src/FOLP/ex/cla.ML
changeset 17480 fd19f77dcf60
parent 3836 f1a1817659e6
     1.1 --- a/src/FOLP/ex/cla.ML	Sat Sep 17 20:49:14 2005 +0200
     1.2 +++ b/src/FOLP/ex/cla.ML	Sun Sep 18 14:25:48 2005 +0200
     1.3 @@ -3,24 +3,20 @@
     1.4      Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     1.5      Copyright   1993  University of Cambridge
     1.6  
     1.7 -Classical First-Order Logic
     1.8 +Classical First-Order Logic.
     1.9  *)
    1.10  
    1.11 -writeln"File FOLP/ex/cla.ML";
    1.12 -
    1.13 -open Cla;    (*in case structure Int is open!*)
    1.14 -
    1.15 -goal FOLP.thy "?p : (P --> Q | R) --> (P-->Q) | (P-->R)";
    1.16 +goal (theory "FOLP") "?p : (P --> Q | R) --> (P-->Q) | (P-->R)";
    1.17  by (fast_tac FOLP_cs 1);
    1.18  result();
    1.19  
    1.20  (*If and only if*)
    1.21  
    1.22 -goal FOLP.thy "?p : (P<->Q) <-> (Q<->P)";
    1.23 +goal (theory "FOLP") "?p : (P<->Q) <-> (Q<->P)";
    1.24  by (fast_tac FOLP_cs 1);
    1.25  result();
    1.26  
    1.27 -goal FOLP.thy "?p : ~ (P <-> ~P)";
    1.28 +goal (theory "FOLP") "?p : ~ (P <-> ~P)";
    1.29  by (fast_tac FOLP_cs 1);
    1.30  result();
    1.31  
    1.32 @@ -37,105 +33,105 @@
    1.33  
    1.34  writeln"Pelletier's examples";
    1.35  (*1*)
    1.36 -goal FOLP.thy "?p : (P-->Q)  <->  (~Q --> ~P)";
    1.37 +goal (theory "FOLP") "?p : (P-->Q)  <->  (~Q --> ~P)";
    1.38  by (fast_tac FOLP_cs 1);
    1.39  result();
    1.40  
    1.41  (*2*)
    1.42 -goal FOLP.thy "?p : ~ ~ P  <->  P";
    1.43 +goal (theory "FOLP") "?p : ~ ~ P  <->  P";
    1.44  by (fast_tac FOLP_cs 1);
    1.45  result();
    1.46  
    1.47  (*3*)
    1.48 -goal FOLP.thy "?p : ~(P-->Q) --> (Q-->P)";
    1.49 +goal (theory "FOLP") "?p : ~(P-->Q) --> (Q-->P)";
    1.50  by (fast_tac FOLP_cs 1);
    1.51  result();
    1.52  
    1.53  (*4*)
    1.54 -goal FOLP.thy "?p : (~P-->Q)  <->  (~Q --> P)";
    1.55 +goal (theory "FOLP") "?p : (~P-->Q)  <->  (~Q --> P)";
    1.56  by (fast_tac FOLP_cs 1);
    1.57  result();
    1.58  
    1.59  (*5*)
    1.60 -goal FOLP.thy "?p : ((P|Q)-->(P|R)) --> (P|(Q-->R))";
    1.61 +goal (theory "FOLP") "?p : ((P|Q)-->(P|R)) --> (P|(Q-->R))";
    1.62  by (fast_tac FOLP_cs 1);
    1.63  result();
    1.64  
    1.65  (*6*)
    1.66 -goal FOLP.thy "?p : P | ~ P";
    1.67 +goal (theory "FOLP") "?p : P | ~ P";
    1.68  by (fast_tac FOLP_cs 1);
    1.69  result();
    1.70  
    1.71  (*7*)
    1.72 -goal FOLP.thy "?p : P | ~ ~ ~ P";
    1.73 +goal (theory "FOLP") "?p : P | ~ ~ ~ P";
    1.74  by (fast_tac FOLP_cs 1);
    1.75  result();
    1.76  
    1.77  (*8.  Peirce's law*)
    1.78 -goal FOLP.thy "?p : ((P-->Q) --> P)  -->  P";
    1.79 +goal (theory "FOLP") "?p : ((P-->Q) --> P)  -->  P";
    1.80  by (fast_tac FOLP_cs 1);
