diff --git a/src/HOL/Library/Sum_of_Squares/positivstellensatz.ML b/src/HOL/Library/Sum_of_Squares/positivstellensatz.ML
--- a/src/HOL/Library/Sum_of_Squares/positivstellensatz.ML
+++ b/src/HOL/Library/Sum_of_Squares/positivstellensatz.ML
@@ -1,779 +1,781 @@
 (*  Title:      HOL/Library/positivstellensatz.ML
     Author:     Amine Chaieb, University of Cambridge
 
 A generic arithmetic prover based on Positivstellensatz certificates
 --- also implements Fourier-Motzkin elimination as a special case
 Fourier-Motzkin elimination.
 *)
 
 (* A functor for finite mappings based on Tables *)
 
 signature FUNC =
 sig
   include TABLE
   val apply : 'a table -> key -> 'a
   val applyd :'a table -> (key -> 'a) -> key -> 'a
   val combine : ('a -> 'a -> 'a) -> ('a -> bool) -> 'a table -> 'a table -> 'a table
   val dom : 'a table -> key list
   val tryapplyd : 'a table -> key -> 'a -> 'a
   val updatep : (key * 'a -> bool) -> key * 'a -> 'a table -> 'a table
   val choose : 'a table -> key * 'a
   val onefunc : key * 'a -> 'a table
 end;
 
 functor FuncFun(Key: KEY) : FUNC =
 struct
 
 structure Tab = Table(Key);
 
 open Tab;
 
 fun dom a = sort Key.ord (Tab.keys a);
 fun applyd f d x = case Tab.lookup f x of
    SOME y => y
  | NONE => d x;
 
 fun apply f x = applyd f (fn _ => raise Tab.UNDEF x) x;
 fun tryapplyd f a d = applyd f (K d) a;
 fun updatep p (k,v) t = if p (k, v) then t else update (k,v) t
 fun combine f z a b =
   let
     fun h (k,v) t = case Tab.lookup t k of
         NONE => Tab.update (k,v) t
       | SOME v' => let val w = f v v'
         in if z w then Tab.delete k t else Tab.update (k,w) t end;
   in Tab.fold h a b end;
 
 fun choose f =
   (case Tab.min f of
     SOME entry => entry
   | NONE => error "FuncFun.choose : Completely empty function")
 
 fun onefunc kv = update kv empty
 
 end;
 
 (* Some standard functors and utility functions for them *)
 
 structure FuncUtil =
 struct
 
 structure Intfunc = FuncFun(type key = int val ord = int_ord);
 structure Ratfunc = FuncFun(type key = Rat.rat val ord = Rat.ord);
 structure Intpairfunc = FuncFun(type key = int*int val ord = prod_ord int_ord int_ord);
 structure Symfunc = FuncFun(type key = string val ord = fast_string_ord);
 structure Termfunc = FuncFun(type key = term val ord = Term_Ord.fast_term_ord);
 structure Ctermfunc = FuncFun(type key = cterm val ord = Thm.fast_term_ord);
 
 type monomial = int Ctermfunc.table;
 val monomial_ord = list_ord (prod_ord Thm.fast_term_ord int_ord) o apply2 Ctermfunc.dest
 structure Monomialfunc = FuncFun(type key = monomial val ord = monomial_ord)
 
 type poly = Rat.rat Monomialfunc.table;
 
 (* The ordering so we can create canonical HOL polynomials.                  *)
 
 fun dest_monomial mon = sort (Thm.fast_term_ord o apply2 fst) (Ctermfunc.dest mon);
 
 fun monomial_order (m1,m2) =
   if Ctermfunc.is_empty m2 then LESS
   else if Ctermfunc.is_empty m1 then GREATER
   else
     let
       val mon1 = dest_monomial m1
       val mon2 = dest_monomial m2
       val deg1 = fold (Integer.add o snd) mon1 0
       val deg2 = fold (Integer.add o snd) mon2 0
     in if deg1 < deg2 then GREATER
        else if deg1 > deg2 then LESS
        else list_ord (prod_ord Thm.fast_term_ord int_ord) (mon1,mon2)
     end;
 
 end
 
 (* positivstellensatz datatype and prover generation *)
 
 signature REAL_ARITH =
 sig
 
   datatype positivstellensatz =
     Axiom_eq of int
   | Axiom_le of int
   | Axiom_lt of int
   | Rational_eq of Rat.rat
   | Rational_le of Rat.rat
   | Rational_lt of Rat.rat
   | Square of FuncUtil.poly
   | Eqmul of FuncUtil.poly * positivstellensatz
   | Sum of positivstellensatz * positivstellensatz
   | Product of positivstellensatz * positivstellensatz;
 
   datatype pss_tree = Trivial | Cert of positivstellensatz | Branch of pss_tree * pss_tree
 
   datatype tree_choice = Left | Right
 
   type prover = tree_choice list ->
     (thm list * thm list * thm list -> positivstellensatz -> thm) ->
       thm list * thm list * thm list -> thm * pss_tree
   type cert_conv = cterm -> thm * pss_tree
 
   val gen_gen_real_arith :
     Proof.context -> (Rat.rat -> cterm) * conv * conv * conv *
      conv * conv * conv * conv * conv * conv * prover -> cert_conv
   val real_linear_prover : (thm list * thm list * thm list -> positivstellensatz -> thm) ->
     thm list * thm list * thm list -> thm * pss_tree
 
   val gen_real_arith : Proof.context ->
     (Rat.rat -> cterm) * conv * conv * conv * conv * conv * conv * conv * prover -> cert_conv
 
   val gen_prover_real_arith : Proof.context -> prover -> cert_conv
 
   val is_ratconst : cterm -> bool
   val dest_ratconst : cterm -> Rat.rat
   val cterm_of_rat : Rat.rat -> cterm
 
 end
 
 structure RealArith : REAL_ARITH =
 struct
 
 open Conv
 (* ------------------------------------------------------------------------- *)
 (* Data structure for Positivstellensatz refutations.                        *)
 (* ------------------------------------------------------------------------- *)
 
 datatype positivstellensatz =
     Axiom_eq of int
   | Axiom_le of int
   | Axiom_lt of int
   | Rational_eq of Rat.rat
   | Rational_le of Rat.rat
   | Rational_lt of Rat.rat
   | Square of FuncUtil.poly
   | Eqmul of FuncUtil.poly * positivstellensatz
   | Sum of positivstellensatz * positivstellensatz
   | Product of positivstellensatz * positivstellensatz;
          (* Theorems used in the procedure *)
 
 datatype pss_tree = Trivial | Cert of positivstellensatz | Branch of pss_tree * pss_tree
 datatype tree_choice = Left | Right
 type prover = tree_choice list ->
   (thm list * thm list * thm list -> positivstellensatz -> thm) ->
     thm list * thm list * thm list -> thm * pss_tree
 type cert_conv = cterm -> thm * pss_tree
 
