diff --git a/src/ZF/arith_data.ML b/src/ZF/arith_data.ML
--- a/src/ZF/arith_data.ML
+++ b/src/ZF/arith_data.ML
@@ -1,283 +1,283 @@
 (*  Title:      ZF/arith_data.ML
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
 
 Arithmetic simplification: cancellation of common terms
 *)
 
 signature ARITH_DATA =
 sig
   (*the main outcome*)
   val nat_cancel: simproc list
   (*tools for use in similar applications*)
   val gen_trans_tac: Proof.context -> thm -> thm option -> tactic
   val prove_conv: string -> tactic list -> Proof.context -> thm list -> term * term -> thm option
   val simplify_meta_eq: thm list -> Proof.context -> thm -> thm
   (*debugging*)
   structure EqCancelNumeralsData   : CANCEL_NUMERALS_DATA
   structure LessCancelNumeralsData : CANCEL_NUMERALS_DATA
   structure DiffCancelNumeralsData : CANCEL_NUMERALS_DATA
 end;
 
 
 structure ArithData: ARITH_DATA =
 struct
 
 val iT = Ind_Syntax.iT;
 
 val zero = \<^Const>\<open>zero\<close>;
 val succ = \<^Const>\<open>succ\<close>;
 fun mk_succ t = succ $ t;
 val one = mk_succ zero;
 
-val mk_plus = FOLogic.mk_binop \<^const_name>\<open>Arith.add\<close>;
+fun mk_plus (t, u) = \<^Const>\<open>Arith.add for t u\<close>;
 
 (*Thus mk_sum[t] yields t+#0; longer sums don't have a trailing zero*)
 fun mk_sum []        = zero
   | mk_sum [t,u]     = mk_plus (t, u)
   | mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
 (*this version ALWAYS includes a trailing zero*)
 fun long_mk_sum []        = zero
   | long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
 val dest_plus = FOLogic.dest_bin \<^const_name>\<open>Arith.add\<close> iT;
 
 (* dest_sum *)
 
 fun dest_sum \<^Const_>\<open>zero\<close> = []
   | dest_sum \<^Const_>\<open>succ for t\<close> = one :: dest_sum t
   | dest_sum \<^Const_>\<open>Arith.add for t u\<close> = dest_sum t @ dest_sum u
   | dest_sum tm = [tm];
 
 (*Apply the given rewrite (if present) just once*)
 fun gen_trans_tac _ _ NONE = all_tac
   | gen_trans_tac ctxt th2 (SOME th) = ALLGOALS (resolve_tac ctxt [th RS th2]);
 
 (*Use <-> or = depending on the type of t*)
 fun mk_eq_iff(t,u) =
   if fastype_of t = iT then FOLogic.mk_eq(t,u)
                        else FOLogic.mk_iff(t,u);
 
 (*We remove equality assumptions because they confuse the simplifier and
   because only type-checking assumptions are necessary.*)
 fun is_eq_thm th =
     can FOLogic.dest_eq (FOLogic.dest_Trueprop (Thm.prop_of th));
 
 fun add_chyps chyps ct = Drule.list_implies (map Thm.cprop_of chyps, ct);
 
 fun prove_conv name tacs ctxt prems (t,u) =
   if t aconv u then NONE
   else
   let val prems' = filter_out is_eq_thm prems
       val goal = Logic.list_implies (map Thm.prop_of prems',
         FOLogic.mk_Trueprop (mk_eq_iff (t, u)));
   in SOME (prems' MRS Goal.prove ctxt [] [] goal (K (EVERY tacs)))
       handle ERROR msg =>
         (warning (msg ^ "\nCancellation failed: no typing information? (" ^ name ^ ")"); NONE)
   end;
 
 
 (*** Use CancelNumerals simproc without binary numerals,
      just for cancellation ***)
 
