src/HOL/Set.ML
 changeset 2499 0bc87b063447 parent 2031 03a843f0f447 child 2608 450c9b682a92
```     1.1 --- a/src/HOL/Set.ML	Thu Jan 09 10:22:42 1997 +0100
1.2 +++ b/src/HOL/Set.ML	Thu Jan 09 10:23:39 1997 +0100
1.3 @@ -10,13 +10,14 @@
1.4
1.5  section "Relating predicates and sets";
1.6
1.7 -val [prem] = goal Set.thy "P(a) ==> a : {x.P(x)}";
1.8 -by (stac mem_Collect_eq 1);
1.9 -by (rtac prem 1);
1.11 +
1.12 +goal Set.thy "!!a. P(a) ==> a : {x.P(x)}";
1.13 +by (Asm_simp_tac 1);
1.14  qed "CollectI";
1.15
1.16 -val prems = goal Set.thy "[| a : {x.P(x)} |] ==> P(a)";
1.17 -by (resolve_tac (prems RL [mem_Collect_eq  RS subst]) 1);
1.18 +val prems = goal Set.thy "!!a. a : {x.P(x)} ==> P(a)";
1.19 +by (Asm_full_simp_tac 1);
1.20  qed "CollectD";
1.21
1.22  val [prem] = goal Set.thy "[| !!x. (x:A) = (x:B) |] ==> A = B";
1.23 @@ -31,6 +32,10 @@
1.24
1.25  val CollectE = make_elim CollectD;
1.26
1.29 +
1.30 +
1.31  section "Bounded quantifiers";
1.32
1.33  val prems = goalw Set.thy [Ball_def]
1.34 @@ -52,6 +57,9 @@
1.35  (*Takes assumptions ! x:A.P(x) and a:A; creates assumption P(a)*)
1.36  fun ball_tac i = etac ballE i THEN contr_tac (i+1);
1.37
1.40 +
1.41  val prems = goalw Set.thy [Bex_def]
1.42      "[| P(x);  x:A |] ==> ? x:A. P(x)";
1.43  by (REPEAT (ares_tac (prems @ [exI,conjI]) 1));
1.44 @@ -69,6 +77,9 @@
1.45  by (REPEAT (eresolve_tac (prems @ [asm_rl,conjE]) 1));
1.46  qed "bexE";
1.47
1.50 +
1.51  (*Trival rewrite rule;   (! x:A.P)=P holds only if A is nonempty!*)
1.52  goalw Set.thy [Ball_def] "(! x:A. True) = True";
1.53  by (Simp_tac 1);
1.54 @@ -134,12 +145,14 @@
1.55  (*Takes assumptions A<=B; c:A and creates the assumption c:B *)
1.56  fun set_mp_tac i = etac subsetCE i  THEN  mp_tac i;
1.57
1.58 -qed_goal "subset_refl" Set.thy "A <= (A::'a set)"
1.59 - (fn _=> [ (REPEAT (ares_tac [subsetI] 1)) ]);
1.62
1.63 -val prems = goal Set.thy "[| A<=B;  B<=C |] ==> A<=(C::'a set)";
1.64 -by (cut_facts_tac prems 1);
1.65 -by (REPEAT (ares_tac [subsetI] 1 ORELSE set_mp_tac 1));
1.66 +qed_goal "subset_refl" Set.thy "A <= (A::'a set)"
1.67 + (fn _=> [Fast_tac 1]);
1.68 +
1.69 +val prems = goal Set.thy "!!B. [| A<=B;  B<=C |] ==> A<=(C::'a set)";
1.70 +by (Fast_tac 1);
1.71  qed "subset_trans";
1.72
1.73
1.74 @@ -189,6 +202,11 @@
1.75
1.76  section "Set complement -- Compl";
1.77
1.78 +qed_goalw "Compl_iff" Set.thy [Compl_def] "(c : Compl(A)) = (c~:A)"
1.79 + (fn _ => [ (Fast_tac 1) ]);
1.80 +
1.82 +
1.83  val prems = goalw Set.thy [Compl_def]
1.84      "[| c:A ==> False |] ==> c : Compl(A)";
1.85  by (REPEAT (ares_tac (prems @ [CollectI,notI]) 1));
1.86 @@ -198,32 +216,36 @@
1.87    Negated assumptions behave like formulae on the right side of the notional
1.88    turnstile...*)
1.89  val major::prems = goalw Set.thy [Compl_def]
1.90 -    "[| c : Compl(A) |] ==> c~:A";