 
     (* Some useful derived rules *)
 fun deduct_antisym_rule tha thb =
     Thm.equal_intr (Thm.implies_intr (Thm.cprop_of thb) tha)
      (Thm.implies_intr (Thm.cprop_of tha) thb);
 
 fun prove_hyp tha thb =
   if exists (curry op aconv (Thm.concl_of tha)) (Thm.hyps_of thb)  (* FIXME !? *)
   then Thm.equal_elim (Thm.symmetric (deduct_antisym_rule tha thb)) tha else thb;
 
 val pth = @{lemma "(((x::real) < y) \<equiv> (y - x > 0))" and "((x \<le> y) \<equiv> (y - x \<ge> 0))" and
      "((x = y) \<equiv> (x - y = 0))" and "((\<not>(x < y)) \<equiv> (x - y \<ge> 0))" and
      "((\<not>(x \<le> y)) \<equiv> (x - y > 0))" and "((\<not>(x = y)) \<equiv> (x - y > 0 \<or> -(x - y) > 0))"
   by (atomize (full), auto simp add: less_diff_eq le_diff_eq not_less)};
 
 val pth_final = @{lemma "(\<not>p \<Longrightarrow> False) \<Longrightarrow> p" by blast}
 val pth_add =
   @{lemma "(x = (0::real) \<Longrightarrow> y = 0 \<Longrightarrow> x + y = 0 )" and "( x = 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x + y \<ge> 0)" and
     "(x = 0 \<Longrightarrow> y > 0 \<Longrightarrow> x + y > 0)" and "(x \<ge> 0 \<Longrightarrow> y = 0 \<Longrightarrow> x + y \<ge> 0)" and
     "(x \<ge> 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x + y \<ge> 0)" and "(x \<ge> 0 \<Longrightarrow> y > 0 \<Longrightarrow> x + y > 0)" and
     "(x > 0 \<Longrightarrow> y = 0 \<Longrightarrow> x + y > 0)" and "(x > 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x + y > 0)" and
     "(x > 0 \<Longrightarrow> y > 0 \<Longrightarrow> x + y > 0)" by simp_all};
 
 val pth_mul =
   @{lemma "(x = (0::real) \<Longrightarrow> y = 0 \<Longrightarrow> x * y = 0)" and "(x = 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x * y = 0)" and
     "(x = 0 \<Longrightarrow> y > 0 \<Longrightarrow> x * y = 0)" and "(x \<ge> 0 \<Longrightarrow> y = 0 \<Longrightarrow> x * y = 0)" and
     "(x \<ge> 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x * y \<ge> 0)" and "(x \<ge> 0 \<Longrightarrow> y > 0 \<Longrightarrow> x * y \<ge> 0)" and
     "(x > 0 \<Longrightarrow>  y = 0 \<Longrightarrow> x * y = 0)" and "(x > 0 \<Longrightarrow> y \<ge> 0 \<Longrightarrow> x * y \<ge> 0)" and
     "(x > 0 \<Longrightarrow>  y > 0 \<Longrightarrow> x * y > 0)"
   by (auto intro: mult_mono[where a="0::real" and b="x" and d="y" and c="0", simplified]
     mult_strict_mono[where b="x" and d="y" and a="0" and c="0", simplified])};
 
 val pth_emul = @{lemma "y = (0::real) \<Longrightarrow> x * y = 0"  by simp};
 val pth_square = @{lemma "x * x \<ge> (0::real)"  by simp};
 
 val weak_dnf_simps =
   List.take (@{thms simp_thms}, 34) @
     @{lemma "((P \<and> (Q \<or> R)) = ((P\<and>Q) \<or> (P\<and>R)))" and "((Q \<or> R) \<and> P) = ((Q\<and>P) \<or> (R\<and>P))" and
       "(P \<and> Q) = (Q \<and> P)" and "((P \<or> Q) = (Q \<or> P))" by blast+};
 
 (*
 val nnfD_simps =
   @{lemma "((~(P & Q)) = (~P | ~Q))" and "((~(P | Q)) = (~P & ~Q) )" and
     "((P --> Q) = (~P | Q) )" and "((P = Q) = ((P & Q) | (~P & ~ Q)))" and
     "((~(P = Q)) = ((P & ~ Q) | (~P & Q)) )" and "((~ ~(P)) = P)" by blast+};
 *)
 
 val choice_iff = @{lemma "(\<forall>x. \<exists>y. P x y) = (\<exists>f. \<forall>x. P x (f x))" by metis};
 val prenex_simps =
   map (fn th => th RS sym)
     ([@{thm "all_conj_distrib"}, @{thm "ex_disj_distrib"}] @
       @{thms "HOL.all_simps"(1-4)} @ @{thms "ex_simps"(1-4)});
 
