src/Sequents/T.thy
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(*  Title:      Modal/T.thy
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    ID:         $Id$
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    Author:     Martin Coen
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    Copyright   1991  University of Cambridge
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*)
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theory T
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imports Modal0
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begin
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axioms
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(* Definition of the star operation using a set of Horn clauses *)
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(* For system T:  gamma * == {P | []P : gamma}                  *)
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(*                delta * == {P | <>P : delta}                  *)
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  lstar0:         "|L>"
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  lstar1:         "$G |L> $H ==> []P, $G |L> P, $H"
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  lstar2:         "$G |L> $H ==>   P, $G |L>    $H"
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  rstar0:         "|R>"
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  rstar1:         "$G |R> $H ==> <>P, $G |R> P, $H"
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  rstar2:         "$G |R> $H ==>   P, $G |R>    $H"
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(* Rules for [] and <> *)
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  boxR:
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   "[| $E |L> $E';  $F |R> $F';  $G |R> $G';
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               $E'        |- $F', P, $G'|] ==> $E          |- $F, []P, $G"
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  boxL:     "$E, P, $F  |-         $G    ==> $E, []P, $F |-          $G"
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  diaR:     "$E         |- $F, P,  $G    ==> $E          |- $F, <>P, $G"
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  diaL:
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   "[| $E |L> $E';  $F |L> $F';  $G |R> $G';
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               $E', P, $F'|-         $G'|] ==> $E, <>P, $F |-          $G"
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ML {* use_legacy_bindings (the_context ()) *}
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end