1.91 +    "c : Compl(A) ==> c~:A";
1.92  by (rtac (major RS CollectD) 1);
1.93  qed "ComplD";
1.94
1.95  val ComplE = make_elim ComplD;
1.96
1.97 -qed_goal "Compl_iff" Set.thy "(c : Compl(A)) = (c~:A)"
1.98 - (fn _ => [ (fast_tac (!claset addSIs [ComplI] addSEs [ComplE]) 1) ]);
1.101
1.102
1.103  section "Binary union -- Un";
1.104
1.105 -val prems = goalw Set.thy [Un_def] "c:A ==> c : A Un B";
1.106 -by (REPEAT (resolve_tac (prems @ [CollectI,disjI1]) 1));
1.107 +qed_goalw "Un_iff" Set.thy [Un_def] "(c : A Un B) = (c:A | c:B)"
1.108 + (fn _ => [ Fast_tac 1 ]);
1.109 +
1.111 +
1.112 +goal Set.thy "!!c. c:A ==> c : A Un B";
1.113 +by (Asm_simp_tac 1);
1.114  qed "UnI1";
1.115
1.116 -val prems = goalw Set.thy [Un_def] "c:B ==> c : A Un B";
1.117 -by (REPEAT (resolve_tac (prems @ [CollectI,disjI2]) 1));
1.118 +goal Set.thy "!!c. c:B ==> c : A Un B";
1.119 +by (Asm_simp_tac 1);
1.120  qed "UnI2";
1.121
1.122  (*Classical introduction rule: no commitment to A vs B*)
1.123  qed_goal "UnCI" Set.thy "(c~:B ==> c:A) ==> c : A Un B"
1.124   (fn prems=>
1.125 -  [ (rtac classical 1),
1.126 -    (REPEAT (ares_tac (prems@[UnI1,notI]) 1)),
1.127 -    (REPEAT (ares_tac (prems@[UnI2,notE]) 1)) ]);
1.128 +  [ (Simp_tac 1),
1.129 +    (REPEAT (ares_tac (prems@[disjCI]) 1)) ]);
1.130
1.131  val major::prems = goalw Set.thy [Un_def]
1.132      "[| c : A Un B;  c:A ==> P;  c:B ==> P |] ==> P";
1.133 @@ -231,23 +253,27 @@
1.134  by (REPEAT (eresolve_tac prems 1));
1.135  qed "UnE";
1.136
1.137 -qed_goal "Un_iff" Set.thy "(c : A Un B) = (c:A | c:B)"
1.138 - (fn _ => [ (fast_tac (!claset addSIs [UnCI] addSEs [UnE]) 1) ]);
1.141
1.142
1.143  section "Binary intersection -- Int";
1.144
1.145 -val prems = goalw Set.thy [Int_def]
1.146 -    "[| c:A;  c:B |] ==> c : A Int B";
1.147 -by (REPEAT (resolve_tac (prems @ [CollectI,conjI]) 1));
1.148 +qed_goalw "Int_iff" Set.thy [Int_def] "(c : A Int B) = (c:A & c:B)"
1.149 + (fn _ => [ (Fast_tac 1) ]);
1.150 +
1.152 +
1.153 +goal Set.thy "!!c. [| c:A;  c:B |] ==> c : A Int B";
1.154 +by (Asm_simp_tac 1);
1.155  qed "IntI";
1.156
1.157 -val [major] = goalw Set.thy [Int_def] "c : A Int B ==> c:A";
1.158 -by (rtac (major RS CollectD RS conjunct1) 1);
1.159 +goal Set.thy "!!c. c : A Int B ==> c:A";
1.160 +by (Asm_full_simp_tac 1);
1.161  qed "IntD1";
1.162
1.163 -val [major] = goalw Set.thy [Int_def] "c : A Int B ==> c:B";
1.164 -by (rtac (major RS CollectD RS conjunct2) 1);
1.165 +goal Set.thy "!!c. c : A Int B ==> c:B";
1.166 +by (Asm_full_simp_tac 1);
1.167  qed "IntD2";
1.168
1.169  val [major,minor] = goal Set.thy
1.170 @@ -257,53 +283,54 @@
1.171  by (rtac (major RS IntD2) 1);
1.172  qed "IntE";
1.173
1.174 -qed_goal "Int_iff" Set.thy "(c : A Int B) = (c:A & c:B)"
1.175 - (fn _ => [ (fast_tac (!claset addSIs [IntI] addSEs [IntE]) 1) ]);
1.176 -
1.179