-val mk_times = FOLogic.mk_binop \<^const_name>\<open>Arith.mult\<close>;
+fun mk_times (t, u) = \<^Const>\<open>Arith.mult for t u\<close>;
 
 fun mk_prod [] = one
   | mk_prod [t] = t
   | mk_prod (t :: ts) = if t = one then mk_prod ts
                         else mk_times (t, mk_prod ts);
 
 val dest_times = FOLogic.dest_bin \<^const_name>\<open>Arith.mult\<close> iT;
 
 fun dest_prod t =
       let val (t,u) = dest_times t
       in  dest_prod t @ dest_prod u  end
       handle TERM _ => [t];
 
 (*Dummy version: the only arguments are 0 and 1*)
 fun mk_coeff (0, t) = zero
   | mk_coeff (1, t) = t
   | mk_coeff _       = raise TERM("mk_coeff", []);
 
 (*Dummy version: the "coefficient" is always 1.
   In the result, the factors are sorted terms*)
 fun dest_coeff t = (1, mk_prod (sort Term_Ord.term_ord (dest_prod t)));
 
 (*Find first coefficient-term THAT MATCHES u*)
 fun find_first_coeff past u [] = raise TERM("find_first_coeff", [])
   | find_first_coeff past u (t::terms) =
         let val (n,u') = dest_coeff t
         in  if u aconv u' then (n, rev past @ terms)
                           else find_first_coeff (t::past) u terms
         end
         handle TERM _ => find_first_coeff (t::past) u terms;
 
 
 (*Simplify #1*n and n*#1 to n*)
 val add_0s = [@{thm add_0_natify}, @{thm add_0_right_natify}];
 val add_succs = [@{thm add_succ}, @{thm add_succ_right}];
 val mult_1s = [@{thm mult_1_natify}, @{thm mult_1_right_natify}];
 val tc_rules = [@{thm natify_in_nat}, @{thm add_type}, @{thm diff_type}, @{thm mult_type}];
 val natifys = [@{thm natify_0}, @{thm natify_ident}, @{thm add_natify1}, @{thm add_natify2},
                @{thm diff_natify1}, @{thm diff_natify2}];
 
 (*Final simplification: cancel + and **)
 fun simplify_meta_eq rules ctxt =
   let val ctxt' =
     put_simpset FOL_ss ctxt
       delsimps @{thms iff_simps} (*these could erase the whole rule!*)
       addsimps rules
       |> fold Simplifier.add_eqcong [@{thm eq_cong2}, @{thm iff_cong2}]
   in mk_meta_eq o simplify ctxt' end;
 
 val final_rules = add_0s @ mult_1s @ [@{thm mult_0}, @{thm mult_0_right}];
 
 structure CancelNumeralsCommon =
   struct
   val mk_sum            = (fn T:typ => mk_sum)
   val dest_sum          = dest_sum
   val mk_coeff          = mk_coeff
   val dest_coeff        = dest_coeff
   val find_first_coeff  = find_first_coeff []
 
   val norm_ss1 =
     simpset_of (put_simpset ZF_ss \<^context> addsimps add_0s @ add_succs @ mult_1s @ @{thms add_ac})
   val norm_ss2 =
     simpset_of (put_simpset ZF_ss \<^context> addsimps add_0s @ mult_1s @ @{thms add_ac} @
       @{thms mult_ac} @ tc_rules @ natifys)
   fun norm_tac ctxt =
     ALLGOALS (asm_simp_tac (put_simpset norm_ss1 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss2 ctxt))
   val numeral_simp_ss =
     simpset_of (put_simpset ZF_ss \<^context> addsimps add_0s @ tc_rules @ natifys)
   fun numeral_simp_tac ctxt =
     ALLGOALS (asm_simp_tac (put_simpset numeral_simp_ss ctxt))
   val simplify_meta_eq  = simplify_meta_eq final_rules
   end;
 
