thm
   val meta_eq_to_iff: thm (* "x == y ==> x = y"                      *)
   val iffD          : thm (* "[| P = Q; Q |] ==> P"                  *)
   val disjE         : thm (* "[| P | Q; P ==> R; Q ==> R |] ==> R"   *)
   val conjE         : thm (* "[| P & Q; [| P; Q |] ==> R |] ==> R"   *)
   val exE           : thm (* "[| EX x. P x; !!x. P x ==> Q |] ==> Q" *)
   val contrapos     : thm (* "[| ~ Q; P ==> Q |] ==> ~ P"            *)
   val contrapos2    : thm (* "[| Q; ~ P ==> ~ Q |] ==> P"            *)
   val notnotD       : thm (* "~ ~ P ==> P"                           *)
   val safe_tac      : Proof.context -> tactic
 end
 
 signature SPLITTER =
 sig
   (* somewhat more internal functions *)
   val cmap_of_split_thms: thm list -> (string * (typ * term * thm * typ * int) list) list
   val split_posns: (string * (typ * term * thm * typ * int) list) list ->
     theory -> typ list -> term -> (thm * (typ * typ * int list) list * int list * typ * term) list
     (* first argument is a "cmap", returns a list of "split packs" *)
   (* the "real" interface, providing a number of tactics *)
   val split_tac       : Proof.context -> thm list -> int -> tactic
   val split_inside_tac: Proof.context -> thm list -> int -> tactic
   val split_asm_tac   : Proof.context -> thm list -> int -> tactic
   val add_split: thm -> Proof.context -> Proof.context
   val add_split_bang: thm -> Proof.context -> Proof.context
   val del_split: thm -> Proof.context -> Proof.context
   val split_modifiers : Method.modifier parser list
 end;
 
 functor Splitter(Data: SPLITTER_DATA): SPLITTER =
 struct
 
 val Const (const_not, _) $ _ =
   Object_Logic.drop_judgment Data.context
     (#1 (Logic.dest_implies (Thm.prop_of Data.notnotD)));
 
 val Const (const_or , _) $ _ $ _ =
   Object_Logic.drop_judgment Data.context
     (#1 (Logic.dest_implies (Thm.prop_of Data.disjE)));
 
 val const_Trueprop = Object_Logic.judgment_name Data.context;
 
 
 fun split_format_err () = error "Wrong format for split rule";
 
 fun split_thm_info thm =
   (case Thm.concl_of (Data.mk_eq thm) of
     Const(\<^const_name>\<open>Pure.eq\<close>, _) $ (Var _ $ t) $ c =>
       (case strip_comb t of
         (Const p, _) => (p, case c of (Const (s, _) $ _) => s = const_not | _ => false)
       | _ => split_format_err ())
   | _ => split_format_err ());
 
 fun cmap_of_split_thms thms =
 let
   val splits = map Data.mk_eq thms
   fun add_thm thm cmap =
     (case Thm.concl_of thm of _ $ (t as _ $ lhs) $ _ =>
        (case strip_comb lhs of (Const(a,aT),args) =>
           let val info = (aT,lhs,thm,fastype_of t,length args)
           in case AList.lookup (op =) cmap a of
                SOME infos => AList.update (op =) (a, info::infos) cmap
              | NONE => (a,[info])::cmap
           end
         | _ => split_format_err())
      | _ => split_format_err())
 in
   fold add_thm splits []
 end;
 
 val abss = fold (Term.abs o pair "");
 
 (* ------------------------------------------------------------------------- *)
 (* mk_case_split_tac                                                         *)
 (* ------------------------------------------------------------------------- *)
 
 fun mk_case_split_tac order =
 let
 
 (************************************************************
    Create lift-theorem "trlift" :
 
    [| !!x. Q x == R x; P(%x. R x) == C |] ==> P (%x. Q x) == C
 
 *************************************************************)
 
 val meta_iffD = Data.meta_eq_to_iff RS Data.iffD;  (* (P == Q) ==> Q ==> P *)
 
