src/Sequents/Modal0.thy
author haftmann
Fri Jun 19 21:08:07 2009 +0200 (2009-06-19)
changeset 31726 ffd2dc631d88
parent 21426 87ac12bed1ab
child 35113 1a0c129bb2e0
permissions -rw-r--r--
merged
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(*  Title:      Sequents/Modal0.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 Modal0
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imports LK0
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uses "modal.ML"
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begin
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consts
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  box           :: "o=>o"       ("[]_" [50] 50)
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  dia           :: "o=>o"       ("<>_" [50] 50)
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  strimp        :: "[o,o]=>o"   (infixr "--<" 25)
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  streqv        :: "[o,o]=>o"   (infixr ">-<" 25)
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  Lstar         :: "two_seqi"
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  Rstar         :: "two_seqi"
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syntax
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  "@Lstar"      :: "two_seqe"   ("(_)|L>(_)" [6,6] 5)
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  "@Rstar"      :: "two_seqe"   ("(_)|R>(_)" [6,6] 5)
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ML {*
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  val Lstar = "Lstar";
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  val Rstar = "Rstar";
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  val SLstar = "@Lstar";
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  val SRstar = "@Rstar";
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  fun star_tr c [s1,s2] = Const(c,dummyT)$ seq_tr s1$ seq_tr s2;
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  fun star_tr' c [s1,s2] = Const(c,dummyT) $ seq_tr' s1 $ seq_tr' s2;
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*}
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parse_translation {* [(SLstar,star_tr Lstar), (SRstar,star_tr Rstar)] *}
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print_translation {* [(Lstar,star_tr' SLstar), (Rstar,star_tr' SRstar)] *}
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defs
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  strimp_def:    "P --< Q == [](P --> Q)"
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  streqv_def:    "P >-< Q == (P --< Q) & (Q --< P)"
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lemmas rewrite_rls = strimp_def streqv_def
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lemma iffR:
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    "[| $H,P |- $E,Q,$F;  $H,Q |- $E,P,$F |] ==> $H |- $E, P <-> Q, $F"
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  apply (unfold iff_def)
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  apply (assumption | rule conjR impR)+
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  done
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lemma iffL:
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    "[| $H,$G |- $E,P,Q;  $H,Q,P,$G |- $E |] ==> $H, P <-> Q, $G |- $E"
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  apply (unfold iff_def)
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  apply (assumption | rule conjL impL basic)+
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  done
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lemmas safe_rls = basic conjL conjR disjL disjR impL impR notL notR iffL iffR
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  and unsafe_rls = allR exL
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  and bound_rls = allL exR
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end