src/Sequents/Modal0.thy
 author paulson Fri, 05 Oct 2007 09:59:03 +0200 changeset 24854 0ebcd575d3c6 parent 21426 87ac12bed1ab child 35113 1a0c129bb2e0 permissions -rw-r--r--
filtering out some package theorems
```
(*  Title:      Sequents/Modal0.thy
ID:         \$Id\$
Author:     Martin Coen
*)

theory Modal0
imports LK0
uses "modal.ML"
begin

consts
box           :: "o=>o"       ("[]_" [50] 50)
dia           :: "o=>o"       ("<>_" [50] 50)
strimp        :: "[o,o]=>o"   (infixr "--<" 25)
streqv        :: "[o,o]=>o"   (infixr ">-<" 25)
Lstar         :: "two_seqi"
Rstar         :: "two_seqi"

syntax
"@Lstar"      :: "two_seqe"   ("(_)|L>(_)" [6,6] 5)
"@Rstar"      :: "two_seqe"   ("(_)|R>(_)" [6,6] 5)

ML {*
val Lstar = "Lstar";
val Rstar = "Rstar";
val SLstar = "@Lstar";
val SRstar = "@Rstar";

fun star_tr c [s1,s2] = Const(c,dummyT)\$ seq_tr s1\$ seq_tr s2;
fun star_tr' c [s1,s2] = Const(c,dummyT) \$ seq_tr' s1 \$ seq_tr' s2;
*}

parse_translation {* [(SLstar,star_tr Lstar), (SRstar,star_tr Rstar)] *}
print_translation {* [(Lstar,star_tr' SLstar), (Rstar,star_tr' SRstar)] *}

defs
strimp_def:    "P --< Q == [](P --> Q)"
streqv_def:    "P >-< Q == (P --< Q) & (Q --< P)"

lemmas rewrite_rls = strimp_def streqv_def

lemma iffR:
"[| \$H,P |- \$E,Q,\$F;  \$H,Q |- \$E,P,\$F |] ==> \$H |- \$E, P <-> Q, \$F"
apply (unfold iff_def)
apply (assumption | rule conjR impR)+
done

lemma iffL:
"[| \$H,\$G |- \$E,P,Q;  \$H,Q,P,\$G |- \$E |] ==> \$H, P <-> Q, \$G |- \$E"
apply (unfold iff_def)
apply (assumption | rule conjL impL basic)+
done

lemmas safe_rls = basic conjL conjR disjL disjR impL impR notL notR iffL iffR
and unsafe_rls = allR exL
and bound_rls = allL exR

end
```