src/HOL/simpdata.ML
author paulson
Thu Aug 06 15:48:13 1998 +0200 (1998-08-06)
changeset 5278 a903b66822e2
parent 5220 07f80f447b27
child 5304 c133f16febc7
permissions -rw-r--r--
even more tidying of Goal commands
     1 (*  Title:      HOL/simpdata.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1991  University of Cambridge
     5 
     6 Instantiation of the generic simplifier.
     7 *)
     8 
     9 section "Simplifier";
    10 
    11 (*** Addition of rules to simpsets and clasets simultaneously ***)
    12 
    13 infix 4 addIffs delIffs;
    14 
    15 (*Takes UNCONDITIONAL theorems of the form A<->B to 
    16         the Safe Intr     rule B==>A and 
    17         the Safe Destruct rule A==>B.
    18   Also ~A goes to the Safe Elim rule A ==> ?R
    19   Failing other cases, A is added as a Safe Intr rule*)
    20 local
    21   val iff_const = HOLogic.eq_const HOLogic.boolT;
    22 
    23   fun addIff ((cla, simp), th) = 
    24       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    25                 (Const("Not", _) $ A) =>
    26                     cla addSEs [zero_var_indexes (th RS notE)]
    27               | (con $ _ $ _) =>
    28                     if con = iff_const
    29                     then cla addSIs [zero_var_indexes (th RS iffD2)]  
    30                               addSDs [zero_var_indexes (th RS iffD1)]
    31                     else  cla addSIs [th]
    32               | _ => cla addSIs [th],
    33        simp addsimps [th])
    34       handle _ => error ("AddIffs: theorem must be unconditional\n" ^ 
    35                          string_of_thm th);
    36 
    37   fun delIff ((cla, simp), th) = 
    38       (case HOLogic.dest_Trueprop (#prop (rep_thm th)) of
    39                 (Const ("Not", _) $ A) =>
    40                     cla delrules [zero_var_indexes (th RS notE)]
    41               | (con $ _ $ _) =>
    42                     if con = iff_const
    43                     then cla delrules [zero_var_indexes (th RS iffD2),
    44                                        make_elim (zero_var_indexes (th RS iffD1))]
    45                     else cla delrules [th]
    46               | _ => cla delrules [th],
    47        simp delsimps [th])
    48       handle _ => (warning("DelIffs: ignoring conditional theorem\n" ^ 
    49                           string_of_thm th); (cla, simp));
    50 
    51   fun store_clasimp (cla, simp) = (claset_ref () := cla; simpset_ref () := simp)
    52 in
    53 val op addIffs = foldl addIff;
    54 val op delIffs = foldl delIff;
    55 fun AddIffs thms = store_clasimp ((claset (), simpset ()) addIffs thms);
    56 fun DelIffs thms = store_clasimp ((claset (), simpset ()) delIffs thms);
    57 end;
    58 
    59 qed_goal "meta_eq_to_obj_eq" HOL.thy "x==y ==> x=y"
    60   (fn [prem] => [rewtac prem, rtac refl 1]);
    61 
    62 local
    63 
    64   fun prover s = prove_goal HOL.thy s (K [Blast_tac 1]);
    65 
    66   val P_imp_P_iff_True = prover "P --> (P = True)" RS mp;
    67   val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
    68 
    69   val not_P_imp_P_iff_F = prover "~P --> (P = False)" RS mp;
    70   val not_P_imp_P_eq_False = not_P_imp_P_iff_F RS eq_reflection;
    71 
    72   fun atomize pairs =
    73     let fun atoms th =
    74           (case concl_of th of
    75              Const("Trueprop",_) $ p =>
    76                (case head_of p of
    77                   Const(a,_) =>
    78                     (case assoc(pairs,a) of
    79                        Some(rls) => flat (map atoms ([th] RL rls))
    80                      | None => [th])
    81                 | _ => [th])
    82            | _ => [th])
    83     in atoms end;
    84 
    85   fun gen_all th = forall_elim_vars (#maxidx(rep_thm th)+1) th;
    86 
    87 in
    88 
    89   fun mk_meta_eq r = r RS eq_reflection;
    90   fun mk_meta_eq_True r = Some(r RS meta_eq_to_obj_eq RS P_imp_P_eq_True);
    91 
    92   fun mk_meta_eq_simp r = case concl_of r of
    93           Const("==",_)$_$_ => r
    94       |   _$(Const("op =",_)$lhs$rhs) => mk_meta_eq r
    95       |   _$(Const("Not",_)$_) => r RS not_P_imp_P_eq_False
    96       |   _ => r RS P_imp_P_eq_True;
    97   (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    98 
    99 val simp_thms = map prover
   100  [ "(x=x) = True",
   101    "(~True) = False", "(~False) = True", "(~ ~ P) = P",
   102    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
   103    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
   104    "(True --> P) = P", "(False --> P) = True", 
   105    "(P --> True) = True", "(P --> P) = True",
   106    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
   107    "(P & True) = P", "(True & P) = P", 
   108    "(P & False) = False", "(False & P) = False",
   109    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
   110    "(P & ~P) = False",    "(~P & P) = False",
   111    "(P | True) = True", "(True | P) = True", 
   112    "(P | False) = P", "(False | P) = P",
   113    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
   114    "(P | ~P) = True",    "(~P | P) = True",
   115    "((~P) = (~Q)) = (P=Q)",
   116    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x", 
