# Theory T

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theory T
imports Modal0
uses [T.ML]
begin

    (*  Title:      Modal/T.thy
        ID:         $Id: T.thy,v 1.2 2005/09/18 13:20:10 wenzelm Exp $
        Author:     Martin Coen
        Copyright   1991  University of Cambridge
    *)

    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