src/FOLP/ex/quant.ML

 
 First-Order Logic: quantifier examples (intuitionistic and classical)
 Needs declarations of the theory "thy" and the tactic "tac"
 *)
 
-writeln"File FOLP/ex/quant.ML";
-
 Goal "?p : (ALL x y. P(x,y))  -->  (ALL y x. P(x,y))";
 by tac;
-result();  
+result();
 
 
 Goal "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))";
 by tac;
-result();  
+result();
 
 
 (*Converse is false*)
 Goal "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
 by tac;
-result();  
+result();
 
 Goal "?p : (ALL x. P-->Q(x))  <->  (P--> (ALL x. Q(x)))";
 by tac;
-result();  
+result();
 
 
 Goal "?p : (ALL x. P(x)-->Q)  <->  ((EX x. P(x)) --> Q)";
 by tac;
-result();  
+result();
 
 
 writeln"Some harder ones";
 
 Goal "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
 by tac;
-result();  
+result();
 (*6 secs*)
 
 (*Converse is false*)
 Goal "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x))  &  (EX x. Q(x))";
 by tac;
-result();  
+result();
 
 
 writeln"Basic test of quantifier reasoning";
 (*TRUE*)
 Goal "?p : (EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))";
-by tac;  
-result();  
+by tac;
+result();
 
 
 Goal "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
-by tac;  
-result();  
+by tac;
+result();
 
 
 writeln"The following should fail, as they are false!";
 
 Goal "?p : (ALL x. EX y. Q(x,y))  -->  (EX y. ALL x. Q(x,y))";
-by tac handle ERROR => writeln"Failed, as expected";  
+by tac handle ERROR => writeln"Failed, as expected";
 (*Check that subgoals remain: proof failed.*)
-getgoal 1; 
+getgoal 1;
 
 Goal "?p : (EX x. Q(x))  -->  (ALL x. Q(x))";
-by tac handle ERROR => writeln"Failed, as expected";  
-getgoal 1; 
+by tac handle ERROR => writeln"Failed, as expected";
+getgoal 1;
 
 Goal "?p : P(?a) --> (ALL x. P(x))";
 by tac handle ERROR => writeln"Failed, as expected";
 (*Check that subgoals remain: proof failed.*)
-getgoal 1;  
+getgoal 1;
 
 Goal
     "?p : (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))";
 by tac handle ERROR => writeln"Failed, as expected";
-getgoal 1;  
+getgoal 1;
 
 
 writeln"Back to things that are provable...";
 
 Goal "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))";
-by tac;  
-result();  
+by tac;
+result();
 
 
 (*An example of why exI should be delayed as long as possible*)
 Goal "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
-by tac;  
-result();  
+by tac;
+result();
 
 Goal "?p : (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)";
-by tac; 
-(*Verify that no subgoals remain.*) 
-uresult();  
+by tac;
+(*Verify that no subgoals remain.*)
+uresult();
 
 
 Goal "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
 by tac;
-result();  
+result();
 
 
 writeln"Some slow ones";
 
 
 (*Principia Mathematica *11.53  *)
 Goal "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))";
 by tac;
-result();  
+result();
 (*6 secs*)
 
 (*Principia Mathematica *11.55  *)
 Goal "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))";
 by tac;
-result();  
+result();
 (*9 secs*)
 
 (*Principia Mathematica *11.61  *)
 Goal "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
 by tac;
-result();  
+result();
 (*3 secs*)
-
-writeln"Reached end of file.";
-