 (** The functor argumnets are declared as separate structures
     so that they can be exported to ease debugging. **)
 
 structure EqCancelNumeralsData =
   struct
   open CancelNumeralsCommon
   val prove_conv = prove_conv "nateq_cancel_numerals"
   val mk_bal   = FOLogic.mk_eq
   val dest_bal = FOLogic.dest_eq
   val bal_add1 = @{thm eq_add_iff [THEN iff_trans]}
   val bal_add2 = @{thm eq_add_iff [THEN iff_trans]}
   fun trans_tac ctxt = gen_trans_tac ctxt @{thm iff_trans}
   end;
 
 structure EqCancelNumerals = CancelNumeralsFun(EqCancelNumeralsData);
 
 structure LessCancelNumeralsData =
   struct
   open CancelNumeralsCommon
   val prove_conv = prove_conv "natless_cancel_numerals"
-  val mk_bal   = FOLogic.mk_binrel \<^const_name>\<open>Ordinal.lt\<close>
+  fun mk_bal (t, u) = \<^Const>\<open>Ordinal.lt for t u\<close>
   val dest_bal = FOLogic.dest_bin \<^const_name>\<open>Ordinal.lt\<close> iT
   val bal_add1 = @{thm less_add_iff [THEN iff_trans]}
   val bal_add2 = @{thm less_add_iff [THEN iff_trans]}
   fun trans_tac ctxt = gen_trans_tac ctxt @{thm iff_trans}
   end;
 
 structure LessCancelNumerals = CancelNumeralsFun(LessCancelNumeralsData);
 
 structure DiffCancelNumeralsData =
   struct
   open CancelNumeralsCommon
   val prove_conv = prove_conv "natdiff_cancel_numerals"
-  val mk_bal   = FOLogic.mk_binop \<^const_name>\<open>Arith.diff\<close>
+  fun mk_bal (t, u) = \<^Const>\<open>Arith.diff for t u\<close>
   val dest_bal = FOLogic.dest_bin \<^const_name>\<open>Arith.diff\<close> iT
   val bal_add1 = @{thm diff_add_eq [THEN trans]}
   val bal_add2 = @{thm diff_add_eq [THEN trans]}
   fun trans_tac ctxt = gen_trans_tac ctxt @{thm trans}
   end;
 
 structure DiffCancelNumerals = CancelNumeralsFun(DiffCancelNumeralsData);
 
 
 val nat_cancel =
  [Simplifier.make_simproc \<^context> "nateq_cancel_numerals"
    {lhss =
      [\<^term>\<open>l #+ m = n\<close>, \<^term>\<open>l = m #+ n\<close>,
       \<^term>\<open>l #* m = n\<close>, \<^term>\<open>l = m #* n\<close>,
       \<^term>\<open>succ(m) = n\<close>, \<^term>\<open>m = succ(n)\<close>],
     proc = K EqCancelNumerals.proc},
   Simplifier.make_simproc \<^context> "natless_cancel_numerals"
    {lhss =
      [\<^term>\<open>l #+ m < n\<close>, \<^term>\<open>l < m #+ n\<close>,
       \<^term>\<open>l #* m < n\<close>, \<^term>\<open>l < m #* n\<close>,
       \<^term>\<open>succ(m) < n\<close>, \<^term>\<open>m < succ(n)\<close>],
     proc = K LessCancelNumerals.proc},
   Simplifier.make_simproc \<^context> "natdiff_cancel_numerals"
    {lhss =
      [\<^term>\<open>(l #+ m) #- n\<close>, \<^term>\<open>l #- (m #+ n)\<close>,
       \<^term>\<open>(l #* m) #- n\<close>, \<^term>\<open>l #- (m #* n)\<close>,
       \<^term>\<open>succ(m) #- n\<close>, \<^term>\<open>m #- succ(n)\<close>],
     proc = K DiffCancelNumerals.proc}];
 
 end;
 
 val _ =
   Theory.setup (Simplifier.map_theory_simpset (fn ctxt =>
     ctxt addsimprocs ArithData.nat_cancel));
 
