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1 (* Title: 91/Modal/ex/Tthms |
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2 ID: $Id$ |
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3 Author: Martin Coen |
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4 Copyright 1991 University of Cambridge |
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5 *) |
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6 |
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7 (* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *) |
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8 |
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9 try "|- []P --> P"; |
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10 try "|- [](P-->Q) --> ([]P-->[]Q)"; (* normality*) |
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11 try "|- (P--<Q) --> []P --> []Q"; |
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12 try "|- P --> <>P"; |
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13 |
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14 try "|- [](P & Q) <-> []P & []Q"; |
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15 try "|- <>(P | Q) <-> <>P | <>Q"; |
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16 try "|- [](P<->Q) <-> (P>-<Q)"; |
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17 try "|- <>(P-->Q) <-> ([]P--><>Q)"; |
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18 try "|- []P <-> ~<>(~P)"; |
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19 try "|- [](~P) <-> ~<>P"; |
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20 try "|- ~[]P <-> <>(~P)"; |
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21 try "|- [][]P <-> ~<><>(~P)"; |
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22 try "|- ~<>(P | Q) <-> ~<>P & ~<>Q"; |
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23 |
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24 try "|- []P | []Q --> [](P | Q)"; |
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25 try "|- <>(P & Q) --> <>P & <>Q"; |
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26 try "|- [](P | Q) --> []P | <>Q"; |
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27 try "|- <>P & []Q --> <>(P & Q)"; |
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28 try "|- [](P | Q) --> <>P | []Q"; |
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29 try "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)"; |
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30 try "|- (P--<Q) & (Q--<R) --> (P--<R)"; |
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31 try "|- []P --> <>Q --> <>(P & Q)"; |
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