diff --git a/src/HOL/Analysis/normarith.ML b/src/HOL/Analysis/normarith.ML
--- a/src/HOL/Analysis/normarith.ML
+++ b/src/HOL/Analysis/normarith.ML
@@ -1,414 +1,412 @@
 (*  Title:      HOL/Analysis/normarith.ML
     Author:     Amine Chaieb, University of Cambridge
 
 Simple decision procedure for linear problems in Euclidean space.
 *)
 
 signature NORM_ARITH =
 sig
  val norm_arith : Proof.context -> conv
  val norm_arith_tac : Proof.context -> int -> tactic
 end
 
 structure NormArith : NORM_ARITH =
 struct
 
  open Conv;
  val bool_eq = op = : bool *bool -> bool
   fun dest_ratconst t = case Thm.term_of t of
-   Const(\<^const_name>\<open>divide\<close>, _)$a$b => Rat.make(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
- | Const(\<^const_name>\<open>inverse\<close>, _)$a => Rat.make(1, HOLogic.dest_number a |> snd)
- | _ => Rat.of_int (HOLogic.dest_number (Thm.term_of t) |> snd)
+    \<^Const_>\<open>divide _ for a b\<close> => Rat.make(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
+  | \<^Const_>\<open>inverse _ for a\<close> => Rat.make(1, HOLogic.dest_number a |> snd)
+  | _ => Rat.of_int (HOLogic.dest_number (Thm.term_of t) |> snd)
  fun is_ratconst t = can dest_ratconst t
  fun augment_norm b t acc = case Thm.term_of t of
-     Const(\<^const_name>\<open>norm\<close>, _) $ _ => insert (eq_pair bool_eq (op aconvc)) (b,Thm.dest_arg t) acc
+     \<^Const_>\<open>norm _ for _\<close> => insert (eq_pair bool_eq (op aconvc)) (b,Thm.dest_arg t) acc
    | _ => acc
  fun find_normedterms t acc = case Thm.term_of t of
-    \<^term>\<open>(+) :: real => _\<close>$_$_ =>
+     \<^Const_>\<open>plus \<^typ>\<open>real\<close> for _ _\<close> =>
             find_normedterms (Thm.dest_arg1 t) (find_normedterms (Thm.dest_arg t) acc)
-      | \<^term>\<open>(*) :: real => _\<close>$_$_ =>
+   | \<^Const_>\<open>times \<^typ>\<open>real\<close> for _ _\<close> =>
             if not (is_ratconst (Thm.dest_arg1 t)) then acc else
             augment_norm (dest_ratconst (Thm.dest_arg1 t) >= @0)
                       (Thm.dest_arg t) acc
-      | _ => augment_norm true t acc
+   | _ => augment_norm true t acc
 
  val cterm_lincomb_neg = FuncUtil.Ctermfunc.map (K ~)
  fun cterm_lincomb_cmul c t =
     if c = @0 then FuncUtil.Ctermfunc.empty else FuncUtil.Ctermfunc.map (fn _ => fn x => x * c) t
  fun cterm_lincomb_add l r = FuncUtil.Ctermfunc.combine (curry op +) (fn x => x = @0) l r
  fun cterm_lincomb_sub l r = cterm_lincomb_add l (cterm_lincomb_neg r)
  fun cterm_lincomb_eq l r = FuncUtil.Ctermfunc.is_empty (cterm_lincomb_sub l r)
 
 (*
  val int_lincomb_neg = FuncUtil.Intfunc.map (K ~)
 *)
  fun int_lincomb_cmul c t =
     if c = @0 then FuncUtil.Intfunc.empty else FuncUtil.Intfunc.map (fn _ => fn x => x * c) t
  fun int_lincomb_add l r = FuncUtil.Intfunc.combine (curry op +) (fn x => x = @0) l r
 (*
  fun int_lincomb_sub l r = int_lincomb_add l (int_lincomb_neg r)
  fun int_lincomb_eq l r = FuncUtil.Intfunc.is_empty (int_lincomb_sub l r)
 *)
 