 val real_abs_thms1 = @{lemma
   "((-1 * \<bar>x::real\<bar> \<ge> r) = (-1 * x \<ge> r \<and> 1 * x \<ge> r))" and
   "((-1 * \<bar>x\<bar> + a \<ge> r) = (a + -1 * x \<ge> r \<and> a + 1 * x \<ge> r))" and
   "((a + -1 * \<bar>x\<bar> \<ge> r) = (a + -1 * x \<ge> r \<and> a + 1 * x \<ge> r))" and
   "((a + -1 * \<bar>x\<bar> + b \<ge> r) = (a + -1 * x + b \<ge> r \<and> a + 1 * x + b \<ge> r))" and
   "((a + b + -1 * \<bar>x\<bar> \<ge> r) = (a + b + -1 * x \<ge> r \<and> a + b + 1 * x \<ge> r))" and
   "((a + b + -1 * \<bar>x\<bar> + c \<ge> r) = (a + b + -1 * x + c \<ge> r \<and> a + b + 1 * x + c \<ge> r))" and
   "((-1 * max x y \<ge> r) = (-1 * x \<ge> r \<and> -1 * y \<ge> r))" and
   "((-1 * max x y + a \<ge> r) = (a + -1 * x \<ge> r \<and> a + -1 * y \<ge> r))" and
   "((a + -1 * max x y \<ge> r) = (a + -1 * x \<ge> r \<and> a + -1 * y \<ge> r))" and
   "((a + -1 * max x y + b \<ge> r) = (a + -1 * x + b \<ge> r \<and> a + -1 * y  + b \<ge> r))" and
   "((a + b + -1 * max x y \<ge> r) = (a + b + -1 * x \<ge> r \<and> a + b + -1 * y \<ge> r))" and
   "((a + b + -1 * max x y + c \<ge> r) = (a + b + -1 * x + c \<ge> r \<and> a + b + -1 * y  + c \<ge> r))" and
   "((1 * min x y \<ge> r) = (1 * x \<ge> r \<and> 1 * y \<ge> r))" and
   "((1 * min x y + a \<ge> r) = (a + 1 * x \<ge> r \<and> a + 1 * y \<ge> r))" and
   "((a + 1 * min x y \<ge> r) = (a + 1 * x \<ge> r \<and> a + 1 * y \<ge> r))" and
   "((a + 1 * min x y + b \<ge> r) = (a + 1 * x + b \<ge> r \<and> a + 1 * y  + b \<ge> r))" and
   "((a + b + 1 * min x y \<ge> r) = (a + b + 1 * x \<ge> r \<and> a + b + 1 * y \<ge> r))" and
   "((a + b + 1 * min x y + c \<ge> r) = (a + b + 1 * x + c \<ge> r \<and> a + b + 1 * y  + c \<ge> r))" and
   "((min x y \<ge> r) = (x \<ge> r \<and> y \<ge> r))" and
   "((min x y + a \<ge> r) = (a + x \<ge> r \<and> a + y \<ge> r))" and
   "((a + min x y \<ge> r) = (a + x \<ge> r \<and> a + y \<ge> r))" and
   "((a + min x y + b \<ge> r) = (a + x + b \<ge> r \<and> a + y  + b \<ge> r))" and
   "((a + b + min x y \<ge> r) = (a + b + x \<ge> r \<and> a + b + y \<ge> r))" and
   "((a + b + min x y + c \<ge> r) = (a + b + x + c \<ge> r \<and> a + b + y + c \<ge> r))" and
   "((-1 * \<bar>x\<bar> > r) = (-1 * x > r \<and> 1 * x > r))" and
   "((-1 * \<bar>x\<bar> + a > r) = (a + -1 * x > r \<and> a + 1 * x > r))" and
   "((a + -1 * \<bar>x\<bar> > r) = (a + -1 * x > r \<and> a + 1 * x > r))" and
   "((a + -1 * \<bar>x\<bar> + b > r) = (a + -1 * x + b > r \<and> a + 1 * x + b > r))" and
   "((a + b + -1 * \<bar>x\<bar> > r) = (a + b + -1 * x > r \<and> a + b + 1 * x > r))" and
   "((a + b + -1 * \<bar>x\<bar> + c > r) = (a + b + -1 * x + c > r \<and> a + b + 1 * x + c > r))" and
   "((-1 * max x y > r) = ((-1 * x > r) \<and> -1 * y > r))" and
   "((-1 * max x y + a > r) = (a + -1 * x > r \<and> a + -1 * y > r))" and
   "((a + -1 * max x y > r) = (a + -1 * x > r \<and> a + -1 * y > r))" and
   "((a + -1 * max x y + b > r) = (a + -1 * x + b > r \<and> a + -1 * y  + b > r))" and
   "((a + b + -1 * max x y > r) = (a + b + -1 * x > r \<and> a + b + -1 * y > r))" and
   "((a + b + -1 * max x y + c > r) = (a + b + -1 * x + c > r \<and> a + b + -1 * y  + c > r))" and
   "((min x y > r) = (x > r \<and> y > r))" and
   "((min x y + a > r) = (a + x > r \<and> a + y > r))" and
   "((a + min x y > r) = (a + x > r \<and> a + y > r))" and
   "((a + min x y + b > r) = (a + x + b > r \<and> a + y  + b > r))" and
   "((a + b + min x y > r) = (a + b + x > r \<and> a + b + y > r))" and
   "((a + b + min x y + c > r) = (a + b + x + c > r \<and> a + b + y + c > r))"
   by auto};
 
 val abs_split' = @{lemma "P \<bar>x::'a::linordered_idom\<bar> == (x \<ge> 0 \<and> P x \<or> x < 0 \<and> P (-x))"
   by (atomize (full)) (auto split: abs_split)};
 
 val max_split = @{lemma "P (max x y) \<equiv> ((x::'a::linorder) \<le> y \<and> P y \<or> x > y \<and> P x)"
   by (atomize (full)) (cases "x \<le> y", auto simp add: max_def)};
 
 val min_split = @{lemma "P (min x y) \<equiv> ((x::'a::linorder) \<le> y \<and> P x \<or> x > y \<and> P y)"
   by (atomize (full)) (cases "x \<le> y", auto simp add: min_def)};
 
 
          (* Miscellaneous *)
 fun literals_conv bops uops cv =
   let
     fun h t =
       (case Thm.term_of t of
         b$_$_ => if member (op aconv) bops b then binop_conv h t else cv t
       | u$_ => if member (op aconv) uops u then arg_conv h t else cv t
       | _ => cv t)
   in h end;
 
 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 \<Rightarrow> _\<close>
-      (Numeral.mk_cnumber \<^ctyp>\<open>real\<close> a))
-      (Numeral.mk_cnumber \<^ctyp>\<open>real\<close> b)
+    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 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_>\<open>divide _ for a b\<close> => Rat.make(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
   | _ => Rat.of_int (HOLogic.dest_number (Thm.term_of t) |> snd)
 fun is_ratconst t = can dest_ratconst t
 