 
 (*examples:
 print_depth 22;
 set timing;
 set simp_trace;
 fun test s = (Goal s; by (Asm_simp_tac 1));
 
 test "x #+ y = x #+ z";
 test "y #+ x = x #+ z";
 test "x #+ y #+ z = x #+ z";
 test "y #+ (z #+ x) = z #+ x";
 test "x #+ y #+ z = (z #+ y) #+ (x #+ w)";
 test "x#*y #+ z = (z #+ y) #+ (y#*x #+ w)";
 
 test "x #+ succ(y) = x #+ z";
 test "x #+ succ(y) = succ(z #+ x)";
 test "succ(x) #+ succ(y) #+ z = succ(z #+ y) #+ succ(x #+ w)";
 
 test "(x #+ y) #- (x #+ z) = w";
 test "(y #+ x) #- (x #+ z) = dd";
 test "(x #+ y #+ z) #- (x #+ z) = dd";
 test "(y #+ (z #+ x)) #- (z #+ x) = dd";
 test "(x #+ y #+ z) #- ((z #+ y) #+ (x #+ w)) = dd";
 test "(x#*y #+ z) #- ((z #+ y) #+ (y#*x #+ w)) = dd";
 
 (*BAD occurrence of natify*)
 test "(x #+ succ(y)) #- (x #+ z) = dd";
 
 test "x #* y2 #+ y #* x2 = y #* x2 #+ x #* y2";
 
 test "(x #+ succ(y)) #- (succ(z #+ x)) = dd";
 test "(succ(x) #+ succ(y) #+ z) #- (succ(z #+ y) #+ succ(x #+ w)) = dd";
 
 (*use of typing information*)
 test "x : nat ==> x #+ y = x";
 test "x : nat --> x #+ y = x";
 test "x : nat ==> x #+ y < x";
 test "x : nat ==> x < y#+x";
 test "x : nat ==> x le succ(x)";
 
 (*fails: no typing information isn't visible*)
 test "x #+ y = x";
 
 test "x #+ y < x #+ z";
 test "y #+ x < x #+ z";
 test "x #+ y #+ z < x #+ z";
 test "y #+ z #+ x < x #+ z";
 test "y #+ (z #+ x) < z #+ x";
 test "x #+ y #+ z < (z #+ y) #+ (x #+ w)";
 test "x#*y #+ z < (z #+ y) #+ (y#*x #+ w)";
 
 test "x #+ succ(y) < x #+ z";
 test "x #+ succ(y) < succ(z #+ x)";
 test "succ(x) #+ succ(y) #+ z < succ(z #+ y) #+ succ(x #+ w)";
 
 test "x #+ succ(y) le succ(z #+ x)";
 *)
diff --git a/src/ZF/int_arith.ML b/src/ZF/int_arith.ML
--- a/src/ZF/int_arith.ML
+++ b/src/ZF/int_arith.ML
@@ -1,327 +1,327 @@
 (*  Title:      ZF/int_arith.ML
     Author:     Larry Paulson
 
 Simprocs for linear arithmetic.
 *)
 
 signature INT_NUMERAL_SIMPROCS =
 sig
   val cancel_numerals: simproc list
   val combine_numerals: simproc
   val combine_numerals_prod: simproc
 end
 
 structure Int_Numeral_Simprocs: INT_NUMERAL_SIMPROCS =
 struct
 
 (* abstract syntax operations *)
 
 fun mk_bit 0 = \<^term>\<open>0\<close>
   | mk_bit 1 = \<^term>\<open>succ(0)\<close>
   | mk_bit _ = raise TERM ("mk_bit", []);
 
 fun dest_bit \<^term>\<open>0\<close> = 0
   | dest_bit \<^term>\<open>succ(0)\<close> = 1
   | dest_bit t = raise TERM ("dest_bit", [t]);
 
 fun mk_bin i =
   let
     fun term_of [] = \<^term>\<open>Pls\<close>
       | term_of [~1] = \<^term>\<open>Min\<close>
       | term_of (b :: bs) = \<^term>\<open>Bit\<close> $ term_of bs $ mk_bit b;
   in term_of (Numeral_Syntax.make_binary i) end;
 
 fun dest_bin tm =
   let
     fun bin_of \<^term>\<open>Pls\<close> = []
       | bin_of \<^term>\<open>Min\<close> = [~1]
       | bin_of (\<^term>\<open>Bit\<close> $ bs $ b) = dest_bit b :: bin_of bs
       | bin_of _ = raise TERM ("dest_bin", [tm]);
   in Numeral_Syntax.dest_binary (bin_of tm) end;
 
