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 +1,275 @@
 (*  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;
 
 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 ***)
 
 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"
   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"
   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)";
 *)