| author | wenzelm |
| Tue, 27 May 1997 15:45:07 +0200 | |
| changeset 3362 | 0b268cff9344 |
| parent 2073 | fb0655539d05 |
| permissions | -rw-r--r-- |
|
2073
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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(* Title: 91/Modal/ex/Tthms |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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ID: $Id$ |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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Author: Martin Coen |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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Copyright 1991 University of Cambridge |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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*) |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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changeset
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(* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *) |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []P --> P"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P-->Q) --> ([]P-->[]Q)"; (* normality*) |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- (P--<Q) --> []P --> []Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- P --> <>P"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P & Q) <-> []P & []Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P | Q) <-> <>P | <>Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P<->Q) <-> (P>-<Q)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P-->Q) <-> ([]P--><>Q)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []P <-> ~<>(~P)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](~P) <-> ~<>P"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- ~[]P <-> <>(~P)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [][]P <-> ~<><>(~P)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- ~<>(P | Q) <-> ~<>P & ~<>Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []P | []Q --> [](P | Q)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P & Q) --> <>P & <>Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P | Q) --> []P | <>Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>P & []Q --> <>(P & Q)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P | Q) --> <>P | []Q"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- (P--<Q) & (Q--<R) --> (P--<R)"; |
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- []P --> <>Q --> <>(P & Q)"; |