1.180  section "Set difference";
1.181
1.182 -qed_goalw "DiffI" Set.thy [set_diff_def]
1.183 -    "[| c : A;  c ~: B |] ==> c : A - B"
1.184 - (fn prems=> [ (REPEAT (resolve_tac (prems @ [CollectI,conjI]) 1)) ]);
1.185 +qed_goalw "Diff_iff" Set.thy [set_diff_def] "(c : A-B) = (c:A & c~:B)"
1.186 + (fn _ => [ (Fast_tac 1) ]);
1.187
1.188 -qed_goalw "DiffD1" Set.thy [set_diff_def]
1.189 -    "c : A - B ==> c : A"
1.190 - (fn [major]=> [ (rtac (major RS CollectD RS conjunct1) 1) ]);
1.192 +
1.193 +qed_goal "DiffI" Set.thy "!!c. [| c : A;  c ~: B |] ==> c : A - B"
1.194 + (fn _=> [ Asm_simp_tac 1 ]);
1.195
1.196 -qed_goalw "DiffD2" Set.thy [set_diff_def]
1.197 -    "[| c : A - B;  c : B |] ==> P"
1.198 - (fn [major,minor]=>
1.199 -     [rtac (minor RS (major RS CollectD RS conjunct2 RS notE)) 1]);
1.200 +qed_goal "DiffD1" Set.thy "!!c. c : A - B ==> c : A"
1.201 + (fn _=> [ (Asm_full_simp_tac 1) ]);
1.202
1.203 -qed_goal "DiffE" Set.thy
1.204 -    "[| c : A - B;  [| c:A; c~:B |] ==> P |] ==> P"
1.205 +qed_goal "DiffD2" Set.thy "!!c. [| c : A - B;  c : B |] ==> P"
1.206 + (fn _=> [ (Asm_full_simp_tac 1) ]);
1.207 +
1.208 +qed_goal "DiffE" Set.thy "[| c : A - B;  [| c:A; c~:B |] ==> P |] ==> P"
1.209   (fn prems=>
1.210    [ (resolve_tac prems 1),
1.211      (REPEAT (ares_tac (prems RL [DiffD1, DiffD2 RS notI]) 1)) ]);
1.212
1.213 -qed_goal "Diff_iff" Set.thy "(c : A-B) = (c:A & c~:B)"
1.214 - (fn _ => [ (fast_tac (!claset addSIs [DiffI] addSEs [DiffE]) 1) ]);
1.217
1.218  section "The empty set -- {}";
1.219
1.220 -qed_goalw "emptyE" Set.thy [empty_def] "a:{} ==> P"
1.221 - (fn [prem] => [rtac (prem RS CollectD RS FalseE) 1]);
1.222 +qed_goalw "empty_iff" Set.thy [empty_def] "(c : {}) = False"
1.223 + (fn _ => [ (Fast_tac 1) ]);
1.224 +
1.226 +
1.227 +qed_goal "emptyE" Set.thy "!!a. a:{} ==> P"
1.228 + (fn _ => [Full_simp_tac 1]);
1.229 +
1.231
1.232  qed_goal "empty_subsetI" Set.thy "{} <= A"
1.233 - (fn _ => [ (REPEAT (ares_tac [equalityI,subsetI,emptyE] 1)) ]);
1.234 + (fn _ => [ (Fast_tac 1) ]);
1.235
1.236  qed_goal "equals0I" Set.thy "[| !!y. y:A ==> False |] ==> A={}"
1.237 - (fn prems=>
1.238 -  [ (REPEAT (ares_tac (prems@[empty_subsetI,subsetI,equalityI]) 1
1.239 -      ORELSE eresolve_tac (prems RL [FalseE]) 1)) ]);
1.240 + (fn [prem]=>
1.241 +  [ (fast_tac (!claset addIs [prem RS FalseE]) 1) ]);
1.242
1.243 -qed_goal "equals0D" Set.thy "[| A={};  a:A |] ==> P"
1.244 - (fn [major,minor]=>
1.245 -  [ (rtac (minor RS (major RS equalityD1 RS subsetD RS emptyE)) 1) ]);
1.246 -
1.247 -qed_goal "empty_iff" Set.thy "(c : {}) = False"
1.248 - (fn _ => [ (fast_tac (!claset addSEs [emptyE]) 1) ]);
1.249 +qed_goal "equals0D" Set.thy "!!a. [| A={};  a:A |] ==> P"
1.250 + (fn _ => [ (Fast_tac 1) ]);
1.251
1.252  goal Set.thy "Ball {} P = True";
1.253  by (simp_tac (HOL_ss addsimps [mem_Collect_eq, Ball_def, empty_def]) 1);
