src/HOL/simpdata.ML
author wenzelm
Fri Jul 20 21:58:19 2001 +0200 (2001-07-20)
changeset 11434 996bd4eb0ef3
parent 11344 57b7ad51971c
child 11451 8abfb4f7bd02
permissions -rw-r--r--
HOL_ss: the_eq_trivial, the_sym_eq_trivial;
     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 for HOL.
     7 *)
     8 
     9 section "Simplifier";
    10 
    11 val [prem] = goal (the_context ()) "x==y ==> x=y";
    12 by (rewtac prem);
    13 by (rtac refl 1);
    14 qed "meta_eq_to_obj_eq";
    15 
    16 Goal "(%s. f s) = f";
    17 br refl 1;
    18 qed "eta_contract_eq";
    19 
    20 local
    21 
    22   fun prover s = prove_goal (the_context ()) s (fn _ => [(Blast_tac 1)]);
    23 
    24 in
    25 
    26 (*Make meta-equalities.  The operator below is Trueprop*)
    27 
    28 fun mk_meta_eq r = r RS eq_reflection;
    29 fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
    30 
    31 val Eq_TrueI  = mk_meta_eq(prover  "P --> (P = True)"  RS mp);
    32 val Eq_FalseI = mk_meta_eq(prover "~P --> (P = False)" RS mp);
    33 
    34 fun mk_eq th = case concl_of th of
    35         Const("==",_)$_$_       => th
    36     |   _$(Const("op =",_)$_$_) => mk_meta_eq th
    37     |   _$(Const("Not",_)$_)    => th RS Eq_FalseI
    38     |   _                       => th RS Eq_TrueI;
    39 (* last 2 lines requires all formulae to be of the from Trueprop(.) *)
    40 
    41 fun mk_eq_True r = Some(r RS meta_eq_to_obj_eq RS Eq_TrueI);
    42 
    43 (*Congruence rules for = (instead of ==)*)
    44 fun mk_meta_cong rl =
    45   standard(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
    46   handle THM _ =>
    47   error("Premises and conclusion of congruence rules must be =-equalities");
    48 
    49 val not_not = prover "(~ ~ P) = P";
    50 
    51 val simp_thms = [not_not] @ map prover
    52  [ "(x=x) = True",
    53    "(~True) = False", "(~False) = True",
    54    "(~P) ~= P", "P ~= (~P)", "(P ~= Q) = (P = (~Q))",
    55    "(True=P) = P", "(P=True) = P", "(False=P) = (~P)", "(P=False) = (~P)",
    56    "(True --> P) = P", "(False --> P) = True",
    57    "(P --> True) = True", "(P --> P) = True",
    58    "(P --> False) = (~P)", "(P --> ~P) = (~P)",
    59    "(P & True) = P", "(True & P) = P",
    60    "(P & False) = False", "(False & P) = False",
    61    "(P & P) = P", "(P & (P & Q)) = (P & Q)",
    62    "(P & ~P) = False",    "(~P & P) = False",
    63    "(P | True) = True", "(True | P) = True",
    64    "(P | False) = P", "(False | P) = P",
    65    "(P | P) = P", "(P | (P | Q)) = (P | Q)",
    66    "(P | ~P) = True",    "(~P | P) = True",
    67    "((~P) = (~Q)) = (P=Q)",
    68    "(!x. P) = P", "(? x. P) = P", "? x. x=t", "? x. t=x",
    69 (* needed for the one-point-rule quantifier simplification procs*)
    70 (*essential for termination!!*)
    71    "(? x. x=t & P(x)) = P(t)",
    72    "(? x. t=x & P(x)) = P(t)",
    73    "(! x. x=t --> P(x)) = P(t)",
    74    "(! x. t=x --> P(x)) = P(t)" ];
    75 
    76 val imp_cong = standard(impI RSN
    77     (2, prove_goal (the_context ()) "(P=P')--> (P'--> (Q=Q'))--> ((P-->Q) = (P'-->Q'))"
    78         (fn _=> [(Blast_tac 1)]) RS mp RS mp));
    79 
    80 (*Miniscoping: pushing in existential quantifiers*)
    81 val ex_simps = map prover
    82                 ["(EX x. P x & Q)   = ((EX x. P x) & Q)",
