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