 
 (*Utilities*)
 
 fun mk_numeral i = \<^Const>\<open>integ_of\<close> $ mk_bin i;
 
 fun dest_numeral \<^Const_>\<open>integ_of for w\<close> = dest_bin w
   | dest_numeral t = raise TERM ("dest_numeral", [t]);
 
 fun find_first_numeral past (t::terms) =
         ((dest_numeral t, rev past @ terms)
          handle TERM _ => find_first_numeral (t::past) terms)
   | find_first_numeral past [] = raise TERM("find_first_numeral", []);
 
 val zero = mk_numeral 0;
-val mk_plus = FOLogic.mk_binop \<^const_name>\<open>zadd\<close>;
+fun mk_plus (t, u) = \<^Const>\<open>zadd for t u\<close>;
 
 (*Thus mk_sum[t] yields t+#0; longer sums don't have a trailing zero*)
 fun mk_sum []        = zero
   | mk_sum [t,u]     = mk_plus (t, u)
   | mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
 (*this version ALWAYS includes a trailing zero*)
 fun long_mk_sum []        = zero
   | long_mk_sum (t :: ts) = mk_plus (t, mk_sum ts);
 
 (*decompose additions AND subtractions as a sum*)
 fun dest_summing (pos, \<^Const_>\<open>zadd for t u\<close>, ts) =
         dest_summing (pos, t, dest_summing (pos, u, ts))
   | dest_summing (pos, \<^Const_>\<open>zdiff for t u\<close>, ts) =
         dest_summing (pos, t, dest_summing (not pos, u, ts))
   | dest_summing (pos, t, ts) =
         if pos then t::ts else \<^Const>\<open>zminus for t\<close> :: ts;
 
 fun dest_sum t = dest_summing (true, t, []);
 
 val one = mk_numeral 1;
-val mk_times = FOLogic.mk_binop \<^const_name>\<open>zmult\<close>;
+fun mk_times (t, u) = \<^Const>\<open>zmult for t u\<close>;
 
 fun mk_prod [] = one
   | mk_prod [t] = t
   | mk_prod (t :: ts) = if t = one then mk_prod ts
                         else mk_times (t, mk_prod ts);
 
 val dest_times = FOLogic.dest_bin \<^const_name>\<open>zmult\<close> \<^typ>\<open>i\<close>;
 
 fun dest_prod t =
       let val (t,u) = dest_times t
       in  dest_prod t @ dest_prod u  end
       handle TERM _ => [t];
 
 (*DON'T do the obvious simplifications; that would create special cases*)
 fun mk_coeff (k, t) = mk_times (mk_numeral k, t);
 
 (*Express t as a product of (possibly) a numeral with other sorted terms*)
 fun dest_coeff sign \<^Const_>\<open>zminus for t\<close> = dest_coeff (~sign) t
   | dest_coeff sign t =
     let val ts = sort Term_Ord.term_ord (dest_prod t)
         val (n, ts') = find_first_numeral [] ts
                           handle TERM _ => (1, ts)
     in (sign*n, mk_prod ts') end;
 
 (*Find first coefficient-term THAT MATCHES u*)
 fun find_first_coeff past u [] = raise TERM("find_first_coeff", [])
   | find_first_coeff past u (t::terms) =
         let val (n,u') = dest_coeff 1 t
         in  if u aconv u' then (n, rev past @ terms)
                           else find_first_coeff (t::past) u terms
         end
         handle TERM _ => find_first_coeff (t::past) u terms;
 