    83                  "(EX x. P & Q x)   = (P & (EX x. Q x))",
    84                  "(EX x. P x | Q)   = ((EX x. P x) | Q)",
    85                  "(EX x. P | Q x)   = (P | (EX x. Q x))",
    86                  "(EX x. P x --> Q) = ((ALL x. P x) --> Q)",
    87                  "(EX x. P --> Q x) = (P --> (EX x. Q x))"];
    88 
    89 (*Miniscoping: pushing in universal quantifiers*)
    90 val all_simps = map prover
    91                 ["(ALL x. P x & Q)   = ((ALL x. P x) & Q)",
    92                  "(ALL x. P & Q x)   = (P & (ALL x. Q x))",
    93                  "(ALL x. P x | Q)   = ((ALL x. P x) | Q)",
    94                  "(ALL x. P | Q x)   = (P | (ALL x. Q x))",
    95                  "(ALL x. P x --> Q) = ((EX x. P x) --> Q)",
    96                  "(ALL x. P --> Q x) = (P --> (ALL x. Q x))"];
    97 
    98 
    99 (* elimination of existential quantifiers in assumptions *)
   100 
   101 val ex_all_equiv =
   102   let val lemma1 = prove_goal (the_context ())
   103         "(? x. P(x) ==> PROP Q) ==> (!!x. P(x) ==> PROP Q)"
   104         (fn prems => [resolve_tac prems 1, etac exI 1]);
   105       val lemma2 = prove_goalw (the_context ()) [Ex_def]
   106         "(!!x. P(x) ==> PROP Q) ==> (? x. P(x) ==> PROP Q)"
   107         (fn prems => [(REPEAT(resolve_tac prems 1))])
   108   in equal_intr lemma1 lemma2 end;
   109 
   110 end;
   111 
   112 bind_thms ("ex_simps", ex_simps);
   113 bind_thms ("all_simps", all_simps);
   114 bind_thm ("not_not", not_not);
   115 bind_thm ("imp_cong", imp_cong);
   116 
   117 (* Elimination of True from asumptions: *)
   118 
   119 val True_implies_equals = prove_goal (the_context ())
   120  "(True ==> PROP P) == PROP P"
   121 (fn _ => [rtac equal_intr_rule 1, atac 2,
   122           METAHYPS (fn prems => resolve_tac prems 1) 1,
   123           rtac TrueI 1]);
   124 
   125 fun prove nm thm  = qed_goal nm (the_context ()) thm (fn _ => [(Blast_tac 1)]);
   126 
   127 prove "eq_commute" "(a=b) = (b=a)";
   128 prove "eq_left_commute" "(P=(Q=R)) = (Q=(P=R))";
   129 prove "eq_assoc" "((P=Q)=R) = (P=(Q=R))";
   130 val eq_ac = [eq_commute, eq_left_commute, eq_assoc];
   131 
   132 prove "neq_commute" "(a~=b) = (b~=a)";
   133 
   134 prove "conj_commute" "(P&Q) = (Q&P)";
   135 prove "conj_left_commute" "(P&(Q&R)) = (Q&(P&R))";
   136 val conj_comms = [conj_commute, conj_left_commute];
   137 prove "conj_assoc" "((P&Q)&R) = (P&(Q&R))";
   138 
   139 prove "disj_commute" "(P|Q) = (Q|P)";
   140 prove "disj_left_commute" "(P|(Q|R)) = (Q|(P|R))";
   141 val disj_comms = [disj_commute, disj_left_commute];
   142 prove "disj_assoc" "((P|Q)|R) = (P|(Q|R))";
   143 
   144 prove "conj_disj_distribL" "(P&(Q|R)) = (P&Q | P&R)";
   145 prove "conj_disj_distribR" "((P|Q)&R) = (P&R | Q&R)";
   146 
   147 prove "disj_conj_distribL" "(P|(Q&R)) = ((P|Q) & (P|R))";
   148 prove "disj_conj_distribR" "((P&Q)|R) = ((P|R) & (Q|R))";
   149 
   150 prove "imp_conjR" "(P --> (Q&R)) = ((P-->Q) & (P-->R))";
   151 prove "imp_conjL" "((P&Q) -->R)  = (P --> (Q --> R))";
   152 prove "imp_disjL" "((P|Q) --> R) = ((P-->R)&(Q-->R))";
   153 
   154 (*These two are specialized, but imp_disj_not1 is useful in Auth/Yahalom.ML*)
   155 prove "imp_disj_not1" "(P --> Q | R) = (~Q --> P --> R)";
   156 prove "imp_disj_not2" "(P --> Q | R) = (~R --> P --> Q)";
   157 
   158 prove "imp_disj1" "((P-->Q)|R) = (P--> Q|R)";