    1.81  result();
    1.82  
    1.83  (*9*)
    1.84 -goal FOLP.thy "?p : ((P|Q) & (~P|Q) & (P| ~Q)) --> ~ (~P | ~Q)";
    1.85 +goal (theory "FOLP") "?p : ((P|Q) & (~P|Q) & (P| ~Q)) --> ~ (~P | ~Q)";
    1.86  by (fast_tac FOLP_cs 1);
    1.87  result();
    1.88  
    1.89  (*10*)
    1.90 -goal FOLP.thy "?p : (Q-->R) & (R-->P&Q) & (P-->Q|R) --> (P<->Q)";
    1.91 +goal (theory "FOLP") "?p : (Q-->R) & (R-->P&Q) & (P-->Q|R) --> (P<->Q)";
    1.92  by (fast_tac FOLP_cs 1);
    1.93  result();
    1.94  
    1.95  (*11.  Proved in each direction (incorrectly, says Pelletier!!)  *)
    1.96 -goal FOLP.thy "?p : P<->P";
    1.97 +goal (theory "FOLP") "?p : P<->P";
    1.98  by (fast_tac FOLP_cs 1);
    1.99  result();
   1.100  
   1.101  (*12.  "Dijkstra's law"*)
   1.102 -goal FOLP.thy "?p : ((P <-> Q) <-> R)  <->  (P <-> (Q <-> R))";
   1.103 +goal (theory "FOLP") "?p : ((P <-> Q) <-> R)  <->  (P <-> (Q <-> R))";
   1.104  by (fast_tac FOLP_cs 1);
   1.105  result();
   1.106  
   1.107  (*13.  Distributive law*)
   1.108 -goal FOLP.thy "?p : P | (Q & R)  <-> (P | Q) & (P | R)";
   1.109 +goal (theory "FOLP") "?p : P | (Q & R)  <-> (P | Q) & (P | R)";
   1.110  by (fast_tac FOLP_cs 1);
   1.111  result();
   1.112  
   1.113  (*14*)
   1.114 -goal FOLP.thy "?p : (P <-> Q) <-> ((Q | ~P) & (~Q|P))";
   1.115 +goal (theory "FOLP") "?p : (P <-> Q) <-> ((Q | ~P) & (~Q|P))";
   1.116  by (fast_tac FOLP_cs 1);
   1.117  result();
   1.118  
   1.119  (*15*)
   1.120 -goal FOLP.thy "?p : (P --> Q) <-> (~P | Q)";
   1.121 +goal (theory "FOLP") "?p : (P --> Q) <-> (~P | Q)";
   1.122  by (fast_tac FOLP_cs 1);
   1.123  result();
   1.124  
   1.125  (*16*)
   1.126 -goal FOLP.thy "?p : (P-->Q) | (Q-->P)";
   1.127 +goal (theory "FOLP") "?p : (P-->Q) | (Q-->P)";
   1.128  by (fast_tac FOLP_cs 1);
   1.129  result();
   1.130  
   1.131  (*17*)
   1.132 -goal FOLP.thy "?p : ((P & (Q-->R))-->S) <-> ((~P | Q | S) & (~P | ~R | S))";
   1.133 +goal (theory "FOLP") "?p : ((P & (Q-->R))-->S) <-> ((~P | Q | S) & (~P | ~R | S))";
   1.134  by (fast_tac FOLP_cs 1);
   1.135  result();
   1.136  
   1.137  writeln"Classical Logic: examples with quantifiers";
   1.138  
   1.139 -goal FOLP.thy "?p : (ALL x. P(x) & Q(x)) <-> (ALL x. P(x))  &  (ALL x. Q(x))";
   1.140 +goal (theory "FOLP") "?p : (ALL x. P(x) & Q(x)) <-> (ALL x. P(x))  &  (ALL x. Q(x))";
   1.141  by (fast_tac FOLP_cs 1);
   1.142  result(); 
   1.143  
   1.144 -goal FOLP.thy "?p : (EX x. P-->Q(x))  <->  (P --> (EX x. Q(x)))";
   1.145 +goal (theory "FOLP") "?p : (EX x. P-->Q(x))  <->  (P --> (EX x. Q(x)))";
   1.146  by (fast_tac FOLP_cs 1);
   1.147  result(); 
   1.148  
   1.149 -goal FOLP.thy "?p : (EX x. P(x)-->Q)  <->  (ALL x. P(x)) --> Q";