-val lift = Goal.prove_global \<^theory>\<open>Pure\<close> ["P", "Q", "R"]
+val lift = Goal.prove_global \<^theory> ["P", "Q", "R"]
   [Syntax.read_prop_global \<^theory>\<open>Pure\<close> "!!x :: 'b. Q(x) == R(x) :: 'c"]
   (Syntax.read_prop_global \<^theory>\<open>Pure\<close> "P(%x. Q(x)) == P(%x. R(x))")
   (fn {context = ctxt, prems} =>
     rewrite_goals_tac ctxt prems THEN resolve_tac ctxt [reflexive_thm] 1)
 
 val _ $ _ $ (_ $ (_ $ abs_lift) $ _) = Thm.prop_of lift;
 
 val trlift = lift RS transitive_thm;
 
 
 (************************************************************************
    Set up term for instantiation of P in the lift-theorem
 
    t     : lefthand side of meta-equality in subgoal
            the lift theorem is applied to (see select)
    pos   : "path" leading to abstraction, coded as a list
    T     : type of body of P(...)
 *************************************************************************)
 
 fun mk_cntxt t pos T =
   let
     fun down [] t = (Bound 0, t)
       | down (p :: ps) t =
           let
             val (h, ts) = strip_comb t
             val (ts1, u :: ts2) = chop p ts
             val (u1, u2) = down ps u
           in
             (list_comb (incr_boundvars 1 h,
                map (incr_boundvars 1) ts1 @ u1 ::
                map (incr_boundvars 1) ts2),
              u2)
           end;
     val (u1, u2) = down (rev pos) t
   in (Abs ("", T, u1), u2) end;
 
 
 (************************************************************************
    Set up term for instantiation of P in the split-theorem
    P(...) == rhs
 
    t     : lefthand side of meta-equality in subgoal
            the split theorem is applied to (see select)
    T     : type of body of P(...)
    tt    : the term  Const(key,..) $ ...
 *************************************************************************)
 
 fun mk_cntxt_splitthm t tt T =
   let fun repl lev t =
     if Envir.aeconv(incr_boundvars lev tt, t) then Bound lev
     else case t of
         (Abs (v, T2, t)) => Abs (v, T2, repl (lev+1) t)
       | (Bound i) => Bound (if i>=lev then i+1 else i)
       | (t1 $ t2) => (repl lev t1) $ (repl lev t2)
       | t => t
   in Abs("", T, repl 0 t) end;
 
 
 (* add all loose bound variables in t to list is *)
 fun add_lbnos t is = add_loose_bnos (t, 0, is);
 
 (* check if the innermost abstraction that needs to be removed
    has a body of type T; otherwise the expansion thm will fail later on
 *)
 fun type_test (T, lbnos, apsns) =
   let val (_, U: typ, _) = nth apsns (foldl1 Int.min lbnos)
   in T = U end;
 
 (*************************************************************************
    Create a "split_pack".
 
    thm   : the relevant split-theorem, i.e. P(...) == rhs , where P(...)
            is of the form
            P( Const(key,...) $ t_1 $ ... $ t_n )      (e.g. key = "if")
    T     : type of P(...)
    T'    : type of term to be scanned
    n     : number of arguments expected by Const(key,...)
    ts    : list of arguments actually found
    apsns : list of tuples of the form (T,U,pos), one tuple for each
            abstraction that is encountered on the way to the position where
            Const(key, ...) $ ...  occurs, where
            T   : type of the variable bound by the abstraction
            U   : type of the abstraction's body
            pos : "path" leading to the body of the abstraction
    pos   : "path" leading to the position where Const(key, ...) $ ...  occurs.
    TB    : type of  Const(key,...) $ t_1 $ ... $ t_n
    t     : the term Const(key,...) $ t_1 $ ... $ t_n
 