   159 prove "imp_disj2" "(Q|(P-->R)) = (P--> Q|R)";
   160 
   161 prove "de_Morgan_disj" "(~(P | Q)) = (~P & ~Q)";
   162 prove "de_Morgan_conj" "(~(P & Q)) = (~P | ~Q)";
   163 prove "not_imp" "(~(P --> Q)) = (P & ~Q)";
   164 prove "not_iff" "(P~=Q) = (P = (~Q))";
   165 prove "disj_not1" "(~P | Q) = (P --> Q)";
   166 prove "disj_not2" "(P | ~Q) = (Q --> P)"; (* changes orientation :-( *)
   167 prove "imp_conv_disj" "(P --> Q) = ((~P) | Q)";
   168 
   169 prove "iff_conv_conj_imp" "(P = Q) = ((P --> Q) & (Q --> P))";
   170 
   171 
   172 (*Avoids duplication of subgoals after split_if, when the true and false
   173   cases boil down to the same thing.*)
   174 prove "cases_simp" "((P --> Q) & (~P --> Q)) = Q";
   175 
   176 prove "not_all" "(~ (! x. P(x))) = (? x.~P(x))";
   177 prove "imp_all" "((! x. P x) --> Q) = (? x. P x --> Q)";
   178 prove "not_ex"  "(~ (? x. P(x))) = (! x.~P(x))";
   179 prove "imp_ex" "((? x. P x) --> Q) = (! x. P x --> Q)";
   180 
   181 prove "ex_disj_distrib" "(? x. P(x) | Q(x)) = ((? x. P(x)) | (? x. Q(x)))";
   182 prove "all_conj_distrib" "(!x. P(x) & Q(x)) = ((! x. P(x)) & (! x. Q(x)))";
   183 
   184 (* '&' congruence rule: not included by default!
   185    May slow rewrite proofs down by as much as 50% *)
   186 
   187 let val th = prove_goal (the_context ())
   188                 "(P=P')--> (P'--> (Q=Q'))--> ((P&Q) = (P'&Q'))"
   189                 (fn _=> [(Blast_tac 1)])
   190 in  bind_thm("conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   191 
   192 let val th = prove_goal (the_context ())
   193                 "(Q=Q')--> (Q'--> (P=P'))--> ((P&Q) = (P'&Q'))"
   194                 (fn _=> [(Blast_tac 1)])
   195 in  bind_thm("rev_conj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   196 
   197 (* '|' congruence rule: not included by default! *)
   198 
   199 let val th = prove_goal (the_context ())
   200                 "(P=P')--> (~P'--> (Q=Q'))--> ((P|Q) = (P'|Q'))"
   201                 (fn _=> [(Blast_tac 1)])
   202 in  bind_thm("disj_cong",standard (impI RSN (2, th RS mp RS mp)))  end;
   203 
   204 prove "eq_sym_conv" "(x=y) = (y=x)";
   205 
   206 
   207 (** if-then-else rules **)
   208 
   209 Goalw [if_def] "(if True then x else y) = x";
   210 by (Blast_tac 1);
   211 qed "if_True";
   212 
   213 Goalw [if_def] "(if False then x else y) = y";
   214 by (Blast_tac 1);
   215 qed "if_False";
   216 
   217 Goalw [if_def] "P ==> (if P then x else y) = x";
   218 by (Blast_tac 1);
   219 qed "if_P";
   220 
   221 Goalw [if_def] "~P ==> (if P then x else y) = y";
   222 by (Blast_tac 1);
   223 qed "if_not_P";
   224 
   225 Goal "P(if Q then x else y) = ((Q --> P(x)) & (~Q --> P(y)))";
   226 by (res_inst_tac [("Q","Q")] (excluded_middle RS disjE) 1);
   227 by (stac if_P 2);
   228 by (stac if_not_P 1);
   229 by (ALLGOALS (Blast_tac));
   230 qed "split_if";
   231 
   232 Goal "P(if Q then x else y) = (~((Q & ~P x) | (~Q & ~P y)))";
   233 by (stac split_if 1);
   234 by (Blast_tac 1);
   235 qed "split_if_asm";
   236 
   237 bind_thms ("if_splits", [split_if, split_if_asm]);
   238 
   239 bind_thm ("if_def2", read_instantiate [("P","\\<lambda>x. x")] split_if);
   240 
   241 Goal "(if c then x else x) = x";
   242 by (stac split_if 1);
   243 by (Blast_tac 1);
   244 qed "if_cancel";
   245 
   246 Goal "(if x = y then y else x) = x";
