src/FOLP/ex/quant.ML

--- a/src/FOLP/ex/quant.ML	Sat Jun 20 20:35:38 1998 +0200
+++ b/src/FOLP/ex/quant.ML	Mon Jun 22 15:09:59 1998 +0200
@@ -9,73 +9,73 @@
 
 writeln"File FOLP/ex/quant.ML";
 
-goal thy "?p : (ALL x y. P(x,y))  -->  (ALL y x. P(x,y))";
+Goal "?p : (ALL x y. P(x,y))  -->  (ALL y x. P(x,y))";
 by tac;
 result();  
 
 
-goal thy "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))";
+Goal "?p : (EX x y. P(x,y)) --> (EX y x. P(x,y))";
 by tac;
 result();  
 
 
 (*Converse is false*)
-goal thy "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
+Goal "?p : (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
 by tac;
 result();  
 
-goal thy "?p : (ALL x. P-->Q(x))  <->  (P--> (ALL x. Q(x)))";
+Goal "?p : (ALL x. P-->Q(x))  <->  (P--> (ALL x. Q(x)))";
 by tac;
 result();  
 
 
-goal thy "?p : (ALL x. P(x)-->Q)  <->  ((EX x. P(x)) --> Q)";
+Goal "?p : (ALL x. P(x)-->Q)  <->  ((EX x. P(x)) --> Q)";
 by tac;
 result();  
 
 
 writeln"Some harder ones";
 
-goal thy "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
+Goal "?p : (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
 by tac;
 result();  
 (*6 secs*)
 
 (*Converse is false*)
-goal thy "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x))  &  (EX x. Q(x))";
+Goal "?p : (EX x. P(x)&Q(x)) --> (EX x. P(x))  &  (EX x. Q(x))";
 by tac;
 result();  
 
 
 writeln"Basic test of quantifier reasoning";
 (*TRUE*)
-goal thy "?p : (EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))";
+Goal "?p : (EX y. ALL x. Q(x,y)) -->  (ALL x. EX y. Q(x,y))";
 by tac;  
 result();  
 
 
-goal thy "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
+Goal "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
 by tac;  
 result();  
 
 
 writeln"The following should fail, as they are false!";
 
-goal thy "?p : (ALL x. EX y. Q(x,y))  -->  (EX y. ALL x. Q(x,y))";
+Goal "?p : (ALL x. EX y. Q(x,y))  -->  (EX y. ALL x. Q(x,y))";
 by tac handle ERROR => writeln"Failed, as expected";  
 (*Check that subgoals remain: proof failed.*)
 getgoal 1; 
 
-goal thy "?p : (EX x. Q(x))  -->  (ALL x. Q(x))";
+Goal "?p : (EX x. Q(x))  -->  (ALL x. Q(x))";
 by tac handle ERROR => writeln"Failed, as expected";  
 getgoal 1; 
 
-goal thy "?p : P(?a) --> (ALL x. P(x))";
+Goal "?p : P(?a) --> (ALL x. P(x))";
 by tac handle ERROR => writeln"Failed, as expected";
 (*Check that subgoals remain: proof failed.*)
 getgoal 1;  
 
-goal thy
+Goal
     "?p : (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))";
 by tac handle ERROR => writeln"Failed, as expected";
 getgoal 1;  
@@ -83,23 +83,23 @@
 
 writeln"Back to things that are provable...";
 
-goal thy "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))";
+Goal "?p : (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))";
 by tac;  
 result();  
 
 
 (*An example of why exI should be delayed as long as possible*)
-goal thy "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
+Goal "?p : (P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
 by tac;  
 result();  
 
-goal thy "?p : (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)";
+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();  
 
 
-goal thy "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
+Goal "?p : (ALL x. Q(x))  -->  (EX x. Q(x))";
 by tac;
 result();  
 
@@ -108,19 +108,19 @@
 
 
 (*Principia Mathematica *11.53  *)
-goal thy "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))";
+Goal "?p : (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))";
 by tac;
 result();  
 (*6 secs*)
 
 (*Principia Mathematica *11.55  *)
-goal thy "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))";
+Goal "?p : (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))";
 by tac;
 result();  
 (*9 secs*)
 
 (*Principia Mathematica *11.61  *)
-goal thy "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
+Goal "?p : (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
 by tac;
 result();  
 (*3 secs*)