    A split pack is a tuple of the form
    (thm, apsns, pos, TB, tt)
    Note : apsns is reversed, so that the outermost quantifier's position
           comes first ! If the terms in ts don't contain variables bound
           by other than meta-quantifiers, apsns is empty, because no further
           lifting is required before applying the split-theorem.
 ******************************************************************************)
 
 fun mk_split_pack (thm, T: typ, T', n, ts, apsns, pos, TB, t) =
   if n > length ts then []
   else let val lev = length apsns
            val lbnos = fold add_lbnos (take n ts) []
            val flbnos = filter (fn i => i < lev) lbnos
            val tt = incr_boundvars (~lev) t
        in if null flbnos then
             if T = T' then [(thm,[],pos,TB,tt)] else []
           else if type_test(T,flbnos,apsns) then [(thm, rev apsns,pos,TB,tt)]
                else []
        end;
 
 
 (****************************************************************************
    Recursively scans term for occurrences of Const(key,...) $ ...
    Returns a list of "split-packs" (one for each occurrence of Const(key,...) )
 
    cmap : association list of split-theorems that should be tried.
           The elements have the format (key,(thm,T,n)) , where
           key : the theorem's key constant ( Const(key,...) $ ... )
           thm : the theorem itself
           T   : type of P( Const(key,...) $ ... )
           n   : number of arguments expected by Const(key,...)
    Ts   : types of parameters
    t    : the term to be scanned
 ******************************************************************************)
 
 (* Simplified first-order matching;
    assumes that all Vars in the pattern are distinct;
    see Pure/pattern.ML for the full version;
 *)
 local
   exception MATCH
 in
   fun typ_match thy (tyenv, TU) = Sign.typ_match thy TU tyenv
     handle Type.TYPE_MATCH => raise MATCH;
 
   fun fomatch thy args =
     let
       fun mtch tyinsts = fn
           (Ts, Var(_,T), t) =>
             typ_match thy (tyinsts, (T, fastype_of1(Ts,t)))
         | (_, Free (a,T), Free (b,U)) =>
             if a=b then typ_match thy (tyinsts,(T,U)) else raise MATCH
         | (_, Const (a,T), Const (b,U)) =>
             if a=b then typ_match thy (tyinsts,(T,U)) else raise MATCH
         | (_, Bound i, Bound j) =>
             if i=j then tyinsts else raise MATCH
         | (Ts, Abs(_,T,t), Abs(_,U,u)) =>
             mtch (typ_match thy (tyinsts,(T,U))) (U::Ts,t,u)
         | (Ts, f$t, g$u) =>
             mtch (mtch tyinsts (Ts,f,g)) (Ts, t, u)
         | _ => raise MATCH
     in (mtch Vartab.empty args; true) handle MATCH => false end;
 end;
 
 fun split_posns (cmap : (string * (typ * term * thm * typ * int) list) list) thy Ts t =
   let
     val T' = fastype_of1 (Ts, t);
     fun posns Ts pos apsns (Abs (_, T, t)) =
           let val U = fastype_of1 (T::Ts,t)
           in posns (T::Ts) (0::pos) ((T, U, pos)::apsns) t end
       | posns Ts pos apsns t =
           let
             val (h, ts) = strip_comb t
             fun iter t (i, a) = (i+1, (posns Ts (i::pos) apsns t) @ a);
             val a =
               case h of
                 Const(c, cT) =>
                   let fun find [] = []
                         | find ((gcT, pat, thm, T, n)::tups) =
                             let val t2 = list_comb (h, take n ts) in
                               if Sign.typ_instance thy (cT, gcT) andalso fomatch thy (Ts, pat, t2)
                               then mk_split_pack(thm,T,T',n,ts,apsns,pos,type_of1(Ts,t2),t2)
                               else find tups
                             end
                   in find (these (AList.lookup (op =) cmap c)) end
               | _ => []
           in snd (fold iter ts (0, a)) end
   in posns Ts [] [] t end;
 
 fun shorter ((_,ps,pos,_,_), (_,qs,qos,_,_)) =
   prod_ord (int_ord o apply2 length) (order o apply2 length)
     ((ps, pos), (qs, qos));
 