   1.150 +goal (theory "FOLP") "?p : (EX x. P(x)-->Q)  <->  (ALL x. P(x)) --> Q";
   1.151  by (fast_tac FOLP_cs 1);
   1.152  result(); 
   1.153  
   1.154 -goal FOLP.thy "?p : (ALL x. P(x)) | Q  <->  (ALL x. P(x) | Q)";
   1.155 +goal (theory "FOLP") "?p : (ALL x. P(x)) | Q  <->  (ALL x. P(x) | Q)";
   1.156  by (fast_tac FOLP_cs 1);
   1.157  result(); 
   1.158  
   1.159 @@ -143,16 +139,16 @@
   1.160  
   1.161  (*Needs multiple instantiation of ALL.*)
   1.162  (*
   1.163 -goal FOLP.thy "?p : (ALL x. P(x)-->P(f(x)))  &  P(d)-->P(f(f(f(d))))";
   1.164 +goal (theory "FOLP") "?p : (ALL x. P(x)-->P(f(x)))  &  P(d)-->P(f(f(f(d))))";
   1.165  by (best_tac FOLP_dup_cs 1);
   1.166  result();
   1.167  *)
   1.168  (*Needs double instantiation of the quantifier*)
   1.169 -goal FOLP.thy "?p : EX x. P(x) --> P(a) & P(b)";
   1.170 +goal (theory "FOLP") "?p : EX x. P(x) --> P(a) & P(b)";
   1.171  by (best_tac FOLP_dup_cs 1);
   1.172  result();
   1.173  
   1.174 -goal FOLP.thy "?p : EX z. P(z) --> (ALL x. P(x))";
   1.175 +goal (theory "FOLP") "?p : EX z. P(z) --> (ALL x. P(x))";
   1.176  by (best_tac FOLP_dup_cs 1);
   1.177  result();
   1.178  
   1.179 @@ -160,45 +156,45 @@
   1.180  writeln"Hard examples with quantifiers";
   1.181  
   1.182  writeln"Problem 18";
   1.183 -goal FOLP.thy "?p : EX y. ALL x. P(y)-->P(x)";
   1.184 +goal (theory "FOLP") "?p : EX y. ALL x. P(y)-->P(x)";
   1.185  by (best_tac FOLP_dup_cs 1);
   1.186  result(); 
   1.187  
   1.188  writeln"Problem 19";
   1.189 -goal FOLP.thy "?p : EX x. ALL y z. (P(y)-->Q(z)) --> (P(x)-->Q(x))";
   1.190 +goal (theory "FOLP") "?p : EX x. ALL y z. (P(y)-->Q(z)) --> (P(x)-->Q(x))";
   1.191  by (best_tac FOLP_dup_cs 1);
   1.192  result();
   1.193  
   1.194  writeln"Problem 20";
   1.195 -goal FOLP.thy "?p : (ALL x y. EX z. ALL w. (P(x)&Q(y)-->R(z)&S(w)))     \
   1.196 +goal (theory "FOLP") "?p : (ALL x y. EX z. ALL w. (P(x)&Q(y)-->R(z)&S(w)))     \
   1.197  \   --> (EX x y. P(x) & Q(y)) --> (EX z. R(z))";
   1.198  by (fast_tac FOLP_cs 1); 
   1.199  result();
   1.200  (*
   1.201  writeln"Problem 21";
   1.202 -goal FOLP.thy "?p : (EX x. P-->Q(x)) & (EX x. Q(x)-->P) --> (EX x. P<->Q(x))";
   1.203 +goal (theory "FOLP") "?p : (EX x. P-->Q(x)) & (EX x. Q(x)-->P) --> (EX x. P<->Q(x))";
   1.204  by (best_tac FOLP_dup_cs 1);
   1.205  result();
   1.206  *)
   1.207  writeln"Problem 22";
   1.208 -goal FOLP.thy "?p : (ALL x. P <-> Q(x))  -->  (P <-> (ALL x. Q(x)))";
   1.209 +goal (theory "FOLP") "?p : (ALL x. P <-> Q(x))  -->  (P <-> (ALL x. Q(x)))";
   1.210  by (fast_tac FOLP_cs 1); 
   1.211  result();
   1.212  
   1.213  writeln"Problem 23";
   1.214 -goal FOLP.thy "?p : (ALL x. P | Q(x))  <->  (P | (ALL x. Q(x)))";
   1.215 +goal (theory "FOLP") "?p : (ALL x. P | Q(x))  <->  (P | (ALL x. Q(x)))";
