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src/FOLP/ex/intro.ML

author | clasohm |

Thu, 16 Sep 1993 12:20:38 +0200 | |

changeset 0 | a5a9c433f639 |

child 1446 | a8387e934fa7 |

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

Initial revision

(* Title: FOL/ex/intro ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1992 University of Cambridge Examples for the manual "Introduction to Isabelle" Derives some inference rules, illustrating the use of definitions To generate similar output to manual, execute these commands: Pretty.setmargin 72; print_depth 0; *) (**** Some simple backward proofs ****) goal FOLP.thy "?p:P|P --> P"; by (resolve_tac [impI] 1); by (resolve_tac [disjE] 1); by (assume_tac 3); by (assume_tac 2); by (assume_tac 1); val mythm = result(); goal FOLP.thy "?p:(P & Q) | R --> (P | R)"; by (resolve_tac [impI] 1); by (eresolve_tac [disjE] 1); by (dresolve_tac [conjunct1] 1); by (resolve_tac [disjI1] 1); by (resolve_tac [disjI2] 2); by (REPEAT (assume_tac 1)); result(); (*Correct version, delaying use of "spec" until last*) goal FOLP.thy "?p:(ALL x y.P(x,y)) --> (ALL z w.P(w,z))"; by (resolve_tac [impI] 1); by (resolve_tac [allI] 1); by (resolve_tac [allI] 1); by (dresolve_tac [spec] 1); by (dresolve_tac [spec] 1); by (assume_tac 1); result(); (**** Demonstration of fast_tac ****) goal FOLP.thy "?p:(EX y. ALL x. J(y,x) <-> ~J(x,x)) \ \ --> ~ (ALL x. EX y. ALL z. J(z,y) <-> ~ J(z,x))"; by (fast_tac FOLP_cs 1); result(); goal FOLP.thy "?p:ALL x. P(x,f(x)) <-> \ \ (EX y. (ALL z. P(z,y) --> P(z,f(x))) & P(x,y))"; by (fast_tac FOLP_cs 1); result(); (**** Derivation of conjunction elimination rule ****) val [major,minor] = goal FOLP.thy "[| p:P&Q; !!x y.[| x:P; y:Q |] ==>f(x,y):R |] ==> ?p:R"; by (resolve_tac [minor] 1); by (resolve_tac [major RS conjunct1] 1); by (resolve_tac [major RS conjunct2] 1); prth (topthm()); result(); (**** Derived rules involving definitions ****) (** Derivation of negation introduction **) val prems = goal FOLP.thy "(!!x.x:P ==> f(x):False) ==> ?p:~P"; by (rewrite_goals_tac [not_def]); by (resolve_tac [impI] 1); by (resolve_tac prems 1); by (assume_tac 1); result(); val [major,minor] = goal FOLP.thy "[| p:~P; q:P |] ==> ?p:R"; by (resolve_tac [FalseE] 1); by (resolve_tac [mp] 1); by (resolve_tac [rewrite_rule [not_def] major] 1); by (resolve_tac [minor] 1); result(); (*Alternative proof of above result*) val [major,minor] = goalw FOLP.thy [not_def] "[| p:~P; q:P |] ==> ?p:R"; by (resolve_tac [minor RS (major RS mp RS FalseE)] 1); result(); writeln"Reached end of file.";