--- a/src/FOL/ex/quant.ML Sun Jul 22 21:20:58 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,129 +0,0 @@
-(* Title: FOL/ex/quant
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1991 University of Cambridge
-
-First-Order Logic: quantifier examples (intuitionistic and classical)
-Needs declarations of the theory "thy" and the tactic "tac"
-*)
-
-writeln"File FOL/ex/quant.";
-
-Goal "(ALL x y. P(x,y)) --> (ALL y x. P(x,y))";
-by tac;
-result();
-
-
-Goal "(EX x y. P(x,y)) --> (EX y x. P(x,y))";
-by tac;
-result();
-
-
-(*Converse is false*)
-Goal "(ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x) | Q(x))";
-by tac;
-result();
-
-Goal "(ALL x. P-->Q(x)) <-> (P--> (ALL x. Q(x)))";
-by tac;
-result();
-
-
-Goal "(ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)";
-by tac;
-result();
-
-
-writeln"Some harder ones";
-
-Goal "(EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
-by tac;
-result();
-(*6 secs*)
-
-(*Converse is false*)
-Goal "(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 "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))";
-by tac;
-result();
-
-
-Goal "(ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"The following should fail, as they are false!";
-
-Goal "(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 "(EX x. Q(x)) --> (ALL x. Q(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-getgoal 1;
-
-Goal "P(?a) --> (ALL x. P(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-Goal
- "(P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))";
-by tac handle ERROR _ => writeln"Failed, as expected";
-getgoal 1;
-
-
-writeln"Back to things that are provable...";
-
-Goal "(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 "(P --> (EX x. Q(x))) & P --> (EX x. Q(x))";
-by tac;
-result();
-
-Goal "(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 "(ALL x. Q(x)) --> (EX x. Q(x))";
-by tac;
-result();
-
-
-writeln"Some slow ones";
-
-
-(*Principia Mathematica *11.53 *)
-Goal "(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 "(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 "(EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
-by tac;
-result();
-(*3 secs*)
-
-writeln"Reached end of file.";
-