--- 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*)