   247 by (stac split_if 1);
   248 by (Blast_tac 1);
   249 qed "if_eq_cancel";
   250 
   251 (*This form is useful for expanding IFs on the RIGHT of the ==> symbol*)
   252 Goal "(if P then Q else R) = ((P-->Q) & (~P-->R))";
   253 by (rtac split_if 1);
   254 qed "if_bool_eq_conj";
   255 
   256 (*And this form is useful for expanding IFs on the LEFT*)
   257 Goal "(if P then Q else R) = ((P&Q) | (~P&R))";
   258 by (stac split_if 1);
   259 by (Blast_tac 1);
   260 qed "if_bool_eq_disj";
   261 
   262 local
   263 val uncurry = prove_goal (the_context()) "P --> Q --> R ==> P & Q --> R"
   264               (fn prems => [cut_facts_tac prems 1, Blast_tac 1]);
   265 
   266 val iff_allI = allI RS
   267     prove_goal (the_context()) "!x. P x = Q x ==> (!x. P x) = (!x. Q x)"
   268                (fn prems => [cut_facts_tac prems 1, Blast_tac 1])
   269 in
   270 
   271 (*** make simplification procedures for quantifier elimination ***)
   272 
   273 structure Quantifier1 = Quantifier1Fun
   274 (struct
   275   (*abstract syntax*)
   276   fun dest_eq((c as Const("op =",_)) $ s $ t) = Some(c,s,t)
   277     | dest_eq _ = None;
   278   fun dest_conj((c as Const("op &",_)) $ s $ t) = Some(c,s,t)
   279     | dest_conj _ = None;
   280   fun dest_imp((c as Const("op -->",_)) $ s $ t) = Some(c,s,t)
   281     | dest_imp _ = None;
   282   val conj = HOLogic.conj
   283   val imp  = HOLogic.imp
   284   (*rules*)
   285   val iff_reflection = eq_reflection
   286   val iffI = iffI
   287   val conjI= conjI
   288   val conjE= conjE
   289   val impI = impI
   290   val mp   = mp
   291   val uncurry = uncurry
   292   val exI  = exI
   293   val exE  = exE
   294   val iff_allI = iff_allI
   295 end);
   296 
   297 end;
   298 
   299 local
   300 val ex_pattern = Thm.read_cterm (Theory.sign_of (the_context ()))
   301     ("EX x. P(x) & Q(x)",HOLogic.boolT)
   302 val all_pattern = Thm.read_cterm (Theory.sign_of (the_context ()))
   303     ("ALL x. P(x) --> Q(x)",HOLogic.boolT)
   304 in
   305 val defEX_regroup = mk_simproc "defined EX" [ex_pattern]
   306       Quantifier1.rearrange_ex
   307 val defALL_regroup = mk_simproc "defined ALL" [all_pattern]
   308       Quantifier1.rearrange_all
   309 end;
   310 
   311 
   312 (*** Case splitting ***)
   313 
   314 structure SplitterData =
   315   struct
   316   structure Simplifier = Simplifier
   317   val mk_eq          = mk_eq
   318   val meta_eq_to_iff = meta_eq_to_obj_eq
   319   val iffD           = iffD2
   320   val disjE          = disjE
   321   val conjE          = conjE
   322   val exE            = exE
   323   val contrapos      = contrapos_nn
   324   val contrapos2     = contrapos_pp
   325   val notnotD        = notnotD
   326   end;
   327 
   328 structure Splitter = SplitterFun(SplitterData);
   329 
   330 val split_tac        = Splitter.split_tac;
   331 val split_inside_tac = Splitter.split_inside_tac;
   332 val split_asm_tac    = Splitter.split_asm_tac;
   333 val op addsplits     = Splitter.addsplits;
   334 val op delsplits     = Splitter.delsplits;
   335 val Addsplits        = Splitter.Addsplits;
   336 val Delsplits        = Splitter.Delsplits;
   337 
   338 (*In general it seems wrong to add distributive laws by default: they
   339   might cause exponential blow-up.  But imp_disjL has been in for a while