 
 (*Simplify #1*n and n*#1 to n*)
 val add_0s = [@{thm zadd_0_intify}, @{thm zadd_0_right_intify}];
 
 val mult_1s = [@{thm zmult_1_intify}, @{thm zmult_1_right_intify},
                @{thm zmult_minus1}, @{thm zmult_minus1_right}];
 
 val tc_rules = [@{thm integ_of_type}, @{thm intify_in_int},
                 @{thm int_of_type}, @{thm zadd_type}, @{thm zdiff_type}, @{thm zmult_type}] @ 
                @{thms bin.intros};
 val intifys = [@{thm intify_ident}, @{thm zadd_intify1}, @{thm zadd_intify2},
                @{thm zdiff_intify1}, @{thm zdiff_intify2}, @{thm zmult_intify1}, @{thm zmult_intify2},
                @{thm zless_intify1}, @{thm zless_intify2}, @{thm zle_intify1}, @{thm zle_intify2}];
 
 (*To perform binary arithmetic*)
 val bin_simps = [@{thm add_integ_of_left}] @ @{thms bin_arith_simps} @ @{thms bin_rel_simps};
 
 (*To evaluate binary negations of coefficients*)
 val zminus_simps = @{thms NCons_simps} @
                    [@{thm integ_of_minus} RS @{thm sym},
                     @{thm bin_minus_1}, @{thm bin_minus_0}, @{thm bin_minus_Pls}, @{thm bin_minus_Min},
                     @{thm bin_pred_1}, @{thm bin_pred_0}, @{thm bin_pred_Pls}, @{thm bin_pred_Min}];
 
 (*To let us treat subtraction as addition*)
 val diff_simps = [@{thm zdiff_def}, @{thm zminus_zadd_distrib}, @{thm zminus_zminus}];
 
 (*push the unary minus down*)
 val int_minus_mult_eq_1_to_2 = @{lemma "$- w $* z = w $* $- z" by simp};
 
 (*to extract again any uncancelled minuses*)
 val int_minus_from_mult_simps =
     [@{thm zminus_zminus}, @{thm zmult_zminus}, @{thm zmult_zminus_right}];
 
 (*combine unary minus with numeric literals, however nested within a product*)
 val int_mult_minus_simps =
     [@{thm zmult_assoc}, @{thm zmult_zminus} RS @{thm sym}, int_minus_mult_eq_1_to_2];
 
 structure CancelNumeralsCommon =
   struct
   val mk_sum = (fn _ : typ => mk_sum)
   val dest_sum = dest_sum
   val mk_coeff = mk_coeff
   val dest_coeff = dest_coeff 1
   val find_first_coeff = find_first_coeff []
   fun trans_tac ctxt = ArithData.gen_trans_tac ctxt @{thm iff_trans}
 
   val norm_ss1 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps add_0s @ mult_1s @ diff_simps @ zminus_simps @ @{thms zadd_ac})
   val norm_ss2 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps bin_simps @ int_mult_minus_simps @ intifys)
   val norm_ss3 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps int_minus_from_mult_simps @ @{thms zadd_ac} @ @{thms zmult_ac} @ tc_rules @ intifys)
   fun norm_tac ctxt =
     ALLGOALS (asm_simp_tac (put_simpset norm_ss1 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss2 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss3 ctxt))
 
   val numeral_simp_ss =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps add_0s @ bin_simps @ tc_rules @ intifys)
   fun numeral_simp_tac ctxt =
     ALLGOALS (simp_tac (put_simpset numeral_simp_ss ctxt))
     THEN ALLGOALS (asm_simp_tac ctxt)
   val simplify_meta_eq  = ArithData.simplify_meta_eq (add_0s @ mult_1s)
   end;
 