 
 (************************************************************
    call split_posns with appropriate parameters
 *************************************************************)
 
 fun select thy cmap state i =
   let
     val goal = Thm.term_of (Thm.cprem_of state i);
     val Ts = rev (map #2 (Logic.strip_params goal));
     val _ $ t $ _ = Logic.strip_assums_concl goal;
   in (Ts, t, sort shorter (split_posns cmap thy Ts t)) end;
 
 fun exported_split_posns cmap thy Ts t =
   sort shorter (split_posns cmap thy Ts t);
 
 (*************************************************************
    instantiate lift theorem
 
    if t is of the form
    ... ( Const(...,...) $ Abs( .... ) ) ...
    then
    P = %a.  ... ( Const(...,...) $ a ) ...
    where a has type T --> U
 
    Ts      : types of parameters
    t       : lefthand side of meta-equality in subgoal
              the split theorem is applied to (see cmap)
    T,U,pos : see mk_split_pack
    state   : current proof state
    i       : no. of subgoal
 **************************************************************)
 
 fun inst_lift ctxt Ts t (T, U, pos) state i =
   let
     val (cntxt, u) = mk_cntxt t pos (T --> U);
     val trlift' = Thm.lift_rule (Thm.cprem_of state i)
       (Thm.rename_boundvars abs_lift u trlift);
     val (Var (P, _), _) =
       strip_comb (fst (Logic.dest_equals
         (Logic.strip_assums_concl (Thm.prop_of trlift'))));
   in infer_instantiate ctxt [(P, Thm.cterm_of ctxt (abss Ts cntxt))] trlift' end;
 
 
 (*************************************************************
    instantiate split theorem
 
    Ts    : types of parameters
    t     : lefthand side of meta-equality in subgoal
            the split theorem is applied to (see cmap)
    tt    : the term  Const(key,..) $ ...
    thm   : the split theorem
    TB    : type of body of P(...)
    state : current proof state
    i     : number of subgoal
 **************************************************************)
 
 fun inst_split ctxt Ts t tt thm TB state i =
   let
     val thm' = Thm.lift_rule (Thm.cprem_of state i) thm;
     val (Var (P, _), _) =
       strip_comb (fst (Logic.dest_equals
         (Logic.strip_assums_concl (Thm.prop_of thm'))));
     val cntxt = mk_cntxt_splitthm t tt TB;
   in infer_instantiate ctxt [(P, Thm.cterm_of ctxt (abss Ts cntxt))] thm' end;
 
 
 (*****************************************************************************
    The split-tactic
 
    splits : list of split-theorems to be tried
    i      : number of subgoal the tactic should be applied to
 *****************************************************************************)
 
 fun split_tac _ [] i = no_tac
   | split_tac ctxt splits i =
   let val cmap = cmap_of_split_thms splits
       fun lift_tac Ts t p st = compose_tac ctxt (false, inst_lift ctxt Ts t p st i, 2) i st
       fun lift_split_tac state =
             let val (Ts, t, splits) = select (Proof_Context.theory_of ctxt) cmap state i
             in case splits of
                  [] => no_tac state
                | (thm, apsns, pos, TB, tt)::_ =>
                    (case apsns of
                       [] =>
                         compose_tac ctxt (false, inst_split ctxt Ts t tt thm TB state i, 0) i state
                     | p::_ => EVERY [lift_tac Ts t p,
                                      resolve_tac ctxt [reflexive_thm] (i+1),
                                      lift_split_tac] state)
             end
   in COND (has_fewer_prems i) no_tac
           (resolve_tac ctxt [meta_iffD] i THEN lift_split_tac)
   end;
 
 in (split_tac, exported_split_posns) end;  (* mk_case_split_tac *)
 
 
 val (split_tac, split_posns) = mk_case_split_tac int_ord;
 
 val (split_inside_tac, _) = mk_case_split_tac (rev_order o int_ord);
 
