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src/FOL/ex/quant.ML

author | haftmann |

Tue, 10 Jul 2007 17:30:50 +0200 | |

changeset 23709 | fd31da8f752a |

parent 18678 | dd0c569fa43d |

permissions | -rw-r--r-- |

moved lfp_induct2 here

(* 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.";