--- a/src/Sequents/ex/LK/quant.ML Fri Feb 05 21:12:45 1999 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,160 +0,0 @@
-(* Title: LK/ex/quant
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1992 University of Cambridge
-
-Classical sequent calculus: examples with quantifiers.
-*)
-
-
-writeln"LK/ex/quant: Examples with quantifiers";
-
-goal LK.thy "|- (ALL x. P) <-> P";
-by (fast_tac LK_pack 1);
-result();
-
-goal LK.thy "|- (ALL x y. P(x,y)) <-> (ALL y x. P(x,y))";
-by (fast_tac LK_pack 1);
-result();
-
-goal LK.thy "ALL u. P(u), ALL v. Q(v) |- ALL u v. P(u) & Q(v)";
-by (fast_tac LK_pack 1);
-result();
-
-writeln"Permutation of existential quantifier.";
-goal LK.thy "|- (EX x y. P(x,y)) <-> (EX y x. P(x,y))";
-by (fast_tac LK_pack 1);
-result();
-
-goal LK.thy "|- (ALL x. P(x) & Q(x)) <-> (ALL x. P(x)) & (ALL x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-
-(*Converse is invalid*)
-goal LK.thy "|- (ALL x. P(x)) | (ALL x. Q(x)) --> (ALL x. P(x)|Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Pushing ALL into an implication.";
-goal LK.thy "|- (ALL x. P --> Q(x)) <-> (P --> (ALL x. Q(x)))";
-by (fast_tac LK_pack 1);
-result();
-
-
-goal LK.thy "|- (ALL x. P(x)-->Q) <-> ((EX x. P(x)) --> Q)";
-by (fast_tac LK_pack 1);
-result();
-
-
-goal LK.thy "|- (EX x. P) <-> P";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Distribution of EX over disjunction.";
-goal LK.thy "|- (EX x. P(x) | Q(x)) <-> (EX x. P(x)) | (EX x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-(*5 secs*)
-
-(*Converse is invalid*)
-goal LK.thy "|- (EX x. P(x) & Q(x)) --> (EX x. P(x)) & (EX x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Harder examples: classical theorems.";
-
-goal LK.thy "|- (EX x. P-->Q(x)) <-> (P --> (EX x. Q(x)))";
-by (fast_tac LK_pack 1);
-result();
-(*3 secs*)
-
-
-goal LK.thy "|- (EX x. P(x)-->Q) <-> (ALL x. P(x)) --> Q";
-by (fast_tac LK_pack 1);
-result();
-(*5 secs*)
-
-
-goal LK.thy "|- (ALL x. P(x)) | Q <-> (ALL x. P(x) | Q)";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Basic test of quantifier reasoning";
-goal LK.thy
- "|- (EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))";
-by (fast_tac LK_pack 1);
-result();
-
-
-goal LK.thy "|- (ALL x. Q(x)) --> (EX x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"The following are invalid!";
-
-(*INVALID*)
-goal LK.thy "|- (ALL x. EX y. Q(x,y)) --> (EX y. ALL x. Q(x,y))";
-by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-(*INVALID*)
-goal LK.thy "|- (EX x. Q(x)) --> (ALL x. Q(x))";
-by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected";
-getgoal 1;
-
-goal LK.thy "|- P(?a) --> (ALL x. P(x))";
-by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected";
-(*Check that subgoals remain: proof failed.*)
-getgoal 1;
-
-goal LK.thy "|- (P(?a) --> (ALL x. Q(x))) --> (ALL x. P(x) --> Q(x))";
-by (fast_tac LK_pack 1) handle ERROR => writeln"Failed, as expected";
-getgoal 1;
-
-
-writeln"Back to things that are provable...";
-
-goal LK.thy "|- (ALL x. P(x)-->Q(x)) & (EX x. P(x)) --> (EX x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-(*An example of why exR should be delayed as long as possible*)
-goal LK.thy "|- (P--> (EX x. Q(x))) & P--> (EX x. Q(x))";
-by (fast_tac LK_pack 1);
-result();
-
-writeln"Solving for a Var";
-goal LK.thy
- "|- (ALL x. P(x)-->Q(f(x))) & (ALL x. Q(x)-->R(g(x))) & P(d) --> R(?a)";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Principia Mathematica *11.53";
-goal LK.thy
- "|- (ALL x y. P(x) --> Q(y)) <-> ((EX x. P(x)) --> (ALL y. Q(y)))";
-by (fast_tac LK_pack 1);
-result();
-
-
-writeln"Principia Mathematica *11.55";
-goal LK.thy "|- (EX x y. P(x) & Q(x,y)) <-> (EX x. P(x) & (EX y. Q(x,y)))";
-by (fast_tac LK_pack 1);
-result();
-
-writeln"Principia Mathematica *11.61";
-goal LK.thy
- "|- (EX y. ALL x. P(x) --> Q(x,y)) --> (ALL x. P(x) --> (EX y. Q(x,y)))";
-by (fast_tac LK_pack 1);
-result();
-
-writeln"Reached end of file.";
-
-(*21 August 88: loaded in 45.7 secs*)