 
 (*****************************************************************************
    The split-tactic for premises
 
    splits : list of split-theorems to be tried
 ****************************************************************************)
 fun split_asm_tac _ [] = K no_tac
   | split_asm_tac ctxt splits =
 
   let val cname_list = map (fst o fst o split_thm_info) splits;
       fun tac (t,i) =
           let val n = find_index (exists_Const (member (op =) cname_list o #1))
                                  (Logic.strip_assums_hyp t);
               fun first_prem_is_disj (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ (Const (c, _)
                     $ (Const (s, _) $ _ $ _ )) $ _ ) = c = const_Trueprop andalso s = const_or
               |   first_prem_is_disj (Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(_,_,t)) =
                                         first_prem_is_disj t
               |   first_prem_is_disj _ = false;
       (* does not work properly if the split variable is bound by a quantifier *)
               fun flat_prems_tac i = SUBGOAL (fn (t,i) =>
                            (if first_prem_is_disj t
                             then EVERY[eresolve_tac ctxt [Data.disjE] i, rotate_tac ~1 i,
                                        rotate_tac ~1  (i+1),
                                        flat_prems_tac (i+1)]
                             else all_tac)
                            THEN REPEAT (eresolve_tac ctxt [Data.conjE,Data.exE] i)
                            THEN REPEAT (dresolve_tac ctxt [Data.notnotD]   i)) i;
           in if n<0 then  no_tac  else (DETERM (EVERY'
                 [rotate_tac n, eresolve_tac ctxt [Data.contrapos2],
                  split_tac ctxt splits,
                  rotate_tac ~1, eresolve_tac ctxt [Data.contrapos], rotate_tac ~1,
                  flat_prems_tac] i))
           end;
   in SUBGOAL tac
   end;
 
 fun gen_split_tac _ [] = K no_tac
   | gen_split_tac ctxt (split::splits) =
       let val (_,asm) = split_thm_info split
       in (if asm then split_asm_tac else split_tac) ctxt [split] ORELSE'
          gen_split_tac ctxt splits
       end;
 
 
 (** declare split rules **)
 
 (* add_split / del_split *)
 
 fun string_of_typ (Type (s, Ts)) =
       (if null Ts then "" else enclose "(" ")" (commas (map string_of_typ Ts))) ^ s
   | string_of_typ _ = "_";
 
 fun split_name (name, T) asm = "split " ^
   (if asm then "asm " else "") ^ name ^ " :: " ^ string_of_typ T;
 
 fun gen_add_split bang split ctxt =
   let
     val (name, asm) = split_thm_info split
     val split0 = Thm.trim_context split
     fun tac ctxt' =
       let val split' = Thm.transfer' ctxt' split0 in
         (if asm then split_asm_tac ctxt' [split']
          else if bang
               then split_tac ctxt' [split'] THEN_ALL_NEW
                    TRY o (SELECT_GOAL (Data.safe_tac ctxt'))
               else split_tac ctxt' [split'])
       end
   in Simplifier.addloop (ctxt, (split_name name asm, tac)) end;
 
 val add_split = gen_add_split false;
 val add_split_bang = gen_add_split true;
 
 fun del_split split ctxt =
   let val (name, asm) = split_thm_info split
   in Simplifier.delloop (ctxt, split_name name asm) end;
 
 
 (* attributes *)
 
 val splitN = "split";
 
 fun split_add bang = Simplifier.attrib (gen_add_split bang);
 val split_del = Simplifier.attrib del_split;
 
 val add_del = Scan.lift
   (Args.bang >> K (split_add true)
    || Args.del >> K split_del
    || Scan.succeed (split_add false));
 
 val _ = Theory.setup
   (Attrib.setup \<^binding>\<open>split\<close> add_del "declare case split rule");
 
 
 (* methods *)
 
 val split_modifiers =
  [Args.$$$ splitN -- Args.colon >> K (Method.modifier (split_add false) \<^here>),
   Args.$$$ splitN -- Args.bang_colon >> K (Method.modifier (split_add true) \<^here>),
   Args.$$$ splitN -- Args.del -- Args.colon >> K (Method.modifier split_del \<^here>)];
 
 val _ =
   Theory.setup
     (Method.setup \<^binding>\<open>split\<close>
       (Attrib.thms >> (fn ths => fn ctxt => SIMPLE_METHOD' (CHANGED_PROP o gen_split_tac ctxt ths)))
       "apply case split rule");
 
 end;