(* Title: Sequents/Modal0.thy Author: Martin Coen Copyright 1991 University of Cambridge *) 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 {* 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 {* [(@{syntax_const "_Lstar"}, star_tr @{const_syntax Lstar}), (@{syntax_const "_Rstar"}, star_tr @{const_syntax Rstar})] *} print_translation {* [(@{const_syntax Lstar}, star_tr' @{syntax_const "_Lstar"}), (@{const_syntax Rstar}, star_tr' @{syntax_const "_Rstar"})] *} 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