 (*
 fun find_term p t = if p t then t else
  case t of
   a$b => (find_term p a handle TERM _ => find_term p b)
  | Abs (_,_,t') => find_term p t'
  | _ => raise TERM ("find_term",[t]);
 *)
 
 fun find_cterm p t =
   if p t then t else
   case Thm.term_of t of
     _$_ => (find_cterm p (Thm.dest_fun t) handle CTERM _ => find_cterm p (Thm.dest_arg t))
   | Abs (_,_,_) => find_cterm p (Thm.dest_abs_global t |> snd)
   | _ => raise CTERM ("find_cterm",[t]);
 
 fun is_comb t = (case Thm.term_of t of _ $ _ => true | _ => false);
 
 fun is_binop ct ct' = ct aconvc (Thm.dest_fun (Thm.dest_fun ct'))
   handle CTERM _ => false;
 
 
 (* Map back polynomials to HOL.                         *)
 
-fun cterm_of_varpow x k = if k = 1 then x else Thm.apply (Thm.apply \<^cterm>\<open>(^) :: real \<Rightarrow> _\<close> x)
-  (Numeral.mk_cnumber \<^ctyp>\<open>nat\<close> k)
+fun cterm_of_varpow x k =
+  if k = 1 then x
+  else \<^instantiate>\<open>x and k = \<open>Numeral.mk_cnumber \<^ctyp>\<open>nat\<close> k\<close> in cterm "x ^ k" for x :: real\<close>
 
 fun cterm_of_monomial m =
   if FuncUtil.Ctermfunc.is_empty m then \<^cterm>\<open>1::real\<close>
   else
     let
       val m' = FuncUtil.dest_monomial m
       val vps = fold_rev (fn (x,k) => cons (cterm_of_varpow x k)) m' []
-    in foldr1 (fn (s, t) => Thm.apply (Thm.apply \<^cterm>\<open>(*) :: real \<Rightarrow> _\<close> s) t) vps
+    in foldr1 (fn (s, t) => \<^instantiate>\<open>s and t in cterm "s * t" for s t :: real\<close>) vps
     end
 
 fun cterm_of_cmonomial (m,c) =
   if FuncUtil.Ctermfunc.is_empty m then cterm_of_rat c
   else if c = @1 then cterm_of_monomial m
-  else Thm.apply (Thm.apply \<^cterm>\<open>(*)::real \<Rightarrow> _\<close> (cterm_of_rat c)) (cterm_of_monomial m);
+  else \<^instantiate>\<open>x = \<open>cterm_of_rat c\<close> and y = \<open>cterm_of_monomial m\<close> in cterm "x * y" for x y :: real\<close>;
 
 fun cterm_of_poly p =
   if FuncUtil.Monomialfunc.is_empty p then \<^cterm>\<open>0::real\<close>
   else
     let
       val cms = map cterm_of_cmonomial
         (sort (prod_ord FuncUtil.monomial_order (K EQUAL)) (FuncUtil.Monomialfunc.dest p))
-    in foldr1 (fn (t1, t2) => Thm.apply(Thm.apply \<^cterm>\<open>(+) :: real \<Rightarrow> _\<close> t1) t2) cms
+    in foldr1 (fn (t1, t2) => \<^instantiate>\<open>t1 and t2 in cterm "t1 + t2" for t1 t2 :: real\<close>) cms
     end;
 
 (* A general real arithmetic prover *)
 
 fun gen_gen_real_arith ctxt (mk_numeric,
        numeric_eq_conv,numeric_ge_conv,numeric_gt_conv,
        poly_conv,poly_neg_conv,poly_add_conv,poly_mul_conv,
        absconv1,absconv2,prover) =
   let
     val pre_ss = put_simpset HOL_basic_ss ctxt addsimps
       @{thms simp_thms ex_simps all_simps not_all not_ex ex_disj_distrib
           all_conj_distrib if_bool_eq_disj}
     val prenex_ss = put_simpset HOL_basic_ss ctxt addsimps prenex_simps
     val skolemize_ss = put_simpset HOL_basic_ss ctxt addsimps [choice_iff]
     val presimp_conv = Simplifier.rewrite pre_ss
     val prenex_conv = Simplifier.rewrite prenex_ss
     val skolemize_conv = Simplifier.rewrite skolemize_ss
     val weak_dnf_ss = put_simpset HOL_basic_ss ctxt addsimps weak_dnf_simps
     val weak_dnf_conv = Simplifier.rewrite weak_dnf_ss
     fun eqT_elim th = Thm.equal_elim (Thm.symmetric th) @{thm TrueI}
     fun oprconv cv ct =
       let val g = Thm.dest_fun2 ct
       in if g aconvc \<^cterm>\<open>(\<le>) :: real \<Rightarrow> _\<close>
             orelse g aconvc \<^cterm>\<open>(<) :: real \<Rightarrow> _\<close>
          then arg_conv cv ct else arg1_conv cv ct
       end
 
     fun real_ineq_conv th ct =
       let
         val th' = (Thm.instantiate (Thm.match (Thm.lhs_of th, ct)) th
           handle Pattern.MATCH => raise CTERM ("real_ineq_conv", [ct]))
       in Thm.transitive th' (oprconv poly_conv (Thm.rhs_of th'))
       end
     val [real_lt_conv, real_le_conv, real_eq_conv,
          real_not_lt_conv, real_not_le_conv, _] =
          map real_ineq_conv pth
     fun match_mp_rule ths ths' =
       let
         fun f ths ths' = case ths of [] => raise THM("match_mp_rule",0,ths)
           | th::ths => (ths' MRS th handle THM _ => f ths ths')
       in f ths ths' end
     fun mul_rule th th' = fconv_rule (arg_conv (oprconv poly_mul_conv))
          (match_mp_rule pth_mul [th, th'])
     fun add_rule th th' = fconv_rule (arg_conv (oprconv poly_add_conv))
          (match_mp_rule pth_add [th, th'])
     fun emul_rule ct th = fconv_rule (arg_conv (oprconv poly_mul_conv))
        (Thm.instantiate' [] [SOME ct] (th RS pth_emul))
     fun square_rule t = fconv_rule (arg_conv (oprconv poly_conv))
        (Thm.instantiate' [] [SOME t] pth_square)
 