1.254 @@ -317,11 +344,16 @@
1.255
1.256  section "Augmenting a set -- insert";
1.257
1.258 -qed_goalw "insertI1" Set.thy [insert_def] "a : insert a B"
1.259 - (fn _ => [rtac (CollectI RS UnI1) 1, rtac refl 1]);
1.260 +qed_goalw "insert_iff" Set.thy [insert_def] "a : insert b A = (a=b | a:A)"
1.261 + (fn _ => [Fast_tac 1]);
1.262 +
1.264
1.265 -qed_goalw "insertI2" Set.thy [insert_def] "a : B ==> a : insert b B"
1.266 - (fn [prem]=> [ (rtac (prem RS UnI2) 1) ]);
1.267 +qed_goal "insertI1" Set.thy "a : insert a B"
1.268 + (fn _ => [Simp_tac 1]);
1.269 +
1.270 +qed_goal "insertI2" Set.thy "!!a. a : B ==> a : insert b B"
1.271 + (fn _=> [Asm_simp_tac 1]);
1.272
1.273  qed_goalw "insertE" Set.thy [insert_def]
1.274      "[| a : insert b A;  a=b ==> P;  a:A ==> P |] ==> P"
1.275 @@ -329,37 +361,35 @@
1.276    [ (rtac (major RS UnE) 1),
1.277      (REPEAT (eresolve_tac (prems @ [CollectE]) 1)) ]);
1.278
1.279 -qed_goal "insert_iff" Set.thy "a : insert b A = (a=b | a:A)"
1.280 - (fn _ => [fast_tac (!claset addIs [insertI1,insertI2] addSEs [insertE]) 1]);
1.281 -
1.282  (*Classical introduction rule*)
1.283  qed_goal "insertCI" Set.thy "(a~:B ==> a=b) ==> a: insert b B"
1.284 - (fn [prem]=>
1.285 -  [ (rtac (disjCI RS (insert_iff RS iffD2)) 1),
1.286 -    (etac prem 1) ]);
1.287 + (fn prems=>
1.288 +  [ (Simp_tac 1),
1.289 +    (REPEAT (ares_tac (prems@[disjCI]) 1)) ]);
1.290 +
1.293
1.294  section "Singletons, using insert";
1.295
1.296  qed_goal "singletonI" Set.thy "a : {a}"
1.297   (fn _=> [ (rtac insertI1 1) ]);
1.298
1.299 -goalw Set.thy [insert_def] "!!a. b : {a} ==> b=a";
1.300 -by (fast_tac (!claset addSEs [emptyE,CollectE,UnE]) 1);
1.301 +goal Set.thy "!!a. b : {a} ==> b=a";
1.302 +by (Fast_tac 1);
1.303  qed "singletonD";
1.304
1.305  bind_thm ("singletonE", make_elim singletonD);
1.306
1.307 -qed_goal "singleton_iff" thy "(b : {a}) = (b=a)" (fn _ => [
1.308 -        rtac iffI 1,
1.309 -        etac singletonD 1,
1.310 -        hyp_subst_tac 1,
1.311 -        rtac singletonI 1]);
1.312 +qed_goal "singleton_iff" thy "(b : {a}) = (b=a)"
1.313 +(fn _ => [Fast_tac 1]);
1.314
1.315 -val [major] = goal Set.thy "{a}={b} ==> a=b";
1.316 -by (rtac (major RS equalityD1 RS subsetD RS singletonD) 1);
1.317 -by (rtac singletonI 1);
1.318 +goal Set.thy "!!a b. {a}={b} ==> a=b";
1.319 +by (fast_tac (!claset addEs [equalityE]) 1);
1.320  qed "singleton_inject";
1.321
1.323 +
1.324
1.325  section "The universal set -- UNIV";
1.326
1.327 @@ -372,10 +402,15 @@
1.328
1.329  section "Unions of families -- UNION x:A. B(x) is Union(B``A)";
1.330
1.331 +goalw Set.thy [UNION_def] "(b: (UN x:A. B(x))) = (EX x:A. b: B(x))";
1.332 +by (Fast_tac 1);
1.333 +qed "UN_iff";
1.334 +
1.336 +
1.337  (*The order of the premises presupposes that A is rigid; b may be flexible*)
