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(* Title: HOL/UNITY/UNITY_tactics.ML
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 2003 University of Cambridge
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Specialized UNITY tactics, and ML bindings of theorems
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*)
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13798
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(*ListOrder*)
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val Le_def = thm "Le_def";
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val Ge_def = thm "Ge_def";
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val prefix_def = thm "prefix_def";
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val Nil_genPrefix = thm "Nil_genPrefix";
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val genPrefix_length_le = thm "genPrefix_length_le";
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val cons_genPrefixE = thm "cons_genPrefixE";
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val Cons_genPrefix_Cons = thm "Cons_genPrefix_Cons";
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val refl_genPrefix = thm "refl_genPrefix";
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val genPrefix_refl = thm "genPrefix_refl";
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val genPrefix_mono = thm "genPrefix_mono";
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val append_genPrefix = thm "append_genPrefix";
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val genPrefix_trans_O = thm "genPrefix_trans_O";
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val genPrefix_trans = thm "genPrefix_trans";
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val prefix_genPrefix_trans = thm "prefix_genPrefix_trans";
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val genPrefix_prefix_trans = thm "genPrefix_prefix_trans";
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val trans_genPrefix = thm "trans_genPrefix";
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val genPrefix_antisym = thm "genPrefix_antisym";
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val antisym_genPrefix = thm "antisym_genPrefix";
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val genPrefix_Nil = thm "genPrefix_Nil";
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val same_genPrefix_genPrefix = thm "same_genPrefix_genPrefix";
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val genPrefix_Cons = thm "genPrefix_Cons";
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val genPrefix_take_append = thm "genPrefix_take_append";
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val genPrefix_append_both = thm "genPrefix_append_both";
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val append_cons_eq = thm "append_cons_eq";
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val append_one_genPrefix = thm "append_one_genPrefix";
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val genPrefix_imp_nth = thm "genPrefix_imp_nth";
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val nth_imp_genPrefix = thm "nth_imp_genPrefix";
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val genPrefix_iff_nth = thm "genPrefix_iff_nth";
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val prefix_refl = thm "prefix_refl";
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val prefix_trans = thm "prefix_trans";
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val prefix_antisym = thm "prefix_antisym";
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val prefix_less_le = thm "prefix_less_le";
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val set_mono = thm "set_mono";
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val Nil_prefix = thm "Nil_prefix";
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val prefix_Nil = thm "prefix_Nil";
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val Cons_prefix_Cons = thm "Cons_prefix_Cons";
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val same_prefix_prefix = thm "same_prefix_prefix";
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val append_prefix = thm "append_prefix";
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val prefix_appendI = thm "prefix_appendI";
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val prefix_Cons = thm "prefix_Cons";
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val append_one_prefix = thm "append_one_prefix";
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val prefix_length_le = thm "prefix_length_le";
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val strict_prefix_length_less = thm "strict_prefix_length_less";
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val mono_length = thm "mono_length";
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val prefix_iff = thm "prefix_iff";
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val prefix_snoc = thm "prefix_snoc";
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val prefix_append_iff = thm "prefix_append_iff";
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val common_prefix_linear = thm "common_prefix_linear";
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val reflexive_Le = thm "reflexive_Le";
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val antisym_Le = thm "antisym_Le";
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val trans_Le = thm "trans_Le";
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val pfixLe_refl = thm "pfixLe_refl";
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val pfixLe_trans = thm "pfixLe_trans";
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val pfixLe_antisym = thm "pfixLe_antisym";
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val prefix_imp_pfixLe = thm "prefix_imp_pfixLe";
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val reflexive_Ge = thm "reflexive_Ge";
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val antisym_Ge = thm "antisym_Ge";
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val trans_Ge = thm "trans_Ge";
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val pfixGe_refl = thm "pfixGe_refl";
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val pfixGe_trans = thm "pfixGe_trans";
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val pfixGe_antisym = thm "pfixGe_antisym";
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val prefix_imp_pfixGe = thm "prefix_imp_pfixGe";
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13797
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(*UNITY*)
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val constrains_def = thm "constrains_def";
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val stable_def = thm "stable_def";
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val invariant_def = thm "invariant_def";
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val increasing_def = thm "increasing_def";
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val Allowed_def = thm "Allowed_def";
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val Id_in_Acts = thm "Id_in_Acts";
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val insert_Id_Acts = thm "insert_Id_Acts";
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val Id_in_AllowedActs = thm "Id_in_AllowedActs";
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val insert_Id_AllowedActs = thm "insert_Id_AllowedActs";
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val Init_eq = thm "Init_eq";
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val Acts_eq = thm "Acts_eq";
