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(* Title: 91/Modal/ex/Tthms
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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 T from Hughes and Cresswell and Hailpern, LNCS 129 *)
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try "|- []P --> P";
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try "|- [](P-->Q) --> ([]P-->[]Q)"; (* normality*)
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try "|- (P--<Q) --> []P --> []Q";
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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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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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try "|- <>P & []Q --> <>(P & Q)";
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try "|- [](P | Q) --> <>P | []Q";
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try "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)";
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try "|- (P--<Q) & (Q--<R) --> (P--<R)";
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try "|- []P --> <>Q --> <>(P & Q)";
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