   117 (*two needed for the one-point-rule quantifier simplification procs*)
   118    "(? x. x=t & P(x)) = P(t)",		(*essential for termination!!*)
   119    "(! x. t=x --> P(x)) = P(t)" ];      (*covers a stray case*)
   120 
   121 (*Add congruence rules for = (instead of ==) *)
   122 infix 4 addcongs delcongs;
   123 
   124 fun mk_meta_cong rl =
   125   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
   126   handle THM _ =>
   127   error("Premises and conclusion of congruence rules must be =-equalities");
   128 
   129 fun ss addcongs congs = ss addeqcongs (map mk_meta_cong congs);
   130 
   131 fun ss delcongs congs = ss deleqcongs (map mk_meta_cong congs);
   132 
   133 fun Addcongs congs = (simpset_ref() := simpset() addcongs congs);
   134 fun Delcongs congs = (simpset_ref() := simpset() delcongs congs);
   135 
   136 fun mksimps pairs = map mk_meta_eq_simp o atomize pairs o gen_all;
   137 
   138 val imp_cong = impI RSN
   139     (2, prove_goal HOL.thy "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
   140         (fn _=> [Blast_tac 1]) RS mp RS mp);
   141 
   142 (*Miniscoping: pushing in existential quantifiers*)
   143 val ex_simps = map prover 
   144                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
   145                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
   146                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
   147                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
   148                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
   149                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
   150 
   151 (*Miniscoping: pushing in universal quantifiers*)
   152 val all_simps = map prover
   153                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
   154                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
   155                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
   156                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
   157                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
   158                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
   159 
   160 
   161 (* elimination of existential quantifiers in assumptions *)
   162 
   163 val ex_all_equiv =
   164   let val lemma1 = prove_goal HOL.thy
   165         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   166         (fn prems => [resolve_tac prems 1, etac exI 1]);
   167       val lemma2 = prove_goalw HOL.thy [Ex_def]
   168         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   169         (fn prems => [REPEAT(resolve_tac prems 1)])
   170   in equal_intr lemma1 lemma2 end;
   171 
   172 end;
   173 
   174 (* Elimination of True from asumptions: *)
   175 
   176 val True_implies_equals = prove_goal HOL.thy
   177  "(True ==> PROP P) == PROP P"
   178 (K [rtac equal_intr_rule 1, atac 2,
   179           METAHYPS (fn prems => resolve_tac prems 1) 1,
   180           rtac TrueI 1]);
   181 
   182 fun prove nm thm  = qed_goal nm HOL.thy thm (K [Blast_tac 1]);
   183 
   184 prove "conj_commute" "(P&Q) = (Q&P)";
   185 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   186 val conj_comms = [conj_commute, conj_left_commute];
   187 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   188 
   189 prove "disj_commute" "(P|Q) = (Q|P)";
   190 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   191 val disj_comms = [disj_commute, disj_left_commute];
   192 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   193 
   194 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   195 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   196 
   197 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   198 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   199 
   200 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   201 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   202 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   203 
   204 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   205 prove "imp_disj_not1" "((P --> Q | R)) = (~Q --> P --> R)";
   206 prove "imp_disj_not2" "((P --> Q | R)) = (~R --> P --> Q)";
   207 
   208 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   209 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   210 
   211 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   212 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   213 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   214 prove "not_iff" "(P~=Q) = (P = (~Q))";
   215 prove "disj_not1" "(~P | Q) = (P --> Q)";
   216 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   217 
   218 (*Avoids duplication of subgoals after split_if, when the true and false 
   219   cases boil down to the same thing.*) 
   220 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   221 
   222 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   223 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   224 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   225 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   226 
   227 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   228 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   229 
   230 (* '&' congruence rule: not included by default!