     fun hol_of_positivstellensatz(eqs,les,lts) proof =
       let
         fun translate prf =
           case prf of
             Axiom_eq n => nth eqs n
           | Axiom_le n => nth les n
           | Axiom_lt n => nth lts n
-          | Rational_eq x => eqT_elim(numeric_eq_conv(Thm.apply \<^cterm>\<open>Trueprop\<close>
-                          (Thm.apply (Thm.apply \<^cterm>\<open>(=)::real \<Rightarrow> _\<close> (mk_numeric x))
-                               \<^cterm>\<open>0::real\<close>)))
-          | Rational_le x => eqT_elim(numeric_ge_conv(Thm.apply \<^cterm>\<open>Trueprop\<close>
-                          (Thm.apply (Thm.apply \<^cterm>\<open>(\<le>)::real \<Rightarrow> _\<close>
-                                     \<^cterm>\<open>0::real\<close>) (mk_numeric x))))
-          | Rational_lt x => eqT_elim(numeric_gt_conv(Thm.apply \<^cterm>\<open>Trueprop\<close>
-                      (Thm.apply (Thm.apply \<^cterm>\<open>(<)::real \<Rightarrow> _\<close> \<^cterm>\<open>0::real\<close>)
-                        (mk_numeric x))))
+          | Rational_eq x =>
+              eqT_elim (numeric_eq_conv
+                \<^instantiate>\<open>x = \<open>mk_numeric x\<close> in cprop "x = 0" for x :: real\<close>)
+          | Rational_le x =>
+              eqT_elim (numeric_ge_conv
+                \<^instantiate>\<open>x = \<open>mk_numeric x\<close> in cprop "x \<ge> 0" for x :: real\<close>)
+          | Rational_lt x =>
+              eqT_elim (numeric_gt_conv
+                \<^instantiate>\<open>x = \<open>mk_numeric x\<close> in cprop "x > 0" for x :: real\<close>)
           | Square pt => square_rule (cterm_of_poly pt)
           | Eqmul(pt,p) => emul_rule (cterm_of_poly pt) (translate p)
           | Sum(p1,p2) => add_rule (translate p1) (translate p2)
           | Product(p1,p2) => mul_rule (translate p1) (translate p2)
       in fconv_rule (first_conv [numeric_ge_conv, numeric_gt_conv, numeric_eq_conv, all_conv])
           (translate proof)
       end
 
     val init_conv = presimp_conv then_conv
         nnf_conv ctxt then_conv skolemize_conv then_conv prenex_conv then_conv
         weak_dnf_conv
 
     val concl = Thm.dest_arg o Thm.cprop_of
     fun is_binop opr ct = (Thm.dest_fun2 ct aconvc opr handle CTERM _ => false)
     val is_req = is_binop \<^cterm>\<open>(=):: real \<Rightarrow> _\<close>
     val is_ge = is_binop \<^cterm>\<open>(\<le>):: real \<Rightarrow> _\<close>
     val is_gt = is_binop \<^cterm>\<open>(<):: real \<Rightarrow> _\<close>
     val is_conj = is_binop \<^cterm>\<open>HOL.conj\<close>
     val is_disj = is_binop \<^cterm>\<open>HOL.disj\<close>
     fun conj_pair th = (th RS @{thm conjunct1}, th RS @{thm conjunct2})
     fun disj_cases th th1 th2 =
       let
         val (p,q) = Thm.dest_binop (concl th)
         val c = concl th1
         val _ =
           if c aconvc (concl th2) then ()
           else error "disj_cases : conclusions not alpha convertible"
       in Thm.implies_elim (Thm.implies_elim
           (Thm.implies_elim (Thm.instantiate' [] (map SOME [p,q,c]) @{thm disjE}) th)
-          (Thm.implies_intr (Thm.apply \<^cterm>\<open>Trueprop\<close> p) th1))
-        (Thm.implies_intr (Thm.apply \<^cterm>\<open>Trueprop\<close> q) th2)
+          (Thm.implies_intr \<^instantiate>\<open>p in cprop p\<close> th1))
+        (Thm.implies_intr \<^instantiate>\<open>q in cprop q\<close> th2)
       end
     fun overall cert_choice dun ths =
       case ths of
         [] =>
         let
           val (eq,ne) = List.partition (is_req o concl) dun
           val (le,nl) = List.partition (is_ge o concl) ne
           val lt = filter (is_gt o concl) nl
         in prover (rev cert_choice) hol_of_positivstellensatz (eq,le,lt) end
       | th::oths =>
         let
           val ct = concl th
         in
           if is_conj ct then
             let
               val (th1,th2) = conj_pair th
             in overall cert_choice dun (th1::th2::oths) end
           else if is_disj ct then
             let
               val (th1, cert1) =
                 overall (Left::cert_choice) dun
                   (Thm.assume (Thm.apply \<^cterm>\<open>Trueprop\<close> (Thm.dest_arg1 ct))::oths)
               val (th2, cert2) =
                 overall (Right::cert_choice) dun
                   (Thm.assume (Thm.apply \<^cterm>\<open>Trueprop\<close> (Thm.dest_arg ct))::oths)
             in (disj_cases th th1 th2, Branch (cert1, cert2)) end
           else overall cert_choice (th::dun) oths
         end
     fun dest_binary b ct =
         if is_binop b ct then Thm.dest_binop ct
         else raise CTERM ("dest_binary",[b,ct])
     val dest_eq = dest_binary \<^cterm>\<open>(=) :: real \<Rightarrow> _\<close>
     val neq_th = nth pth 5
     fun real_not_eq_conv ct =
       let
         val (l,r) = dest_eq (Thm.dest_arg ct)
         val th = Thm.instantiate (TVars.empty, Vars.make [(\<^var>\<open>?x::real\<close>,l),(\<^var>\<open>?y::real\<close>,r)]) neq_th
         val th_p = poly_conv(Thm.dest_arg(Thm.dest_arg1(Thm.rhs_of th)))
         val th_x = Drule.arg_cong_rule \<^cterm>\<open>uminus :: real \<Rightarrow> _\<close> th_p
         val th_n = fconv_rule (arg_conv poly_neg_conv) th_x
         val th' = Drule.binop_cong_rule \<^cterm>\<open>HOL.disj\<close>
-          (Drule.arg_cong_rule (Thm.apply \<^cterm>\<open>(<)::real \<Rightarrow> _\<close> \<^cterm>\<open>0::real\<close>) th_p)
-          (Drule.arg_cong_rule (Thm.apply \<^cterm>\<open>(<)::real \<Rightarrow> _\<close> \<^cterm>\<open>0::real\<close>) th_n)
+          (Drule.arg_cong_rule \<^cterm>\<open>(<) (0::real)\<close> th_p)
+          (Drule.arg_cong_rule \<^cterm>\<open>(<) (0::real)\<close> th_n)
       in Thm.transitive th th'
       end
     fun equal_implies_1_rule PQ =
       let
         val P = Thm.lhs_of PQ
       in Thm.implies_intr P (Thm.equal_elim PQ (Thm.assume P))
       end
     (*FIXME!!! Copied from groebner.ml*)
     val strip_exists =
       let
         fun h (acc, t) =
           case Thm.term_of t of
-            Const(\<^const_name>\<open>Ex\<close>,_)$Abs(_,_,_) =>
+            \<^Const_>\<open>Ex _ for \<open>Abs _\<close>\<close> =>
               h (Thm.dest_abs_global (Thm.dest_arg t) |>> (fn v => v::acc))
           | _ => (acc,t)
       in fn t => h ([],t)
       end
     fun name_of x =
       case Thm.term_of x of
         Free(s,_) => s
       | Var ((s,_),_) => s
       | _ => "x"
 