   1.216  by (best_tac FOLP_cs 1);  
   1.217  result();
   1.218  
   1.219  writeln"Problem 24";
   1.220 -goal FOLP.thy "?p : ~(EX x. S(x)&Q(x)) & (ALL x. P(x) --> Q(x)|R(x)) &  \
   1.221 +goal (theory "FOLP") "?p : ~(EX x. S(x)&Q(x)) & (ALL x. P(x) --> Q(x)|R(x)) &  \
   1.222  \    (~(EX x. P(x)) --> (EX x. Q(x))) & (ALL x. Q(x)|R(x) --> S(x))  \
   1.223  \   --> (EX x. P(x)&R(x))";
   1.224  by (fast_tac FOLP_cs 1); 
   1.225  result();
   1.226  (*
   1.227  writeln"Problem 25";
   1.228 -goal FOLP.thy "?p : (EX x. P(x)) &  \
   1.229 +goal (theory "FOLP") "?p : (EX x. P(x)) &  \
   1.230  \       (ALL x. L(x) --> ~ (M(x) & R(x))) &  \
   1.231  \       (ALL x. P(x) --> (M(x) & L(x))) &   \
   1.232  \       ((ALL x. P(x)-->Q(x)) | (EX x. P(x)&R(x)))  \
   1.233 @@ -207,14 +203,14 @@
   1.234  result();
   1.235  
   1.236  writeln"Problem 26";
   1.237 -goal FOLP.thy "?u : ((EX x. p(x)) <-> (EX x. q(x))) &   \
   1.238 +goal (theory "FOLP") "?u : ((EX x. p(x)) <-> (EX x. q(x))) &   \
   1.239  \     (ALL x. ALL y. p(x) & q(y) --> (r(x) <-> s(y)))   \
   1.240  \ --> ((ALL x. p(x)-->r(x)) <-> (ALL x. q(x)-->s(x)))";
   1.241  by (fast_tac FOLP_cs 1);
   1.242  result();
   1.243  *)
   1.244  writeln"Problem 27";
   1.245 -goal FOLP.thy "?p : (EX x. P(x) & ~Q(x)) &   \
   1.246 +goal (theory "FOLP") "?p : (EX x. P(x) & ~Q(x)) &   \
   1.247  \             (ALL x. P(x) --> R(x)) &   \
   1.248  \             (ALL x. M(x) & L(x) --> P(x)) &   \
   1.249  \             ((EX x. R(x) & ~ Q(x)) --> (ALL x. L(x) --> ~ R(x)))  \
   1.250 @@ -223,7 +219,7 @@
   1.251  result();
   1.252  
   1.253  writeln"Problem 28.  AMENDED";
   1.254 -goal FOLP.thy "?p : (ALL x. P(x) --> (ALL x. Q(x))) &   \
   1.255 +goal (theory "FOLP") "?p : (ALL x. P(x) --> (ALL x. Q(x))) &   \
   1.256  \       ((ALL x. Q(x)|R(x)) --> (EX x. Q(x)&S(x))) &  \
   1.257  \       ((EX x. S(x)) --> (ALL x. L(x) --> M(x)))  \
   1.258  \   --> (ALL x. P(x) & L(x) --> M(x))";
   1.259 @@ -231,21 +227,21 @@
   1.260  result();
   1.261  
   1.262  writeln"Problem 29.  Essentially the same as Principia Mathematica *11.71";
   1.263 -goal FOLP.thy "?p : (EX x. P(x)) & (EX y. Q(y))  \
   1.264 +goal (theory "FOLP") "?p : (EX x. P(x)) & (EX y. Q(y))  \
   1.265  \   --> ((ALL x. P(x)-->R(x)) & (ALL y. Q(y)-->S(y))   <->     \
   1.266  \        (ALL x y. P(x) & Q(y) --> R(x) & S(y)))";
   1.267  by (fast_tac FOLP_cs 1); 
   1.268  result();
   1.269  
   1.270  writeln"Problem 30";
   1.271 -goal FOLP.thy "?p : (ALL x. P(x) | Q(x) --> ~ R(x)) & \
   1.272 +goal (theory "FOLP") "?p : (ALL x. P(x) | Q(x) --> ~ R(x)) & \
   1.273  \       (ALL x. (Q(x) --> ~ S(x)) --> P(x) & R(x))  \
   1.274  \   --> (ALL x. S(x))";
   1.275  by (fast_tac FOLP_cs 1);  
   1.276  result();