   231    May slow rewrite proofs down by as much as 50% *)
   232 
   233 let val th = prove_goal HOL.thy 
   234                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   235                 (fn _=> [Blast_tac 1])
   236 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   237 
   238 let val th = prove_goal HOL.thy 
   239                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   240                 (fn _=> [Blast_tac 1])
   241 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   242 
   243 (* '|' congruence rule: not included by default! *)
   244 
   245 let val th = prove_goal HOL.thy 
   246                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   247                 (fn _=> [Blast_tac 1])
   248 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   249 
   250 prove "eq_sym_conv" "(x=y) = (y=x)";
   251 
   252 qed_goalw "o_apply" HOL.thy [o_def] "(f o g) x = f (g x)"
   253  (K [rtac refl 1]);
   254 
   255 
   256 (** if-then-else rules **)
   257 
   258 qed_goalw "if_True" HOL.thy [if_def] "(if True then x else y) = x"
   259  (K [Blast_tac 1]);
   260 
   261 qed_goalw "if_False" HOL.thy [if_def] "(if False then x else y) = y"
   262  (K [Blast_tac 1]);
   263 
   264 qed_goal "if_P" HOL.thy "P ==> (if P then x else y) = x"
   265  (fn [prem] => [ stac (prem RS eqTrueI) 1, rtac if_True 1 ]);
   266 (*
   267 qed_goal "if_not_P" HOL.thy "~P ==> (if P then x else y) = y"
   268  (fn [prem] => [ stac (prem RS not_P_imp_P_iff_F) 1, rtac if_False 1 ]);
   269 *)
   270 qed_goalw "if_not_P" HOL.thy [if_def] "!!P. ~P ==> (if P then x else y) = y"
   271  (K [Blast_tac 1]);
   272 
   273 qed_goal "split_if" HOL.thy
   274     "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))" (K [
   275 	res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1,
   276          stac if_P 2,
   277          stac if_not_P 1,
   278          ALLGOALS (Blast_tac)]);
   279 (* for backwards compatibility: *)
   280 val expand_if = split_if;
   281 
   282 qed_goal "split_if_asm" HOL.thy
   283     "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))"
   284     (K [stac split_if 1,
   285 	Blast_tac 1]);
   286 
   287 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   288 qed_goal "if_bool_eq_conj" HOL.thy
   289     "(if P then Q else R) = ((P-->Q) & (~P-->R))"
   290     (K [rtac split_if 1]);
   291 
   292 (*And this form is useful for expanding IFs on the LEFT*)
   293 qed_goal "if_bool_eq_disj" HOL.thy
   294     "(if P then Q else R) = ((P&Q) | (~P&R))"
   295     (K [stac split_if 1,
   296 	Blast_tac 1]);
   297 
   298 
   299 (*** make simplification procedures for quantifier elimination ***)
   300 
   301 structure Quantifier1 = Quantifier1Fun(
   302 struct
   303   (*abstract syntax*)
   304   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   305     | dest_eq _ = None;
   306   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   307     | dest_conj _ = None;
   308   val conj = HOLogic.conj
   309   val imp  = HOLogic.imp
   310   (*rules*)
   311   val iff_reflection = eq_reflection
   312   val iffI = iffI
   313   val sym  = sym
   314   val conjI= conjI
   315   val conjE= conjE
   316   val impI = impI
   317   val impE = impE
   318   val mp   = mp
