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src/FOL/FOL_lemmas1.ML

author | wenzelm |

Tue, 13 Jun 2006 23:41:39 +0200 | |

changeset 19876 | 11d447d5d68c |

parent 9264 | 051592f4236a |

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

tuned;

(* Title: FOL/FOL_lemmas1.ML ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1991 University of Cambridge Tactics and lemmas for theory FOL (classical First-Order Logic). *) val classical = thm "classical"; bind_thm ("ccontr", FalseE RS classical); (*** Classical introduction rules for | and EX ***) val prems = Goal "(~Q ==> P) ==> P|Q"; by (rtac classical 1); by (REPEAT (ares_tac (prems@[disjI1,notI]) 1)); by (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ; qed "disjCI"; (*introduction rule involving only EX*) val prems = Goal "( ~(EX x. P(x)) ==> P(a)) ==> EX x. P(x)"; by (rtac classical 1); by (eresolve_tac (prems RL [exI]) 1) ; qed "ex_classical"; (*version of above, simplifying ~EX to ALL~ *) val [prem]= Goal "(ALL x. ~P(x) ==> P(a)) ==> EX x. P(x)"; by (rtac ex_classical 1); by (resolve_tac [notI RS allI RS prem] 1); by (etac notE 1); by (etac exI 1) ; qed "exCI"; Goal"~P | P"; by (rtac disjCI 1); by (assume_tac 1) ; qed "excluded_middle"; (*For disjunctive case analysis*) fun excluded_middle_tac sP = res_inst_tac [("Q",sP)] (excluded_middle RS disjE); val [p1,p2] = Goal"[| P ==> Q; ~P ==> Q |] ==> Q"; by (rtac (excluded_middle RS disjE) 1); by (etac p2 1); by (etac p1 1); qed "case_split_thm"; (*HOL's more natural case analysis tactic*) fun case_tac a = res_inst_tac [("P",a)] case_split_thm; (*** Special elimination rules *) (*Classical implies (-->) elimination. *) val major::prems = Goal "[| P-->Q; ~P ==> R; Q ==> R |] ==> R"; by (resolve_tac [excluded_middle RS disjE] 1); by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ; qed "impCE"; (*This version of --> elimination works on Q before P. It works best for those cases in which P holds "almost everywhere". Can't install as default: would break old proofs.*) val major::prems = Goal "[| P-->Q; Q ==> R; ~P ==> R |] ==> R"; by (resolve_tac [excluded_middle RS disjE] 1); by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ; qed "impCE'"; (*Double negation law*) Goal"~~P ==> P"; by (rtac classical 1); by (etac notE 1); by (assume_tac 1); qed "notnotD"; val [p1,p2] = Goal"[| Q; ~ P ==> ~ Q |] ==> P"; by (rtac classical 1); by (dtac p2 1); by (etac notE 1); by (rtac p1 1); qed "contrapos2"; (*** Tactics for implication and contradiction ***) (*Classical <-> elimination. Proof substitutes P=Q in ~P ==> ~Q and P ==> Q *) val major::prems = Goalw [iff_def] "[| P<->Q; [| P; Q |] ==> R; [| ~P; ~Q |] ==> R |] ==> R"; by (rtac (major RS conjE) 1); by (REPEAT_FIRST (etac impCE)); by (REPEAT (DEPTH_SOLVE_1 (mp_tac 1 ORELSE ares_tac prems 1))); qed "iffCE";