   1.277  
   1.278  writeln"Problem 31";
   1.279 -goal FOLP.thy "?p : ~(EX x. P(x) & (Q(x) | R(x))) & \
   1.280 +goal (theory "FOLP") "?p : ~(EX x. P(x) & (Q(x) | R(x))) & \
   1.281  \       (EX x. L(x) & P(x)) & \
   1.282  \       (ALL x. ~ R(x) --> M(x))  \
   1.283  \   --> (EX x. L(x) & M(x))";
   1.284 @@ -253,7 +249,7 @@
   1.285  result();
   1.286  
   1.287  writeln"Problem 32";
   1.288 -goal FOLP.thy "?p : (ALL x. P(x) & (Q(x)|R(x))-->S(x)) & \
   1.289 +goal (theory "FOLP") "?p : (ALL x. P(x) & (Q(x)|R(x))-->S(x)) & \
   1.290  \       (ALL x. S(x) & R(x) --> L(x)) & \
   1.291  \       (ALL x. M(x) --> R(x))  \
   1.292  \   --> (ALL x. P(x) & M(x) --> L(x))";
   1.293 @@ -261,18 +257,18 @@
   1.294  result();
   1.295  
   1.296  writeln"Problem 33";
   1.297 -goal FOLP.thy "?p : (ALL x. P(a) & (P(x)-->P(b))-->P(c))  <->    \
   1.298 +goal (theory "FOLP") "?p : (ALL x. P(a) & (P(x)-->P(b))-->P(c))  <->    \
   1.299  \    (ALL x. (~P(a) | P(x) | P(c)) & (~P(a) | ~P(b) | P(c)))";
   1.300  by (best_tac FOLP_cs 1);
   1.301  result();
   1.302  
   1.303  writeln"Problem 35";
   1.304 -goal FOLP.thy "?p : EX x y. P(x,y) -->  (ALL u v. P(u,v))";
   1.305 +goal (theory "FOLP") "?p : EX x y. P(x,y) -->  (ALL u v. P(u,v))";
   1.306  by (best_tac FOLP_dup_cs 1);
   1.307  result();
   1.308  
   1.309  writeln"Problem 36";
   1.310 -goal FOLP.thy
   1.311 +goal (theory "FOLP")
   1.312  "?p : (ALL x. EX y. J(x,y)) & \
   1.313  \     (ALL x. EX y. G(x,y)) & \
   1.314  \     (ALL x y. J(x,y) | G(x,y) --> (ALL z. J(y,z) | G(y,z) --> H(x,z)))   \
   1.315 @@ -281,7 +277,7 @@
   1.316  result();
   1.317  
   1.318  writeln"Problem 37";
   1.319 -goal FOLP.thy "?p : (ALL z. EX w. ALL x. EX y. \
   1.320 +goal (theory "FOLP") "?p : (ALL z. EX w. ALL x. EX y. \
   1.321  \          (P(x,z)-->P(y,w)) & P(y,z) & (P(y,w) --> (EX u. Q(u,w)))) & \
   1.322  \       (ALL x z. ~P(x,z) --> (EX y. Q(y,z))) & \
   1.323  \       ((EX x y. Q(x,y)) --> (ALL x. R(x,x)))  \
   1.324 @@ -290,24 +286,24 @@
   1.325  result();
   1.326  
   1.327  writeln"Problem 39";
   1.328 -goal FOLP.thy "?p : ~ (EX x. ALL y. F(y,x) <-> ~F(y,y))";
   1.329 +goal (theory "FOLP") "?p : ~ (EX x. ALL y. F(y,x) <-> ~F(y,y))";
   1.330  by (fast_tac FOLP_cs 1);
   1.331  result();
   1.332  
   1.333  writeln"Problem 40.  AMENDED";
   1.334 -goal FOLP.thy "?p : (EX y. ALL x. F(x,y) <-> F(x,x)) -->  \
   1.335 +goal (theory "FOLP") "?p : (EX y. ALL x. F(x,y) <-> F(x,x)) -->  \
   1.336  \             ~(ALL x. EX y. ALL z. F(z,y) <-> ~ F(z,x))";
   1.337  by (fast_tac FOLP_cs 1);
   1.338  result();
   1.339  
   1.340  writeln"Problem 41";
   1.341 -goal FOLP.thy "?p : (ALL z. EX y. ALL x. f(x,y) <-> f(x,z) & ~ f(x,x))  \