1.338 -val prems = goalw Set.thy [UNION_def]
1.339 -    "[| a:A;  b: B(a) |] ==> b: (UN x:A. B(x))";
1.340 -by (REPEAT (resolve_tac (prems @ [bexI,CollectI]) 1));
1.341 +goal Set.thy "!!b. [| a:A;  b: B(a) |] ==> b: (UN x:A. B(x))";
1.342 +by (Auto_tac());
1.343  qed "UN_I";
1.344
1.345  val major::prems = goalw Set.thy [UNION_def]
1.346 @@ -384,6 +419,9 @@
1.347  by (REPEAT (ares_tac prems 1));
1.348  qed "UN_E";
1.349
1.352 +
1.353  val prems = goal Set.thy
1.354      "[| A=B;  !!x. x:B ==> C(x) = D(x) |] ==> \
1.355  \    (UN x:A. C(x)) = (UN x:B. D(x))";
1.356 @@ -395,15 +433,19 @@
1.357
1.358  section "Intersections of families -- INTER x:A. B(x) is Inter(B``A)";
1.359
1.360 +goalw Set.thy [INTER_def] "(b: (INT x:A. B(x))) = (ALL x:A. b: B(x))";
1.361 +by (Auto_tac());
1.362 +qed "INT_iff";
1.363 +
1.365 +
1.366  val prems = goalw Set.thy [INTER_def]
1.367      "(!!x. x:A ==> b: B(x)) ==> b : (INT x:A. B(x))";
1.368  by (REPEAT (ares_tac ([CollectI,ballI] @ prems) 1));
1.369  qed "INT_I";
1.370
1.371 -val major::prems = goalw Set.thy [INTER_def]
1.372 -    "[| b : (INT x:A. B(x));  a:A |] ==> b: B(a)";
1.373 -by (rtac (major RS CollectD RS bspec) 1);
1.374 -by (resolve_tac prems 1);
1.375 +goal Set.thy "!!b. [| b : (INT x:A. B(x));  a:A |] ==> b: B(a)";
1.376 +by (Auto_tac());
1.377  qed "INT_D";
1.378
1.379  (*"Classical" elimination -- by the Excluded Middle on a:A *)
1.380 @@ -413,6 +455,9 @@
1.381  by (REPEAT (eresolve_tac prems 1));
1.382  qed "INT_E";
1.383
1.386 +
1.387  val prems = goal Set.thy
1.388      "[| A=B;  !!x. x:B ==> C(x) = D(x) |] ==> \
1.389  \    (INT x:A. C(x)) = (INT x:B. D(x))";
1.390 @@ -424,10 +469,16 @@
1.391
1.392  section "Unions over a type; UNION1(B) = Union(range(B))";
1.393
1.394 +goalw Set.thy [UNION1_def] "(b: (UN x. B(x))) = (EX x. b: B(x))";
1.395 +by (Simp_tac 1);
1.396 +by (Fast_tac 1);
1.397 +qed "UN1_iff";
1.398 +
1.400 +
1.401  (*The order of the premises presupposes that A is rigid; b may be flexible*)
1.402 -val prems = goalw Set.thy [UNION1_def]
1.403 -    "b: B(x) ==> b: (UN x. B(x))";
1.404 -by (REPEAT (resolve_tac (prems @ [TrueI, CollectI RS UN_I]) 1));
1.405 +goal Set.thy "!!b. b: B(x) ==> b: (UN x. B(x))";
1.406 +by (Auto_tac());
1.407  qed "UN1_I";
1.408
1.409  val major::prems = goalw Set.thy [UNION1_def]
1.410 @@ -436,25 +487,43 @@
1.411  by (REPEAT (ares_tac prems 1));
1.412  qed "UN1_E";
1.413
1.416 +
1.417
1.418  section "Intersections over a type; INTER1(B) = Inter(range(B))";
1.419
1.420 +goalw Set.thy [INTER1_def] "(b: (INT x. B(x))) = (ALL x. b: B(x))";
1.421 +by (Simp_tac 1);
1.422 +by (Fast_tac 1);
1.423 +qed "INT1_iff";
1.424 +
1.426 +
1.427  val prems = goalw Set.thy [INTER1_def]
1.428      "(!!x. b: B(x)) ==> b : (INT x. B(x))";
1.429  by (REPEAT (ares_tac (INT_I::prems) 1));
1.430  qed "INT1_I";
1.431