     fun mk_forall x th =
       let
-        val T = Thm.typ_of_cterm x
-        val all = Thm.cterm_of ctxt (Const (\<^const_name>\<open>All\<close>, (T --> \<^typ>\<open>bool\<close>) --> \<^typ>\<open>bool\<close>))
+        val T = Thm.ctyp_of_cterm x
+        val all = \<^instantiate>\<open>'a = T in cterm All\<close>
       in Drule.arg_cong_rule all (Thm.abstract_rule (name_of x) x th) end
 
     val specl = fold_rev (fn x => fn th => Thm.instantiate' [] [SOME x] (th RS spec));
 
-    fun ext T = Thm.cterm_of ctxt (Const (\<^const_name>\<open>Ex\<close>, (T --> \<^typ>\<open>bool\<close>) --> \<^typ>\<open>bool\<close>))
-    fun mk_ex v t = Thm.apply (ext (Thm.typ_of_cterm v)) (Thm.lambda v t)
+    fun mk_ex v t =
+      \<^instantiate>\<open>'a = \<open>Thm.ctyp_of_cterm v\<close> and P = \<open>Thm.lambda v t\<close>
+        in cprop "Ex P" for P :: "'a \<Rightarrow> bool"\<close>
 
     fun choose v th th' =
       case Thm.concl_of th of
-        \<^term>\<open>Trueprop\<close> $ (Const(\<^const_name>\<open>Ex\<close>,_)$_) =>
-        let
-          val p = (funpow 2 Thm.dest_arg o Thm.cprop_of) th
-          val T = Thm.dest_ctyp0 (Thm.ctyp_of_cterm p)
-          val th0 = fconv_rule (Thm.beta_conversion true)
-            (Thm.instantiate' [SOME T] [SOME p, (SOME o Thm.dest_arg o Thm.cprop_of) th'] exE)
-          val pv = (Thm.rhs_of o Thm.beta_conversion true)
-            (Thm.apply \<^cterm>\<open>Trueprop\<close> (Thm.apply p v))
-          val th1 = Thm.forall_intr v (Thm.implies_intr pv th')
-        in Thm.implies_elim (Thm.implies_elim th0 th) th1  end
+        \<^Const_>\<open>Trueprop for \<^Const_>\<open>Ex _ for _\<close>\<close> =>
+          let
+            val p = (funpow 2 Thm.dest_arg o Thm.cprop_of) th
+            val T = Thm.dest_ctyp0 (Thm.ctyp_of_cterm p)
+            val th0 = fconv_rule (Thm.beta_conversion true)
+              (Thm.instantiate' [SOME T] [SOME p, (SOME o Thm.dest_arg o Thm.cprop_of) th'] exE)
+            val pv = (Thm.rhs_of o Thm.beta_conversion true)
+              (Thm.apply \<^cterm>\<open>Trueprop\<close> (Thm.apply p v))
+            val th1 = Thm.forall_intr v (Thm.implies_intr pv th')
+          in Thm.implies_elim (Thm.implies_elim th0 th) th1  end
       | _ => raise THM ("choose",0,[th, th'])
 
     fun simple_choose v th =
-      choose v
-        (Thm.assume
-          ((Thm.apply \<^cterm>\<open>Trueprop\<close> o mk_ex v) (Thm.dest_arg (hd (Thm.chyps_of th))))) th
+      choose v (Thm.assume (mk_ex v (Thm.dest_arg (hd (Thm.chyps_of th))))) th
 
     val strip_forall =
       let
         fun h (acc, t) =
           case Thm.term_of t of
-            Const(\<^const_name>\<open>All\<close>,_)$Abs(_,_,_) =>
+            \<^Const_>\<open>All _ for \<open>Abs _\<close>\<close> =>
               h (Thm.dest_abs_global (Thm.dest_arg t) |>> (fn v => v::acc))
           | _ => (acc,t)
       in fn t => h ([],t)
       end
 
