src/Sequents/T.thy
 author wenzelm Tue, 13 Jun 2006 23:41:39 +0200 changeset 19876 11d447d5d68c parent 17481 75166ebb619b child 21426 87ac12bed1ab permissions -rw-r--r--
tuned;
```
(*  Title:      Modal/T.thy
ID:         \$Id\$
Author:     Martin Coen
*)

theory T
imports Modal0
begin

axioms
(* Definition of the star operation using a set of Horn clauses *)
(* For system T:  gamma * == {P | []P : gamma}                  *)
(*                delta * == {P | <>P : delta}                  *)

lstar0:         "|L>"
lstar1:         "\$G |L> \$H ==> []P, \$G |L> P, \$H"
lstar2:         "\$G |L> \$H ==>   P, \$G |L>    \$H"
rstar0:         "|R>"
rstar1:         "\$G |R> \$H ==> <>P, \$G |R> P, \$H"
rstar2:         "\$G |R> \$H ==>   P, \$G |R>    \$H"

(* Rules for [] and <> *)

boxR:
"[| \$E |L> \$E';  \$F |R> \$F';  \$G |R> \$G';
\$E'        |- \$F', P, \$G'|] ==> \$E          |- \$F, []P, \$G"
boxL:     "\$E, P, \$F  |-         \$G    ==> \$E, []P, \$F |-          \$G"
diaR:     "\$E         |- \$F, P,  \$G    ==> \$E          |- \$F, <>P, \$G"
diaL:
"[| \$E |L> \$E';  \$F |L> \$F';  \$G |R> \$G';
\$E', P, \$F'|-         \$G'|] ==> \$E, <>P, \$F |-          \$G"

ML {* use_legacy_bindings (the_context ()) *}

end
```