 fun vector_lincomb t = case Thm.term_of t of
-   Const(\<^const_name>\<open>plus\<close>, _) $ _ $ _ =>
+   \<^Const_>\<open>plus _ for _ _\<close> =>
     cterm_lincomb_add (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(\<^const_name>\<open>minus\<close>, _) $ _ $ _ =>
+ | \<^Const_>\<open>minus _ for _ _\<close> =>
     cterm_lincomb_sub (vector_lincomb (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(\<^const_name>\<open>scaleR\<close>, _)$_$_ =>
+ | \<^Const_>\<open>scaleR _ for _ _\<close> =>
     cterm_lincomb_cmul (dest_ratconst (Thm.dest_arg1 t)) (vector_lincomb (Thm.dest_arg t))
- | Const(\<^const_name>\<open>uminus\<close>, _)$_ =>
+ | \<^Const_>\<open>uminus _ for _\<close> =>
      cterm_lincomb_neg (vector_lincomb (Thm.dest_arg t))
 (* FIXME: how should we handle numerals?
  | Const(@ {const_name vec},_)$_ =>
    let
      val b = ((snd o HOLogic.dest_number o term_of o Thm.dest_arg) t = 0
                handle TERM _=> false)
    in if b then FuncUtil.Ctermfunc.onefunc (t,@1)
       else FuncUtil.Ctermfunc.empty
    end
 *)
  | _ => FuncUtil.Ctermfunc.onefunc (t,@1)
 
  fun vector_lincombs ts =
   fold_rev
    (fn t => fn fns => case AList.lookup (op aconvc) fns t of
      NONE =>
        let val f = vector_lincomb t
        in case find_first (fn (_,f') => cterm_lincomb_eq f f') fns of
            SOME (_,f') => (t,f') :: fns
          | NONE => (t,f) :: fns
        end
    | SOME _ => fns) ts []
 
 fun replacenegnorms cv t = case Thm.term_of t of
-  \<^term>\<open>(+) :: real => _\<close>$_$_ => binop_conv (replacenegnorms cv) t
-| \<^term>\<open>(*) :: real => _\<close>$_$_ =>
+  \<^Const_>\<open>plus \<^typ>\<open>real\<close> for _ _\<close> => binop_conv (replacenegnorms cv) t
+| \<^Const_>\<open>times \<^typ>\<open>real\<close> for _ _\<close> =>
     if dest_ratconst (Thm.dest_arg1 t) < @0 then arg_conv cv t else Thm.reflexive t
 | _ => Thm.reflexive t
 (*
 fun flip v eq =
   if FuncUtil.Ctermfunc.defined eq v
   then FuncUtil.Ctermfunc.update (v, ~ (FuncUtil.Ctermfunc.apply eq v)) eq else eq
 *)
 fun allsubsets s = case s of
   [] => [[]]
 |(a::t) => let val res = allsubsets t in
                map (cons a) res @ res end
 fun evaluate env lin =
  FuncUtil.Intfunc.fold (fn (x,c) => fn s => s + c * (FuncUtil.Intfunc.apply env x))
    lin @0
 
 fun solve (vs,eqs) = case (vs,eqs) of
   ([],[]) => SOME (FuncUtil.Intfunc.onefunc (0,@1))
  |(_,eq::oeqs) =>
    (case filter (member (op =) vs) (FuncUtil.Intfunc.dom eq) of (*FIXME use find_first here*)
      [] => NONE
     | v::_ =>
        if FuncUtil.Intfunc.defined eq v
        then
         let
          val c = FuncUtil.Intfunc.apply eq v
          val vdef = int_lincomb_cmul (~ (Rat.inv c)) eq
          fun eliminate eqn = if not (FuncUtil.Intfunc.defined eqn v) then eqn
                              else int_lincomb_add (int_lincomb_cmul (FuncUtil.Intfunc.apply eqn v) vdef) eqn
         in (case solve (remove (op =) v vs, map eliminate oeqs) of
             NONE => NONE
           | SOME soln => SOME (FuncUtil.Intfunc.update (v, evaluate soln (FuncUtil.Intfunc.delete_safe v vdef)) soln))
         end
        else NONE)
 
 fun combinations k l = if k = 0 then [[]] else
  case l of
   [] => []
 | h::t => map (cons h) (combinations (k - 1) t) @ combinations k t
 
 fun vertices vs eqs =
  let
   fun vertex cmb = case solve(vs,cmb) of
     NONE => NONE
    | SOME soln => SOME (map (fn v => FuncUtil.Intfunc.tryapplyd soln v @0) vs)
   val rawvs = map_filter vertex (combinations (length vs) eqs)
   val unset = filter (forall (fn c => c >= @0)) rawvs
  in fold_rev (insert (eq_list op =)) unset []
  end
 