   1.342 +goal (theory "FOLP") "?p : (ALL z. EX y. ALL x. f(x,y) <-> f(x,z) & ~ f(x,x))  \
   1.343  \         --> ~ (EX z. ALL x. f(x,z))";
   1.344  by (best_tac FOLP_cs 1);
   1.345  result();
   1.346  
   1.347  writeln"Problem 44";
   1.348 -goal FOLP.thy "?p : (ALL x. f(x) -->                                    \
   1.349 +goal (theory "FOLP") "?p : (ALL x. f(x) -->                                    \
   1.350  \             (EX y. g(y) & h(x,y) & (EX y. g(y) & ~ h(x,y))))  &       \
   1.351  \             (EX x. j(x) & (ALL y. g(y) --> h(x,y)))                   \
   1.352  \             --> (EX x. j(x) & ~f(x))";
   1.353 @@ -317,44 +313,42 @@
   1.354  writeln"Problems (mainly) involving equality or functions";
   1.355  
   1.356  writeln"Problem 48";
   1.357 -goal FOLP.thy "?p : (a=b | c=d) & (a=c | b=d) --> a=d | b=c";
   1.358 +goal (theory "FOLP") "?p : (a=b | c=d) & (a=c | b=d) --> a=d | b=c";
   1.359  by (fast_tac FOLP_cs 1);
   1.360  result();
   1.361  
   1.362  writeln"Problem 50";  
   1.363  (*What has this to do with equality?*)
   1.364 -goal FOLP.thy "?p : (ALL x. P(a,x) | (ALL y. P(x,y))) --> (EX x. ALL y. P(x,y))";
   1.365 +goal (theory "FOLP") "?p : (ALL x. P(a,x) | (ALL y. P(x,y))) --> (EX x. ALL y. P(x,y))";
   1.366  by (best_tac FOLP_dup_cs 1);
   1.367  result();
   1.368  
   1.369  writeln"Problem 56";
   1.370 -goal FOLP.thy
   1.371 +goal (theory "FOLP")
   1.372   "?p : (ALL x. (EX y. P(y) & x=f(y)) --> P(x)) <-> (ALL x. P(x) --> P(f(x)))";
   1.373  by (fast_tac FOLP_cs 1);
   1.374  result();
   1.375  
   1.376  writeln"Problem 57";
   1.377 -goal FOLP.thy
   1.378 +goal (theory "FOLP")
   1.379  "?p : P(f(a,b), f(b,c)) & P(f(b,c), f(a,c)) & \
   1.380  \     (ALL x y z. P(x,y) & P(y,z) --> P(x,z))    -->   P(f(a,b), f(a,c))";
   1.381  by (fast_tac FOLP_cs 1);
   1.382  result();
   1.383  
   1.384  writeln"Problem 58  NOT PROVED AUTOMATICALLY";
   1.385 -goal FOLP.thy "?p : (ALL x y. f(x)=g(y)) --> (ALL x y. f(f(x))=f(g(y)))";
   1.386 +goal (theory "FOLP") "?p : (ALL x y. f(x)=g(y)) --> (ALL x y. f(f(x))=f(g(y)))";
   1.387  val f_cong = read_instantiate [("t","f")] subst_context;
   1.388  by (fast_tac (FOLP_cs addIs [f_cong]) 1);
   1.389  result();
   1.390  
   1.391  writeln"Problem 59";
   1.392 -goal FOLP.thy "?p : (ALL x. P(x) <-> ~P(f(x))) --> (EX x. P(x) & ~P(f(x)))";
   1.393 +goal (theory "FOLP") "?p : (ALL x. P(x) <-> ~P(f(x))) --> (EX x. P(x) & ~P(f(x)))";
   1.394  by (best_tac FOLP_dup_cs 1);
   1.395  result();
   1.396  
   1.397  writeln"Problem 60";
   1.398 -goal FOLP.thy
   1.399 +goal (theory "FOLP")
   1.400  "?p : ALL x. P(x,f(x)) <-> (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))";
   1.401  by (fast_tac FOLP_cs 1);
   1.402  result();
   1.403 -
   1.404 -writeln"Reached end of file.";