 
 structure EqCancelNumerals = CancelNumeralsFun
  (open CancelNumeralsCommon
   val prove_conv = ArithData.prove_conv "inteq_cancel_numerals"
   val mk_bal   = FOLogic.mk_eq
   val dest_bal = FOLogic.dest_eq
   val bal_add1 = @{thm eq_add_iff1} RS @{thm iff_trans}
   val bal_add2 = @{thm eq_add_iff2} RS @{thm iff_trans}
 );
 
 structure LessCancelNumerals = CancelNumeralsFun
  (open CancelNumeralsCommon
   val prove_conv = ArithData.prove_conv "intless_cancel_numerals"
-  val mk_bal   = FOLogic.mk_binrel \<^const_name>\<open>zless\<close>
+  fun mk_bal (t, u) = \<^Const>\<open>zless for t u\<close>
   val dest_bal = FOLogic.dest_bin \<^const_name>\<open>zless\<close> \<^typ>\<open>i\<close>
   val bal_add1 = @{thm less_add_iff1} RS @{thm iff_trans}
   val bal_add2 = @{thm less_add_iff2} RS @{thm iff_trans}
 );
 
 structure LeCancelNumerals = CancelNumeralsFun
  (open CancelNumeralsCommon
   val prove_conv = ArithData.prove_conv "intle_cancel_numerals"
-  val mk_bal   = FOLogic.mk_binrel \<^const_name>\<open>zle\<close>
+  fun mk_bal (t, u) = \<^Const>\<open>zle for t u\<close>
   val dest_bal = FOLogic.dest_bin \<^const_name>\<open>zle\<close> \<^typ>\<open>i\<close>
   val bal_add1 = @{thm le_add_iff1} RS @{thm iff_trans}
   val bal_add2 = @{thm le_add_iff2} RS @{thm iff_trans}
 );
 
 val cancel_numerals =
  [Simplifier.make_simproc \<^context> "inteq_cancel_numerals"
    {lhss =
      [\<^term>\<open>l $+ m = n\<close>, \<^term>\<open>l = m $+ n\<close>,
       \<^term>\<open>l $- m = n\<close>, \<^term>\<open>l = m $- n\<close>,
       \<^term>\<open>l $* m = n\<close>, \<^term>\<open>l = m $* n\<close>],
     proc = K EqCancelNumerals.proc},
   Simplifier.make_simproc \<^context> "intless_cancel_numerals"
    {lhss =
      [\<^term>\<open>l $+ m $< n\<close>, \<^term>\<open>l $< m $+ n\<close>,
       \<^term>\<open>l $- m $< n\<close>, \<^term>\<open>l $< m $- n\<close>,
       \<^term>\<open>l $* m $< n\<close>, \<^term>\<open>l $< m $* n\<close>],
     proc = K LessCancelNumerals.proc},
   Simplifier.make_simproc \<^context> "intle_cancel_numerals"
    {lhss =
      [\<^term>\<open>l $+ m $\<le> n\<close>, \<^term>\<open>l $\<le> m $+ n\<close>,
       \<^term>\<open>l $- m $\<le> n\<close>, \<^term>\<open>l $\<le> m $- n\<close>,
       \<^term>\<open>l $* m $\<le> n\<close>, \<^term>\<open>l $\<le> m $* n\<close>],
     proc = K LeCancelNumerals.proc}];
 
 
 (*version without the hyps argument*)
 fun prove_conv_nohyps name tacs sg = ArithData.prove_conv name tacs sg [];
 
 structure CombineNumeralsData =
   struct
   type coeff = int
   val iszero = (fn x => x = 0)
   val add = op + 
   val mk_sum = (fn _ : typ => long_mk_sum) (*to work for #2*x $+ #3*x *)
   val dest_sum = dest_sum
   val mk_coeff = mk_coeff
   val dest_coeff = dest_coeff 1
   val left_distrib = @{thm left_zadd_zmult_distrib} RS @{thm trans}
   val prove_conv = prove_conv_nohyps "int_combine_numerals"
   fun trans_tac ctxt = ArithData.gen_trans_tac ctxt @{thm trans}
 