 val subsumes = eq_list (fn (x, y) => Rat.abs x <= Rat.abs y)
 
 fun subsume todo dun = case todo of
  [] => dun
 |v::ovs =>
    let val dun' = if exists (fn w => subsumes (w, v)) dun then dun
                   else v:: filter (fn w => not (subsumes (v, w))) dun
    in subsume ovs dun'
    end;
 
 fun match_mp PQ P = P RS PQ;
 
 fun cterm_of_rat x =
 let val (a, b) = Rat.dest x
 in
- if b = 1 then Numeral.mk_cnumber \<^ctyp>\<open>real\<close> a
-  else Thm.apply (Thm.apply \<^cterm>\<open>(/) :: real => _\<close>
-                   (Numeral.mk_cnumber \<^ctyp>\<open>real\<close> a))
-        (Numeral.mk_cnumber \<^ctyp>\<open>real\<close> b)
+  if b = 1 then Numeral.mk_cnumber \<^ctyp>\<open>real\<close> a
+  else
+    \<^instantiate>\<open>
+        a = \<open>Numeral.mk_cnumber \<^ctyp>\<open>real\<close> a\<close> and
+        b = \<open>Numeral.mk_cnumber \<^ctyp>\<open>real\<close> b\<close>
+      in cterm \<open>a / b\<close> for a b :: real\<close>
 end;
 
 fun norm_cmul_rule c th = Thm.instantiate' [] [SOME (cterm_of_rat c)] (th RS @{thm norm_cmul_rule_thm});
 
 fun norm_add_rule th1 th2 = [th1, th2] MRS @{thm norm_add_rule_thm};
 
   (* I think here the static context should be sufficient!! *)
 fun inequality_canon_rule ctxt =
  let
   (* FIXME : Should be computed statically!! *)
   val real_poly_conv =
     Semiring_Normalizer.semiring_normalize_wrapper ctxt
      (the (Semiring_Normalizer.match ctxt \<^cterm>\<open>(0::real) + 1\<close>))
  in
   fconv_rule (arg_conv ((rewr_conv @{thm ge_iff_diff_ge_0}) then_conv
     arg_conv (Numeral_Simprocs.field_comp_conv ctxt then_conv real_poly_conv)))
 end;
 
  val apply_pth1 = rewr_conv @{thm pth_1};
  val apply_pth2 = rewr_conv @{thm pth_2};
  val apply_pth3 = rewr_conv @{thm pth_3};
  val apply_pth4 = rewrs_conv @{thms pth_4};
  val apply_pth5 = rewr_conv @{thm pth_5};
  val apply_pth6 = rewr_conv @{thm pth_6};
  val apply_pth7 = rewrs_conv @{thms pth_7};
  fun apply_pth8 ctxt =
   rewr_conv @{thm pth_8} then_conv
   arg1_conv (Numeral_Simprocs.field_comp_conv ctxt) then_conv
   (try_conv (rewr_conv (mk_meta_eq @{thm scaleR_zero_left})));
  fun apply_pth9 ctxt =
   rewrs_conv @{thms pth_9} then_conv
   arg1_conv (arg1_conv (Numeral_Simprocs.field_comp_conv ctxt));
  val apply_ptha = rewr_conv @{thm pth_a};
  val apply_pthb = rewrs_conv @{thms pth_b};
  val apply_pthc = rewrs_conv @{thms pth_c};
  val apply_pthd = try_conv (rewr_conv @{thm pth_d});
 
 fun headvector t = case t of
-  Const(\<^const_name>\<open>plus\<close>, _)$
-   (Const(\<^const_name>\<open>scaleR\<close>, _)$_$v)$_ => v
- | Const(\<^const_name>\<open>scaleR\<close>, _)$_$v => v
+   \<^Const_>\<open>plus _ for \<^Const_>\<open>scaleR _ for _ v\<close> _\<close> => v
+ | \<^Const_>\<open>scaleR _ for _ v\<close> => v
  | _ => error "headvector: non-canonical term"
 
 fun vector_cmul_conv ctxt ct =
    ((apply_pth5 then_conv arg1_conv (Numeral_Simprocs.field_comp_conv ctxt)) else_conv
     (apply_pth6 then_conv binop_conv (vector_cmul_conv ctxt))) ct
 