     fun f ct =
       let
         val nnf_norm_conv' =
           nnf_conv ctxt then_conv
           literals_conv [\<^term>\<open>HOL.conj\<close>, \<^term>\<open>HOL.disj\<close>] []
           (Conv.cache_conv
             (first_conv [real_lt_conv, real_le_conv,
                          real_eq_conv, real_not_lt_conv,
                          real_not_le_conv, real_not_eq_conv, all_conv]))
         fun absremover ct = (literals_conv [\<^term>\<open>HOL.conj\<close>, \<^term>\<open>HOL.disj\<close>] []
                   (try_conv (absconv1 then_conv binop_conv (arg_conv poly_conv))) then_conv
                   try_conv (absconv2 then_conv nnf_norm_conv' then_conv binop_conv absremover)) ct
-        val nct = Thm.apply \<^cterm>\<open>Trueprop\<close> (Thm.apply \<^cterm>\<open>Not\<close> ct)
+        val nct = \<^instantiate>\<open>ct in cprop "\<not> ct"\<close>
         val th0 = (init_conv then_conv arg_conv nnf_norm_conv') nct
         val tm0 = Thm.dest_arg (Thm.rhs_of th0)
         val (th, certificates) =
           if tm0 aconvc \<^cterm>\<open>False\<close> then (equal_implies_1_rule th0, Trivial) else
           let
             val (evs,bod) = strip_exists tm0
             val (avs,ibod) = strip_forall bod
             val th1 = Drule.arg_cong_rule \<^cterm>\<open>Trueprop\<close> (fold mk_forall avs (absremover ibod))
             val (th2, certs) = overall [] [] [specl avs (Thm.assume (Thm.rhs_of th1))]
             val th3 =
               fold simple_choose evs
                 (prove_hyp (Thm.equal_elim th1 (Thm.assume (Thm.apply \<^cterm>\<open>Trueprop\<close> bod))) th2)
           in (Drule.implies_intr_hyps (prove_hyp (Thm.equal_elim th0 (Thm.assume nct)) th3), certs)
           end
       in (Thm.implies_elim (Thm.instantiate' [] [SOME ct] pth_final) th, certificates)
       end
   in f
   end;
 
 (* A linear arithmetic prover *)
 local
   val linear_add = FuncUtil.Ctermfunc.combine (curry op +) (fn z => z = @0)
   fun linear_cmul c = FuncUtil.Ctermfunc.map (fn _ => fn x => c * x)
   val one_tm = \<^cterm>\<open>1::real\<close>
   fun contradictory p (e,_) = ((FuncUtil.Ctermfunc.is_empty e) andalso not(p @0)) orelse
      ((eq_set (op aconvc) (FuncUtil.Ctermfunc.dom e, [one_tm])) andalso
        not(p(FuncUtil.Ctermfunc.apply e one_tm)))
 
   fun linear_ineqs vars (les,lts) =
     case find_first (contradictory (fn x => x > @0)) lts of
       SOME r => r
     | NONE =>
       (case find_first (contradictory (fn x => x > @0)) les of
          SOME r => r
        | NONE =>
          if null vars then error "linear_ineqs: no contradiction" else
          let
            val ineqs = les @ lts
            fun blowup v =
              length(filter (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 = @0) ineqs) +
              length(filter (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 > @0) ineqs) *
              length(filter (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 < @0) ineqs)
            val v = fst(hd(sort (fn ((_,i),(_,j)) => int_ord (i,j))
              (map (fn v => (v,blowup v)) vars)))
            fun addup (e1,p1) (e2,p2) acc =
              let
                val c1 = FuncUtil.Ctermfunc.tryapplyd e1 v @0
                val c2 = FuncUtil.Ctermfunc.tryapplyd e2 v @0
              in
                if c1 * c2 >= @0 then acc else
                let
                  val e1' = linear_cmul (abs c2) e1
                  val e2' = linear_cmul (abs c1) e2
                  val p1' = Product(Rational_lt (abs c2), p1)
                  val p2' = Product(Rational_lt (abs c1), p2)
                in (linear_add e1' e2',Sum(p1',p2'))::acc
                end
              end
            val (les0,les1) =
              List.partition (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 = @0) les
            val (lts0,lts1) =
              List.partition (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 = @0) lts
            val (lesp,lesn) =
              List.partition (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 > @0) les1
            val (ltsp,ltsn) =
              List.partition (fn (e,_) => FuncUtil.Ctermfunc.tryapplyd e v @0 > @0) lts1
            val les' = fold_rev (fn ep1 => fold_rev (addup ep1) lesp) lesn les0
            val lts' = fold_rev (fn ep1 => fold_rev (addup ep1) (lesp@ltsp)) ltsn
                       (fold_rev (fn ep1 => fold_rev (addup ep1) (lesn@ltsn)) ltsp lts0)
          in linear_ineqs (remove (op aconvc) v vars) (les',lts')
          end)
 
   fun linear_eqs(eqs,les,lts) =
     case find_first (contradictory (fn x => x = @0)) eqs of
       SOME r => r
     | NONE =>
       (case eqs of
          [] =>
          let val vars = remove (op aconvc) one_tm
              (fold_rev (union (op aconvc) o FuncUtil.Ctermfunc.dom o fst) (les@lts) [])
          in linear_ineqs vars (les,lts) end
        | (e,p)::es =>
          if FuncUtil.Ctermfunc.is_empty e then linear_eqs (es,les,lts) else
          let
            val (x,c) = FuncUtil.Ctermfunc.choose (FuncUtil.Ctermfunc.delete_safe one_tm e)
            fun xform (inp as (t,q)) =
              let val d = FuncUtil.Ctermfunc.tryapplyd t x @0 in
                if d = @0 then inp else
                let
                  val k = ~ d * abs c / c
                  val e' = linear_cmul k e
                  val t' = linear_cmul (abs c) t
                  val p' = Eqmul(FuncUtil.Monomialfunc.onefunc (FuncUtil.Ctermfunc.empty, k),p)
                  val q' = Product(Rational_lt (abs c), q)
                in (linear_add e' t',Sum(p',q'))
                end
              end
          in linear_eqs(map xform es,map xform les,map xform lts)
          end)
 
   fun linear_prover (eq,le,lt) =
     let
       val eqs = map_index (fn (n, p) => (p,Axiom_eq n)) eq
       val les = map_index (fn (n, p) => (p,Axiom_le n)) le
       val lts = map_index (fn (n, p) => (p,Axiom_lt n)) lt
     in linear_eqs(eqs,les,lts)
     end
 
