--- a/src/Modal/ex/S4thms.ML Thu Oct 10 11:09:03 1996 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-(* Title: 91/Modal/ex/S4thms
- ID: $Id$
- Author: Martin Coen
- Copyright 1991 University of Cambridge
-*)
-
-(* Theorems of system S4 from Hughes and Cresswell, p.46 *)
-
-try "|- []A --> A"; (* refexivity *)
-try "|- []A --> [][]A"; (* transitivity *)
-try "|- []A --> <>A"; (* seriality *)
-try "|- <>[](<>A --> []<>A)";
-try "|- <>[](<>[]A --> []A)";
-try "|- []P <-> [][]P";
-try "|- <>P <-> <><>P";
-try "|- <>[]<>P --> <>P";
-try "|- []<>P <-> []<>[]<>P";
-try "|- <>[]P <-> <>[]<>[]P";
-
-(* Theorems for system S4 from Hughes and Cresswell, p.60 *)
-
-try "|- []P | []Q <-> []([]P | []Q)";
-try "|- ((P>-<Q) --< R) --> ((P>-<Q) --< []R)";
-
-(* These are from Hailpern, LNCS 129 *)
-
-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 | []Q --> [](P | Q)";
-try "|- <>(P & Q) --> <>P & <>Q";
-try "|- [](P | Q) --> []P | <>Q";
-try "|- <>P & []Q --> <>(P & Q)";
-try "|- [](P | Q) --> <>P | []Q";
-