 fun vector_add_conv ctxt ct = apply_pth7 ct
  handle CTERM _ =>
   (apply_pth8 ctxt ct
    handle CTERM _ =>
     (case Thm.term_of ct of
-     Const(\<^const_name>\<open>plus\<close>,_)$lt$rt =>
+     \<^Const_>\<open>plus _ for lt rt\<close> =>
       let
        val l = headvector lt
        val r = headvector rt
       in (case Term_Ord.fast_term_ord (l,r) of
          LESS => (apply_pthb then_conv arg_conv (vector_add_conv ctxt)
                   then_conv apply_pthd) ct
         | GREATER => (apply_pthc then_conv arg_conv (vector_add_conv ctxt)
                      then_conv apply_pthd) ct
         | EQUAL => (apply_pth9 ctxt then_conv
                 ((apply_ptha then_conv (vector_add_conv ctxt)) else_conv
               arg_conv (vector_add_conv ctxt) then_conv apply_pthd)) ct)
       end
      | _ => Thm.reflexive ct))
 
 fun vector_canon_conv ctxt ct = case Thm.term_of ct of
- Const(\<^const_name>\<open>plus\<close>,_)$_$_ =>
+  \<^Const_>\<open>plus _ for _ _\<close> =>
   let
    val ((p,l),r) = Thm.dest_comb ct |>> Thm.dest_comb
    val lth = vector_canon_conv ctxt l
    val rth = vector_canon_conv ctxt r
    val th = Drule.binop_cong_rule p lth rth
   in fconv_rule (arg_conv (vector_add_conv ctxt)) th end
 
-| Const(\<^const_name>\<open>scaleR\<close>, _)$_$_ =>
+| \<^Const_>\<open>scaleR _ for _ _\<close> =>
   let
    val (p,r) = Thm.dest_comb ct
    val rth = Drule.arg_cong_rule p (vector_canon_conv ctxt r)
   in fconv_rule (arg_conv (apply_pth4 else_conv (vector_cmul_conv ctxt))) rth
   end
 
-| Const(\<^const_name>\<open>minus\<close>,_)$_$_ => (apply_pth2 then_conv (vector_canon_conv ctxt)) ct
+| \<^Const_>\<open>minus _ for _ _\<close> => (apply_pth2 then_conv (vector_canon_conv ctxt)) ct
 
-| Const(\<^const_name>\<open>uminus\<close>,_)$_ => (apply_pth3 then_conv (vector_canon_conv ctxt)) ct
+| \<^Const_>\<open>uminus _ for _\<close> => (apply_pth3 then_conv (vector_canon_conv ctxt)) ct
 
 (* FIXME
 | Const(@{const_name vec},_)$n =>
   let val n = Thm.dest_arg ct
   in if is_ratconst n andalso not (dest_ratconst n =/ @0)
      then Thm.reflexive ct else apply_pth1 ct
   end
 *)
 | _ => apply_pth1 ct
 
 fun norm_canon_conv ctxt ct = case Thm.term_of ct of
-  Const(\<^const_name>\<open>norm\<close>,_)$_ => arg_conv (vector_canon_conv ctxt) ct
+   \<^Const_>\<open>norm _ for _\<close> => arg_conv (vector_canon_conv ctxt) ct
  | _ => raise CTERM ("norm_canon_conv", [ct])
 
 fun int_flip v eq =
   if FuncUtil.Intfunc.defined eq v
   then FuncUtil.Intfunc.update (v, ~ (FuncUtil.Intfunc.apply eq v)) eq else eq;
 