   319   val exI  = exI
   320   val exE  = exE
   321   val allI = allI
   322   val allE = allE
   323 end);
   324 
   325 local
   326 val ex_pattern =
   327   read_cterm (sign_of HOL.thy) ("EX x. P(x) & Q(x)",HOLogic.boolT)
   328 
   329 val all_pattern =
   330   read_cterm (sign_of HOL.thy) ("ALL x. P(x) & P'(x) --> Q(x)",HOLogic.boolT)
   331 
   332 in
   333 val defEX_regroup =
   334   mk_simproc "defined EX" [ex_pattern] Quantifier1.rearrange_ex;
   335 val defALL_regroup =
   336   mk_simproc "defined ALL" [all_pattern] Quantifier1.rearrange_all;
   337 end;
   338 
   339 
   340 (*** Case splitting ***)
   341 
   342 local val mktac = mk_case_split_tac (meta_eq_to_obj_eq RS iffD2)
   343 in
   344 fun split_tac splits = mktac (map mk_meta_eq splits)
   345 end;
   346 
   347 local val mktac = mk_case_split_inside_tac (meta_eq_to_obj_eq RS iffD2)
   348 in
   349 fun split_inside_tac splits = mktac (map mk_meta_eq splits)
   350 end;
   351 
   352 val split_asm_tac = mk_case_split_asm_tac split_tac 
   353 			(disjE,conjE,exE,contrapos,contrapos2,notnotD);
   354 
   355 infix 4 addsplits delsplits;
   356 
   357 fun ss addsplits splits =
   358   let fun addsplit (ss,split) =
   359         let val (name,asm) = split_thm_info split 
   360         in ss addloop ("split "^ name ^ (if asm then " asm" else ""),
   361 		       (if asm then split_asm_tac else split_tac) [split]) end
   362   in foldl addsplit (ss,splits) end;
   363 
   364 fun ss delsplits splits =
   365   let fun delsplit(ss,split) =
   366         let val (name,asm) = split_thm_info split 
   367         in ss delloop ("split "^ name ^ (if asm then " asm" else "")) end
   368   in foldl delsplit (ss,splits) end;
   369 
   370 fun Addsplits splits = (simpset_ref() := simpset() addsplits splits);
   371 fun Delsplits splits = (simpset_ref() := simpset() delsplits splits);
   372 
   373 qed_goal "if_cancel" HOL.thy "(if c then x else x) = x"
   374   (K [split_tac [split_if] 1, Blast_tac 1]);
   375 
   376 qed_goal "if_eq_cancel" HOL.thy "(if x = y then y else x) = x"
   377   (K [split_tac [split_if] 1, Blast_tac 1]);
   378 
   379 (** 'if' congruence rules: neither included by default! *)
   380 
   381 (*Simplifies x assuming c and y assuming ~c*)
   382 qed_goal "if_cong" HOL.thy
   383   "[| b=c; c ==> x=u; ~c ==> y=v |] ==>\
   384 \  (if b then x else y) = (if c then u else v)"
   385   (fn rew::prems =>
   386    [stac rew 1, stac split_if 1, stac split_if 1,
   387     blast_tac (HOL_cs addDs prems) 1]);
   388 
   389 (*Prevents simplification of x and y: much faster*)
   390 qed_goal "if_weak_cong" HOL.thy
   391   "b=c ==> (if b then x else y) = (if c then x else y)"
   392   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   393 
   394 (*Prevents simplification of t: much faster*)
   395 qed_goal "let_weak_cong" HOL.thy
   396   "a = b ==> (let x=a in t(x)) = (let x=b in t(x))"
   397   (fn [prem] => [rtac (prem RS arg_cong) 1]);
   398 
   399 (*In general it seems wrong to add distributive laws by default: they
   400   might cause exponential blow-up.  But imp_disjL has been in for a while
   401   and cannot be removed without affecting existing proofs.  Moreover, 
