diff -r 000000000000 -r a5a9c433f639 src/Modal/ex/Tthms.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Modal/ex/Tthms.ML Thu Sep 16 12:20:38 1993 +0200 @@ -0,0 +1,31 @@ +(* Title: 91/Modal/ex/Tthms + ID: $Id$ + Author: Martin Coen + Copyright 1991 University of Cambridge +*) + +(* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *) + +try "|- []P --> P"; +try "|- [](P-->Q) --> ([]P-->[]Q)"; (* normality*) +try "|- (P-- []P --> []Q"; +try "|- P --> <>P"; + +try "|- [](P & Q) <-> []P & []Q"; +try "|- <>(P | Q) <-> <>P | <>Q"; +try "|- [](P<->Q) <-> (P>-(P-->Q) <-> ([]P--><>Q)"; +try "|- []P <-> ~<>(~P)"; +try "|- [](~P) <-> ~<>P"; +try "|- ~[]P <-> <>(~P)"; +try "|- [][]P <-> ~<><>(~P)"; +try "|- ~<>(P | Q) <-> ~<>P & ~<>Q"; + +try "|- []P | []Q --> [](P | Q)"; +try "|- <>(P & Q) --> <>P & <>Q"; +try "|- [](P | Q) --> []P | <>Q"; +try "|- <>P & []Q --> <>(P & Q)"; +try "|- [](P | Q) --> <>P | []Q"; +try "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)"; +try "|- (P-- (P-- <>Q --> <>(P & Q)";