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src/Sequents/T.thy

changeset 21426 | 87ac12bed1ab |

parent 17481 | 75166ebb619b |

child 21590 | ef7278f553eb |

--- a/src/Sequents/T.thy Mon Nov 20 21:23:12 2006 +0100 +++ b/src/Sequents/T.thy Mon Nov 20 23:47:10 2006 +0100 @@ -31,6 +31,46 @@ "[| $E |L> $E'; $F |L> $F'; $G |R> $G'; $E', P, $F'|- $G'|] ==> $E, <>P, $F |- $G" -ML {* use_legacy_bindings (the_context ()) *} +ML {* +structure T_Prover = Modal_ProverFun +( + val rewrite_rls = thms "rewrite_rls" + val safe_rls = thms "safe_rls" + val unsafe_rls = thms "unsafe_rls" @ [thm "boxR", thm "diaL"] + val bound_rls = thms "bound_rls" @ [thm "boxL", thm "diaR"] + val aside_rls = [thm "lstar0", thm "lstar1", thm "lstar2", thm "rstar0", + thm "rstar1", thm "rstar2"] +) +*} + +method_setup T_solve = +{* Method.no_args (Method.SIMPLE_METHOD (T_Prover.solve_tac 2)) *} "T solver" + + +(* Theorems of system T from Hughes and Cresswell and Hailpern, LNCS 129 *) + +lemma "|- []P --> P" by T_solve +lemma "|- [](P-->Q) --> ([]P-->[]Q)" by T_solve (* normality*) +lemma "|- (P--<Q) --> []P --> []Q" by T_solve +lemma "|- P --> <>P" by T_solve + +lemma "|- [](P & Q) <-> []P & []Q" by T_solve +lemma "|- <>(P | Q) <-> <>P | <>Q" by T_solve +lemma "|- [](P<->Q) <-> (P>-<Q)" by T_solve +lemma "|- <>(P-->Q) <-> ([]P--><>Q)" by T_solve +lemma "|- []P <-> ~<>(~P)" by T_solve +lemma "|- [](~P) <-> ~<>P" by T_solve +lemma "|- ~[]P <-> <>(~P)" by T_solve +lemma "|- [][]P <-> ~<><>(~P)" by T_solve +lemma "|- ~<>(P | Q) <-> ~<>P & ~<>Q" by T_solve + +lemma "|- []P | []Q --> [](P | Q)" by T_solve +lemma "|- <>(P & Q) --> <>P & <>Q" by T_solve +lemma "|- [](P | Q) --> []P | <>Q" by T_solve +lemma "|- <>P & []Q --> <>(P & Q)" by T_solve +lemma "|- [](P | Q) --> <>P | []Q" by T_solve +lemma "|- <>(P-->(Q & R)) --> ([]P --> <>Q) & ([]P--><>R)" by T_solve +lemma "|- (P--<Q) & (Q--<R) --> (P--<R)" by T_solve +lemma "|- []P --> <>Q --> <>(P & Q)" by T_solve end