   fun lin_of_hol ct =
     if ct aconvc \<^cterm>\<open>0::real\<close> then FuncUtil.Ctermfunc.empty
     else if not (is_comb ct) then FuncUtil.Ctermfunc.onefunc (ct, @1)
     else if is_ratconst ct then FuncUtil.Ctermfunc.onefunc (one_tm, dest_ratconst ct)
     else
       let val (lop,r) = Thm.dest_comb ct
       in
         if not (is_comb lop) then FuncUtil.Ctermfunc.onefunc (ct, @1)
         else
           let val (opr,l) = Thm.dest_comb lop
           in
             if opr aconvc \<^cterm>\<open>(+) :: real \<Rightarrow> _\<close>
             then linear_add (lin_of_hol l) (lin_of_hol r)
             else if opr aconvc \<^cterm>\<open>(*) :: real \<Rightarrow> _\<close>
                     andalso is_ratconst l then FuncUtil.Ctermfunc.onefunc (r, dest_ratconst l)
             else FuncUtil.Ctermfunc.onefunc (ct, @1)
           end
       end
 
   fun is_alien ct =
     case Thm.term_of ct of
-      Const(\<^const_name>\<open>of_nat\<close>, _)$ n => not (can HOLogic.dest_number n)
-    | Const(\<^const_name>\<open>of_int\<close>, _)$ n => not (can HOLogic.dest_number n)
+      \<^Const_>\<open>of_nat _ for n\<close> => not (can HOLogic.dest_number n)
+    | \<^Const_>\<open>of_int _ for n\<close> => not (can HOLogic.dest_number n)
     | _ => false
 in
 fun real_linear_prover translator (eq,le,lt) =
   let
     val lhs = lin_of_hol o Thm.dest_arg1 o Thm.dest_arg o Thm.cprop_of
     val rhs = lin_of_hol o Thm.dest_arg o Thm.dest_arg o Thm.cprop_of
     val eq_pols = map lhs eq
     val le_pols = map rhs le
     val lt_pols = map rhs lt
     val aliens = filter is_alien
       (fold_rev (union (op aconvc) o FuncUtil.Ctermfunc.dom)
                 (eq_pols @ le_pols @ lt_pols) [])
     val le_pols' = le_pols @ map (fn v => FuncUtil.Ctermfunc.onefunc (v,@1)) aliens
     val (_,proof) = linear_prover (eq_pols,le_pols',lt_pols)
     val le' = le @ map (fn a => Thm.instantiate' [] [SOME (Thm.dest_arg a)] @{thm of_nat_0_le_iff}) aliens
   in ((translator (eq,le',lt) proof), Trivial)
   end
 end;
 
 (* A less general generic arithmetic prover dealing with abs,max and min*)
 
 local
   val absmaxmin_elim_ss1 =
     simpset_of (put_simpset HOL_basic_ss \<^context> addsimps real_abs_thms1)
   fun absmaxmin_elim_conv1 ctxt =
     Simplifier.rewrite (put_simpset absmaxmin_elim_ss1 ctxt)
 
   val absmaxmin_elim_conv2 =
     let
       val pth_abs = Thm.instantiate' [SOME \<^ctyp>\<open>real\<close>] [] abs_split'
       val pth_max = Thm.instantiate' [SOME \<^ctyp>\<open>real\<close>] [] max_split
       val pth_min = Thm.instantiate' [SOME \<^ctyp>\<open>real\<close>] [] min_split
       val abs_tm = \<^cterm>\<open>abs :: real \<Rightarrow> _\<close>
       val p_v = (("P", 0), \<^typ>\<open>real \<Rightarrow> bool\<close>)
       val x_v = (("x", 0), \<^typ>\<open>real\<close>)
       val y_v = (("y", 0), \<^typ>\<open>real\<close>)
       val is_max = is_binop \<^cterm>\<open>max :: real \<Rightarrow> _\<close>
       val is_min = is_binop \<^cterm>\<open>min :: real \<Rightarrow> _\<close>
       fun is_abs t = is_comb t andalso Thm.dest_fun t aconvc abs_tm
       fun eliminate_construct p c tm =
         let
           val t = find_cterm p tm
           val th0 = (Thm.symmetric o Thm.beta_conversion false) (Thm.apply (Thm.lambda t tm) t)
           val (p,ax) = (Thm.dest_comb o Thm.rhs_of) th0
         in fconv_rule(arg_conv(binop_conv (arg_conv (Thm.beta_conversion false))))
                      (Thm.transitive th0 (c p ax))
         end
 
       val elim_abs = eliminate_construct is_abs
         (fn p => fn ax =>
           Thm.instantiate (TVars.empty, Vars.make [(p_v,p), (x_v, Thm.dest_arg ax)]) pth_abs)
       val elim_max = eliminate_construct is_max
         (fn p => fn ax =>
           let val (ax,y) = Thm.dest_comb ax
           in Thm.instantiate (TVars.empty, Vars.make [(p_v,p), (x_v, Thm.dest_arg ax), (y_v,y)])
                              pth_max end)
       val elim_min = eliminate_construct is_min
         (fn p => fn ax =>
           let val (ax,y) = Thm.dest_comb ax
           in Thm.instantiate (TVars.empty, Vars.make [(p_v,p), (x_v, Thm.dest_arg ax), (y_v,y)])
                              pth_min end)
     in first_conv [elim_abs, elim_max, elim_min, all_conv]
     end;
 in
 fun gen_real_arith ctxt (mkconst,eq,ge,gt,norm,neg,add,mul,prover) =
   gen_gen_real_arith ctxt
     (mkconst,eq,ge,gt,norm,neg,add,mul,
      absmaxmin_elim_conv1 ctxt,absmaxmin_elim_conv2,prover)
 end;
 
 (* An instance for reals*)
 
 fun gen_prover_real_arith ctxt prover =
   let
     val {add, mul, neg, pow = _, sub = _, main} =
         Semiring_Normalizer.semiring_normalizers_ord_wrapper ctxt
         (the (Semiring_Normalizer.match ctxt \<^cterm>\<open>(0::real) + 1\<close>))
         Thm.term_ord
   in gen_real_arith ctxt
      (cterm_of_rat,
       Numeral_Simprocs.field_comp_conv ctxt,
       Numeral_Simprocs.field_comp_conv ctxt,
       Numeral_Simprocs.field_comp_conv ctxt,
       main ctxt, neg ctxt, add ctxt, mul ctxt, prover)
   end;
 
 end