 local
  val pth_zero = @{thm norm_zero}
  val tv_n =
   (dest_TVar o Thm.typ_of_cterm o Thm.dest_arg o Thm.dest_arg1 o Thm.dest_arg o Thm.cprop_of)
     pth_zero
  val concl = Thm.dest_arg o Thm.cprop_of
  fun real_vector_combo_prover ctxt translator (nubs,ges,gts) =
   let
    (* FIXME: Should be computed statically!!*)
    val real_poly_conv =
       Semiring_Normalizer.semiring_normalize_wrapper ctxt
        (the (Semiring_Normalizer.match ctxt \<^cterm>\<open>(0::real) + 1\<close>))
    val sources = map (Thm.dest_arg o Thm.dest_arg1 o concl) nubs
    val rawdests = fold_rev (find_normedterms o Thm.dest_arg o concl) (ges @ gts) []
    val _ = if not (forall fst rawdests) then error "real_vector_combo_prover: Sanity check"
            else ()
    val dests = distinct (op aconvc) (map snd rawdests)
    val srcfuns = map vector_lincomb sources
    val destfuns = map vector_lincomb dests
    val vvs = fold_rev (union (op aconvc) o FuncUtil.Ctermfunc.dom) (srcfuns @ destfuns) []
    val n = length srcfuns
    val nvs = 1 upto n
    val srccombs = srcfuns ~~ nvs
    fun consider d =
     let
      fun coefficients x =
       let
        val inp =
         if FuncUtil.Ctermfunc.defined d x
         then FuncUtil.Intfunc.onefunc (0, ~ (FuncUtil.Ctermfunc.apply d x))
         else FuncUtil.Intfunc.empty
       in fold_rev (fn (f,v) => fn g => if FuncUtil.Ctermfunc.defined f x then FuncUtil.Intfunc.update (v, FuncUtil.Ctermfunc.apply f x) g else g) srccombs inp
       end
      val equations = map coefficients vvs
      val inequalities = map (fn n => FuncUtil.Intfunc.onefunc (n,@1)) nvs
      fun plausiblevertices f =
       let
        val flippedequations = map (fold_rev int_flip f) equations
        val constraints = flippedequations @ inequalities
        val rawverts = vertices nvs constraints
        fun check_solution v =
         let
           val f = fold_rev FuncUtil.Intfunc.update (nvs ~~ v) (FuncUtil.Intfunc.onefunc (0, @1))
         in forall (fn e => evaluate f e = @0) flippedequations
         end
        val goodverts = filter check_solution rawverts
        val signfixups = map (fn n => if member (op =) f n then ~1 else 1) nvs
       in map (map2 (fn s => fn c => Rat.of_int s * c) signfixups) goodverts
       end
      val allverts = fold_rev append (map plausiblevertices (allsubsets nvs)) []
     in subsume allverts []
     end
    fun compute_ineq v =
     let
      val ths = map_filter (fn (v,t) => if v = @0 then NONE
                                      else SOME(norm_cmul_rule v t))
                             (v ~~ nubs)
      fun end_itlist f xs = split_last xs |> uncurry (fold_rev f)
     in inequality_canon_rule ctxt (end_itlist norm_add_rule ths)
     end
    val ges' = map_filter (try compute_ineq) (fold_rev (append o consider) destfuns []) @
                  map (inequality_canon_rule ctxt) nubs @ ges
    val zerodests = filter
         (fn t => null (FuncUtil.Ctermfunc.dom (vector_lincomb t))) (map snd rawdests)
 
   in fst (RealArith.real_linear_prover translator
         (map (fn t =>
           Drule.instantiate_normalize (TVars.make [(tv_n, Thm.ctyp_of_cterm t)], Vars.empty) pth_zero)
             zerodests,
         map (fconv_rule (try_conv (Conv.top_sweep_conv norm_canon_conv ctxt) then_conv
                        arg_conv (arg_conv real_poly_conv))) ges',
         map (fconv_rule (try_conv (Conv.top_sweep_conv norm_canon_conv ctxt) then_conv
                        arg_conv (arg_conv real_poly_conv))) gts))
   end
 in val real_vector_combo_prover = real_vector_combo_prover
 end;
 
