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