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src/Sequents/Modal/S43thms.ML
author kleing
Sat, 30 Apr 2005 14:18:36 +0200
changeset 15900 d6156cb8dc2e
parent 6252 935f183bf406
permissions -rw-r--r--
fixed typo
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(*  Title:      91/Modal/ex/S43thms
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    ID:         $Id$
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    Author:     Martin Coen
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    Copyright   1991  University of Cambridge
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*)
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(* Theorems of system S43 *)













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try "|- <>[]P --> []<>P";













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try "|- <>[]P --> [][]<>P";













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try "|- [](<>P | <>Q) --> []<>P | []<>Q";













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try "|- <>[]P & <>[]Q --> <>([]P & []Q)";













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try "|- []([]P --> []Q) | []([]Q --> []P)";













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try "|- [](<>P --> <>Q) | [](<>Q --> <>P)";













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try "|- []([]P --> Q) | []([]Q --> P)";













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try "|- [](P --> <>Q) | [](Q --> <>P)";













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try "|- [](P --> []Q-->R) | [](P | ([]R --> Q))";













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try "|- [](P | (Q --> <>C)) | [](P --> C --> <>Q)";













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try "|- []([]P | Q) & [](P | []Q) --> []P | []Q";













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try "|- <>P & <>Q --> <>(<>P & Q) | <>(P & <>Q)";













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try "|- [](P | Q) & []([]P | Q) & [](P | []Q) --> []P | []Q";













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try "|- <>P & <>Q --> <>(P & Q) | <>(<>P & Q) | <>(P & <>Q)";













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try "|- <>[]<>P <-> []<>P";













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try "|- []<>[]P <-> <>[]P";













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(* These are from Hailpern, LNCS 129 *)













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try "|- [](P & Q) <-> []P & []Q";













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try "|- <>(P | Q) <-> <>P | <>Q";













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try "|- <>(P --> Q) <-> []P --> <>Q";













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try "|- [](P --> Q) --> <>P --> <>Q";













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try "|- []P --> []<>P";













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try "|- <>[]P --> <>P";













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try "|- []<>[]P --> []<>P";













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try "|- <>[]P --> <>[]<>P";













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try "|- <>[]P --> []<>P";













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try "|- []<>[]P <-> <>[]P";













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try "|- <>[]<>P <-> []<>P";













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try "|- []P | []Q --> [](P | Q)";













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try "|- <>(P & Q) --> <>P & <>Q";













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try "|- [](P | Q) --> []P | <>Q";













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try "|- <>P & []Q --> <>(P & Q)";













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examples made separate dirs;



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try "|- [](P | Q) --> <>P | []Q";













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try "|- [](P | Q) --> []<>P | []<>Q";













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try "|- <>[]P & <>[]Q --> <>(P & Q)";













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try "|- <>[](P & Q) <-> <>[]P & <>[]Q";













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try "|- []<>(P | Q) <-> []<>P | []<>Q";















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