 local
  val pth = @{thm norm_imp_pos_and_ge}
  val norm_mp = match_mp pth
  val concl = Thm.dest_arg o Thm.cprop_of
  fun conjunct1 th = th RS @{thm conjunct1}
  fun conjunct2 th = th RS @{thm conjunct2}
 fun real_vector_ineq_prover ctxt translator (ges,gts) =
  let
 (*   val _ = error "real_vector_ineq_prover: pause" *)
   val ntms = fold_rev find_normedterms (map (Thm.dest_arg o concl) (ges @ gts)) []
   val lctab = vector_lincombs (map snd (filter (not o fst) ntms))
   val (fxns, ctxt') = Variable.variant_fixes (replicate (length lctab) "x") ctxt
-  fun instantiate_cterm' ty tms = Drule.cterm_rule (Thm.instantiate' ty tms)
   fun mk_norm t =
-    let val T = Thm.typ_of_cterm t
-    in Thm.apply (Thm.cterm_of ctxt' (Const (\<^const_name>\<open>norm\<close>, T --> \<^typ>\<open>real\<close>))) t end
+    let val T = Thm.ctyp_of_cterm t
+    in \<^instantiate>\<open>'a = T and t in cterm \<open>norm t\<close>\<close> end
   fun mk_equals l r =
-    let
-      val T = Thm.typ_of_cterm l
-      val eq = Thm.cterm_of ctxt (Const (\<^const_name>\<open>Pure.eq\<close>, T --> T --> propT))
-    in Thm.apply (Thm.apply eq l) r end
+    let val T = Thm.ctyp_of_cterm l
+    in \<^instantiate>\<open>'a = T and l and r in cterm \<open>l \<equiv> r\<close>\<close> end
   val asl = map2 (fn (t,_) => fn n => Thm.assume (mk_equals (mk_norm t) (Thm.cterm_of ctxt' (Free(n,\<^typ>\<open>real\<close>))))) lctab fxns
   val replace_conv = try_conv (rewrs_conv asl)
   val replace_rule = fconv_rule (funpow 2 arg_conv (replacenegnorms replace_conv))
   val ges' =
        fold_rev (fn th => fn ths => conjunct1(norm_mp th)::ths)
               asl (map replace_rule ges)
   val gts' = map replace_rule gts
   val nubs = map (conjunct2 o norm_mp) asl
   val th1 = real_vector_combo_prover ctxt' translator (nubs,ges',gts')
   val shs = filter (member (fn (t,th) => t aconvc Thm.cprop_of th) asl) (Thm.chyps_of th1)
   val th11 = hd (Variable.export ctxt' ctxt [fold Thm.implies_intr shs th1])
   val cps = map (swap o Thm.dest_equals) (cprems_of th11)
   val th12 = Drule.instantiate_normalize (TVars.empty, Vars.make (map (apfst (dest_Var o Thm.term_of)) cps)) th11
   val th13 = fold Thm.elim_implies (map (Thm.reflexive o snd) cps) th12;
  in hd (Variable.export ctxt' ctxt [th13])
  end
 in val real_vector_ineq_prover = real_vector_ineq_prover
 end;
 
 local
  val rawrule = fconv_rule (arg_conv (rewr_conv @{thm real_eq_0_iff_le_ge_0}))
  fun conj_pair th = (th RS @{thm conjunct1}, th RS @{thm conjunct2})
   (* FIXME: Lookup in the context every time!!! Fix this !!!*)
  fun splitequation ctxt th acc =
   let
    val real_poly_neg_conv = #neg
        (Semiring_Normalizer.semiring_normalizers_ord_wrapper ctxt
         (the (Semiring_Normalizer.match ctxt \<^cterm>\<open>(0::real) + 1\<close>)) Thm.term_ord)
    val (th1,th2) = conj_pair(rawrule th)
   in th1::fconv_rule (arg_conv (arg_conv (real_poly_neg_conv ctxt))) th2::acc
   end
 in fun real_vector_prover ctxt _ translator (eqs,ges,gts) =
      (real_vector_ineq_prover ctxt translator
          (fold_rev (splitequation ctxt) eqs ges,gts), RealArith.Trivial)
 end;
 
   fun init_conv ctxt =
    Simplifier.rewrite (put_simpset HOL_basic_ss ctxt
     addsimps ([(*@{thm vec_0}, @{thm vec_1},*) @{thm dist_norm}, @{thm right_minus},
       @{thm diff_self}, @{thm norm_zero}] @ @{thms arithmetic_simps} @ @{thms norm_pths}))
    then_conv Numeral_Simprocs.field_comp_conv ctxt
    then_conv nnf_conv ctxt
 
  fun pure ctxt = fst o RealArith.gen_prover_real_arith ctxt (real_vector_prover ctxt);
  fun norm_arith ctxt ct =
   let
    val ctxt' = Variable.declare_term (Thm.term_of ct) ctxt
    val th = init_conv ctxt' ct
   in Thm.equal_elim (Drule.arg_cong_rule \<^cterm>\<open>Trueprop\<close> (Thm.symmetric th))
                 (pure ctxt' (Thm.rhs_of th))
  end
 
  fun norm_arith_tac ctxt =
    clarify_tac (put_claset HOL_cs ctxt) THEN'
    Object_Logic.full_atomize_tac ctxt THEN'
    CSUBGOAL ( fn (p,i) => resolve_tac ctxt [norm_arith ctxt (Thm.dest_arg p )] i);
 
 end;