   340   and cannot be removed without affecting existing proofs.  Moreover,
   341   rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
   342   grounds that it allows simplification of R in the two cases.*)
   343 
   344 val mksimps_pairs =
   345   [("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
   346    ("All", [spec]), ("True", []), ("False", []),
   347    ("If", [if_bool_eq_conj RS iffD1])];
   348 
   349 (* ###FIXME: move to Provers/simplifier.ML
   350 val mk_atomize:      (string * thm list) list -> thm -> thm list
   351 *)
   352 (* ###FIXME: move to Provers/simplifier.ML *)
   353 fun mk_atomize pairs =
   354   let fun atoms th =
   355         (case concl_of th of
   356            Const("Trueprop",_) $ p =>
   357              (case head_of p of
   358                 Const(a,_) =>
   359                   (case assoc(pairs,a) of
   360                      Some(rls) => flat (map atoms ([th] RL rls))
   361                    | None => [th])
   362               | _ => [th])
   363          | _ => [th])
   364   in atoms end;
   365 
   366 fun mksimps pairs = (map mk_eq o mk_atomize pairs o forall_elim_vars_safe);
   367 
   368 fun unsafe_solver_tac prems =
   369   FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac FalseE];
   370 val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
   371 
   372 (*No premature instantiation of variables during simplification*)
   373 fun safe_solver_tac prems =
   374   FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
   375          eq_assume_tac, ematch_tac [FalseE]];
   376 val safe_solver = mk_solver "HOL safe" safe_solver_tac;
   377 
   378 val HOL_basic_ss =
   379   empty_ss setsubgoaler asm_simp_tac
   380     setSSolver safe_solver
   381     setSolver unsafe_solver
   382     setmksimps (mksimps mksimps_pairs)
   383     setmkeqTrue mk_eq_True
   384     setmkcong mk_meta_cong;
   385 
   386 val HOL_ss =
   387     HOL_basic_ss addsimps
   388      ([triv_forall_equality, (* prunes params *)
   389        True_implies_equals, (* prune asms `True' *)
   390        eta_contract_eq, (* prunes eta-expansions *)
   391        if_True, if_False, if_cancel, if_eq_cancel,
   392        imp_disjL, conj_assoc, disj_assoc,
   393        de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, not_imp,
   394        disj_not1, not_all, not_ex, cases_simp, some_eq_trivial, some_sym_eq_trivial,
   395        thm "the_eq_trivial", the_sym_eq_trivial, thm "plus_ac0.zero", thm "plus_ac0_zero_right"]
   396      @ ex_simps @ all_simps @ simp_thms)
   397      addsimprocs [defALL_regroup,defEX_regroup]
   398      addcongs [imp_cong]
   399      addsplits [split_if];
   400 
   401 fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
   402 fun hol_rewrite_cterm rews =
   403   #2 o Thm.dest_comb o #prop o Thm.crep_thm o Simplifier.full_rewrite (HOL_basic_ss addsimps rews);
   404 
   405 
   406 (*Simplifies x assuming c and y assuming ~c*)
   407 val prems = Goalw [if_def]
   408   "[| b=c; c ==> x=u; ~c ==> y=v |] ==> \
   409 \  (if b then x else y) = (if c then u else v)";
   410 by (asm_simp_tac (HOL_ss addsimps prems) 1);
   411 qed "if_cong";
   412 
   413 (*Prevents simplification of x and y: faster and allows the execution
   414   of functional programs. NOW THE DEFAULT.*)
   415 Goal "b=c ==> (if b then x else y) = (if c then x else y)";