   val norm_ss1 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps add_0s @ mult_1s @ diff_simps @ zminus_simps @ @{thms zadd_ac} @ intifys)
   val norm_ss2 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps bin_simps @ int_mult_minus_simps @ intifys)
   val norm_ss3 =
     simpset_of (put_simpset ZF_ss \<^context>
       addsimps int_minus_from_mult_simps @ @{thms zadd_ac} @ @{thms zmult_ac} @ tc_rules @ intifys)
   fun norm_tac ctxt =
     ALLGOALS (asm_simp_tac (put_simpset norm_ss1 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss2 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss3 ctxt))
 
   val numeral_simp_ss =
     simpset_of (put_simpset ZF_ss \<^context> addsimps add_0s @ bin_simps @ tc_rules @ intifys)
   fun numeral_simp_tac ctxt =
     ALLGOALS (simp_tac (put_simpset numeral_simp_ss ctxt))
   val simplify_meta_eq  = ArithData.simplify_meta_eq (add_0s @ mult_1s)
   end;
 
 structure CombineNumerals = CombineNumeralsFun(CombineNumeralsData);
 
 val combine_numerals =
   Simplifier.make_simproc \<^context> "int_combine_numerals"
     {lhss = [\<^term>\<open>i $+ j\<close>, \<^term>\<open>i $- j\<close>],
      proc = K CombineNumerals.proc};
 
 
 
 (** Constant folding for integer multiplication **)
 
 (*The trick is to regard products as sums, e.g. #3 $* x $* #4 as
   the "sum" of #3, x, #4; the literals are then multiplied*)
 
 
 structure CombineNumeralsProdData =
 struct
   type coeff = int
   val iszero = (fn x => x = 0)
   val add = op *
   val mk_sum = (fn _ : typ => mk_prod)
   val dest_sum = dest_prod
   fun mk_coeff(k,t) =
     if t = one then mk_numeral k
     else raise TERM("mk_coeff", [])
   fun dest_coeff t = (dest_numeral t, one)  (*We ONLY want pure numerals.*)
   val left_distrib = @{thm zmult_assoc} RS @{thm sym} RS @{thm trans}
   val prove_conv = prove_conv_nohyps "int_combine_numerals_prod"
   fun trans_tac ctxt = ArithData.gen_trans_tac ctxt @{thm trans}
 
   val norm_ss1 =
     simpset_of (put_simpset ZF_ss \<^context> addsimps mult_1s @ diff_simps @ zminus_simps)
   val norm_ss2 =
     simpset_of (put_simpset ZF_ss \<^context> addsimps [@{thm zmult_zminus_right} RS @{thm sym}] @
     bin_simps @ @{thms zmult_ac} @ tc_rules @ intifys)
   fun norm_tac ctxt =
     ALLGOALS (asm_simp_tac (put_simpset norm_ss1 ctxt))
     THEN ALLGOALS (asm_simp_tac (put_simpset norm_ss2 ctxt))
 
   val numeral_simp_ss =
     simpset_of (put_simpset ZF_ss \<^context> addsimps bin_simps @ tc_rules @ intifys)
   fun numeral_simp_tac ctxt =
     ALLGOALS (simp_tac (put_simpset numeral_simp_ss ctxt))
   val simplify_meta_eq  = ArithData.simplify_meta_eq (mult_1s);
 end;
 
 
 structure CombineNumeralsProd = CombineNumeralsFun(CombineNumeralsProdData);
 
 val combine_numerals_prod =
   Simplifier.make_simproc \<^context> "int_combine_numerals_prod"
    {lhss = [\<^term>\<open>i $* j\<close>], proc = K CombineNumeralsProd.proc};
 
 end;
 
 val _ =
   Theory.setup (Simplifier.map_theory_simpset (fn ctxt =>
     ctxt addsimprocs
       (Int_Numeral_Simprocs.cancel_numerals @
        [Int_Numeral_Simprocs.combine_numerals,
         Int_Numeral_Simprocs.combine_numerals_prod])));