   402   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   403   grounds that it allows simplification of R in the two cases.*)
   404 
   405 val mksimps_pairs =
   406   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   407    ("All", [spec]), ("True", []), ("False", []),
   408    ("If", [if_bool_eq_conj RS iffD1])];
   409 
   410 fun unsafe_solver prems = FIRST'[resolve_tac (reflexive_thm::TrueI::refl::prems),
   411 				 atac, etac FalseE];
   412 (*No premature instantiation of variables during simplification*)
   413 fun   safe_solver prems = FIRST'[match_tac (reflexive_thm::TrueI::prems),
   414 				 eq_assume_tac, ematch_tac [FalseE]];
   415 
   416 val HOL_basic_ss = empty_ss setsubgoaler asm_simp_tac
   417 			    setSSolver   safe_solver
   418 			    setSolver  unsafe_solver
   419 			    setmksimps (mksimps mksimps_pairs)
   420 			    setmkeqTrue mk_meta_eq_True;
   421 
   422 val HOL_ss = 
   423     HOL_basic_ss addsimps 
   424      ([triv_forall_equality, (* prunes params *)
   425        True_implies_equals, (* prune asms `True' *)
   426        if_True, if_False, if_cancel, if_eq_cancel,
   427        o_apply, imp_disjL, conj_assoc, disj_assoc,
   428        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   429        disj_not1, not_all, not_ex, cases_simp]
   430      @ ex_simps @ all_simps @ simp_thms)
   431      addsimprocs [defALL_regroup,defEX_regroup]
   432      addcongs [imp_cong]
   433      addsplits [split_if];
   434 
   435 qed_goal "if_distrib" HOL.thy
   436   "f(if c then x else y) = (if c then f x else f y)" 
   437   (K [simp_tac (HOL_ss setloop (split_tac [split_if])) 1]);
   438 
   439 qed_goalw "o_assoc" HOL.thy [o_def] "f o (g o h) = f o g o h"
   440   (K [rtac ext 1, rtac refl 1]);
   441 
   442 
   443 (*For expand_case_tac*)
   444 val prems = goal HOL.thy "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   445 by (case_tac "P" 1);
   446 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   447 val expand_case = result();
   448 
   449 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   450   during unification.*)
   451 fun expand_case_tac P i =
   452     res_inst_tac [("P",P)] expand_case i THEN
   453     Simp_tac (i+1) THEN 
   454     Simp_tac i;
   455 
   456 
   457 (* install implicit simpset *)
   458 
   459 simpset_ref() := HOL_ss;
   460 
   461 
   462 
   463 (*** integration of simplifier with classical reasoner ***)
   464 
   465 (* rot_eq_tac rotates the first equality premise of subgoal i to the front,
   466    fails if there is no equaliy or if an equality is already at the front *)
   467 local
   468   fun is_eq (Const ("Trueprop", _) $ (Const("op ="  ,_) $ _ $ _)) = true
   469     | is_eq _ = false;
   470   val find_eq = find_index is_eq;
   471 in
   472 val rot_eq_tac = 
   473      SUBGOAL (fn (Bi,i) => let val n = find_eq (Logic.strip_assums_hyp Bi) in
   474 		if n>0 then rotate_tac n i else no_tac end)
   475 end;
   476 
   477 
   478 structure Clasimp = ClasimpFun
   479  (structure Simplifier = Simplifier and Classical = Classical and Blast = Blast
   480   val op addcongs = op addcongs and op delcongs = op delcongs
   481   and op addSaltern = op addSaltern and op addbefore = op addbefore);
   482 
   483 open Clasimp;
   484 
   485 val HOL_css = (HOL_cs, HOL_ss);