1.432 -val [major] = goalw Set.thy [INTER1_def]
1.433 -    "b : (INT x. B(x)) ==> b: B(a)";
1.434 -by (rtac (TrueI RS (CollectI RS (major RS INT_D))) 1);
1.435 +goal Set.thy "!!b. b : (INT x. B(x)) ==> b: B(a)";
1.436 +by (Asm_full_simp_tac 1);
1.437  qed "INT1_D";
1.438
1.441 +
1.442 +
1.443  section "Union";
1.444
1.445 +goalw Set.thy [Union_def] "(A : Union(C)) = (EX X:C. A:X)";
1.446 +by (Fast_tac 1);
1.447 +qed "Union_iff";
1.448 +
1.450 +
1.451  (*The order of the premises presupposes that C is rigid; A may be flexible*)
1.452 -val prems = goalw Set.thy [Union_def]
1.453 -    "[| X:C;  A:X |] ==> A : Union(C)";
1.454 -by (REPEAT (resolve_tac (prems @ [UN_I]) 1));
1.455 +goal Set.thy "!!X. [| X:C;  A:X |] ==> A : Union(C)";
1.456 +by (Auto_tac());
1.457  qed "UnionI";
1.458
1.459  val major::prems = goalw Set.thy [Union_def]
1.460 @@ -463,8 +532,18 @@
1.461  by (REPEAT (ares_tac prems 1));
1.462  qed "UnionE";
1.463
1.466 +
1.467 +
1.468  section "Inter";
1.469
1.470 +goalw Set.thy [Inter_def] "(A : Inter(C)) = (ALL X:C. A:X)";
1.471 +by (Fast_tac 1);
1.472 +qed "Inter_iff";
1.473 +
1.475 +
1.476  val prems = goalw Set.thy [Inter_def]
1.477      "[| !!X. X:C ==> A:X |] ==> A : Inter(C)";
1.478  by (REPEAT (ares_tac ([INT_I] @ prems) 1));
1.479 @@ -472,10 +551,8 @@
1.480
1.481  (*A "destruct" rule -- every X in C contains A as an element, but
1.482    A:X can hold when X:C does not!  This rule is analogous to "spec". *)
1.483 -val major::prems = goalw Set.thy [Inter_def]
1.484 -    "[| A : Inter(C);  X:C |] ==> A:X";
1.485 -by (rtac (major RS INT_D) 1);
1.486 -by (resolve_tac prems 1);
1.487 +goal Set.thy "!!X. [| A : Inter(C);  X:C |] ==> A:X";
1.488 +by (Auto_tac());
1.489  qed "InterD";
1.490
1.491  (*"Classical" elimination rule -- does not require proving X:C *)
1.492 @@ -485,8 +562,17 @@
1.493  by (REPEAT (eresolve_tac prems 1));
1.494  qed "InterE";
1.495
1.498 +
1.499 +
1.500  section "The Powerset operator -- Pow";
1.501
1.502 +qed_goalw "Pow_iff" Set.thy [Pow_def] "(A : Pow(B)) = (A <= B)"
1.503 + (fn _ => [ (Asm_simp_tac 1) ]);
1.504 +
1.506 +
1.507  qed_goalw "PowI" Set.thy [Pow_def] "!!A B. A <= B ==> A : Pow(B)"
1.508   (fn _ => [ (etac CollectI 1) ]);
1.509
1.510 @@ -501,8 +587,11 @@
1.511  (*** Set reasoning tools ***)
1.512
1.513
1.515  val mem_simps = [insert_iff, empty_iff, Un_iff, Int_iff, Compl_iff, Diff_iff,
1.516 -                 mem_Collect_eq];
1.517 +                 mem_Collect_eq,
1.518 +		 UN_iff, UN1_iff, Union_iff,
1.519 +		 INT_iff, INT1_iff, Inter_iff];
1.520
1.521  (*Not for Addsimps -- it can cause goals to blow up!*)
1.522  goal Set.thy "(a : (if Q then x else y)) = ((Q --> a:x) & (~Q --> a : y))";
1.523 @@ -511,6 +600,5 @@
1.524
1.525  val mksimps_pairs = ("Ball",[bspec]) :: mksimps_pairs;
1.526
1.527 -simpset := !simpset addsimps mem_simps