   416 by (etac arg_cong 1);
   417 qed "if_weak_cong";
   418 
   419 (*Prevents simplification of t: much faster*)
   420 Goal "a = b ==> (let x=a in t(x)) = (let x=b in t(x))";
   421 by (etac arg_cong 1);
   422 qed "let_weak_cong";
   423 
   424 Goal "f(if c then x else y) = (if c then f x else f y)";
   425 by (simp_tac (HOL_ss setloop (split_tac [split_if])) 1);
   426 qed "if_distrib";
   427 
   428 (*For expand_case_tac*)
   429 val prems = Goal "[| P ==> Q(True); ~P ==> Q(False) |] ==> Q(P)";
   430 by (case_tac "P" 1);
   431 by (ALLGOALS (asm_simp_tac (HOL_ss addsimps prems)));
   432 qed "expand_case";
   433 
   434 (*Used in Auth proofs.  Typically P contains Vars that become instantiated
   435   during unification.*)
   436 fun expand_case_tac P i =
   437     res_inst_tac [("P",P)] expand_case i THEN
   438     Simp_tac (i+1) THEN
   439     Simp_tac i;
   440 
   441 (*This lemma restricts the effect of the rewrite rule u=v to the left-hand
   442   side of an equality.  Used in {Integ,Real}/simproc.ML*)
   443 Goal "x=y ==> (x=z) = (y=z)";
   444 by (asm_simp_tac HOL_ss 1);
   445 qed "restrict_to_left";
   446 
   447 (* default simpset *)
   448 val simpsetup =
   449   [fn thy => (simpset_ref_of thy := HOL_ss addcongs [if_weak_cong]; thy)];
   450 
   451 
   452 (*** integration of simplifier with classical reasoner ***)
   453 
   454 structure Clasimp = ClasimpFun
   455  (structure Simplifier = Simplifier and Splitter = Splitter
   456   and Classical  = Classical and Blast = Blast
   457   val iffD1 = iffD1 val iffD2 = iffD2 val notE = notE
   458   val cla_make_elim = cla_make_elim);
   459 open Clasimp;
   460 
   461 val HOL_css = (HOL_cs, HOL_ss);
   462 
   463 
   464 
   465 (*** A general refutation procedure ***)
   466 
   467 (* Parameters:
   468 
   469    test: term -> bool
   470    tests if a term is at all relevant to the refutation proof;
   471    if not, then it can be discarded. Can improve performance,
   472    esp. if disjunctions can be discarded (no case distinction needed!).
   473 
   474    prep_tac: int -> tactic
   475    A preparation tactic to be applied to the goal once all relevant premises
   476    have been moved to the conclusion.
   477 
   478    ref_tac: int -> tactic
   479    the actual refutation tactic. Should be able to deal with goals
   480    [| A1; ...; An |] ==> False
   481    where the Ai are atomic, i.e. no top-level &, | or EX
   482 *)
   483 
   484 fun refute_tac test prep_tac ref_tac =
   485   let val nnf_simps =
   486         [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
   487          not_all,not_ex,not_not];
   488       val nnf_simpset =
   489         empty_ss setmkeqTrue mk_eq_True
   490                  setmksimps (mksimps mksimps_pairs)
   491                  addsimps nnf_simps;
   492       val prem_nnf_tac = full_simp_tac nnf_simpset;
   493 
   494       val refute_prems_tac =
   495         REPEAT(eresolve_tac [conjE, exE] 1 ORELSE
   496                filter_prems_tac test 1 ORELSE
   497                etac disjE 1) THEN
   498         ((etac notE 1 THEN eq_assume_tac 1) ORELSE
   499          ref_tac 1);
   500   in EVERY'[TRY o filter_prems_tac test,
   501             DETERM o REPEAT o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   502             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   503   end;