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val AllowedActs_eq = thm "AllowedActs_eq";
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val surjective_mk_program = thm "surjective_mk_program";
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val program_equalityI = thm "program_equalityI";
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val program_equalityE = thm "program_equalityE";
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val program_equality_iff = thm "program_equality_iff";
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val def_prg_Init = thm "def_prg_Init";
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val def_prg_Acts = thm "def_prg_Acts";
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val def_prg_AllowedActs = thm "def_prg_AllowedActs";
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val def_prg_simps = thm "def_prg_simps";
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val def_act_simp = thm "def_act_simp";
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val def_set_simp = thm "def_set_simp";
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val constrainsI = thm "constrainsI";
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val constrainsD = thm "constrainsD";
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val constrains_empty = thm "constrains_empty";
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val constrains_empty2 = thm "constrains_empty2";
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val constrains_UNIV = thm "constrains_UNIV";
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val constrains_UNIV2 = thm "constrains_UNIV2";
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val constrains_weaken_R = thm "constrains_weaken_R";
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val constrains_weaken_L = thm "constrains_weaken_L";
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val constrains_weaken = thm "constrains_weaken";
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val constrains_Un = thm "constrains_Un";
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val constrains_UN = thm "constrains_UN";
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val constrains_Un_distrib = thm "constrains_Un_distrib";
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val constrains_UN_distrib = thm "constrains_UN_distrib";
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val constrains_Int_distrib = thm "constrains_Int_distrib";
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val constrains_INT_distrib = thm "constrains_INT_distrib";
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val constrains_Int = thm "constrains_Int";
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val constrains_INT = thm "constrains_INT";
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val constrains_imp_subset = thm "constrains_imp_subset";
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val constrains_trans = thm "constrains_trans";
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val constrains_cancel = thm "constrains_cancel";
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val unlessI = thm "unlessI";
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val unlessD = thm "unlessD";
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val stableI = thm "stableI";
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val stableD = thm "stableD";
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val stable_UNIV = thm "stable_UNIV";
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val stable_Un = thm "stable_Un";
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val stable_UN = thm "stable_UN";
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val stable_Int = thm "stable_Int";
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val stable_INT = thm "stable_INT";
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val stable_constrains_Un = thm "stable_constrains_Un";
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val stable_constrains_Int = thm "stable_constrains_Int";
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val stable_constrains_stable = thm "stable_constrains_stable";
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val invariantI = thm "invariantI";
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val invariant_Int = thm "invariant_Int";
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val increasingD = thm "increasingD";
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val increasing_constant = thm "increasing_constant";
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val mono_increasing_o = thm "mono_increasing_o";
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val strict_increasingD = thm "strict_increasingD";
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val elimination = thm "elimination";
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val elimination_sing = thm "elimination_sing";
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val constrains_strongest_rhs = thm "constrains_strongest_rhs";
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val strongest_rhs_is_strongest = thm "strongest_rhs_is_strongest";
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val Un_Diff_Diff = thm "Un_Diff_Diff";
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val Int_Union_Union = thm "Int_Union_Union";
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val Image_less_than = thm "Image_less_than";
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val Image_inverse_less_than = thm "Image_inverse_less_than";
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(*WFair*)
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val stable_transient_empty = thm "stable_transient_empty";
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val transient_strengthen = thm "transient_strengthen";
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val transientI = thm "transientI";
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val transientE = thm "transientE";
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val transient_UNIV = thm "transient_UNIV";
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val transient_empty = thm "transient_empty";
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val ensuresI = thm "ensuresI";
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val ensuresD = thm "ensuresD";
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val ensures_weaken_R = thm "ensures_weaken_R";
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val stable_ensures_Int = thm "stable_ensures_Int";
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val stable_transient_ensures = thm "stable_transient_ensures";
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val ensures_eq = thm "ensures_eq";
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val leadsTo_Basis = thm "leadsTo_Basis";
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val leadsTo_Trans = thm "leadsTo_Trans";
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val transient_imp_leadsTo = thm "transient_imp_leadsTo";
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val leadsTo_Un_duplicate = thm "leadsTo_Un_duplicate";
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val leadsTo_Un_duplicate2 = thm "leadsTo_Un_duplicate2";
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val leadsTo_Union = thm "leadsTo_Union";
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val leadsTo_Union_Int = thm "leadsTo_Union_Int";
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val leadsTo_UN = thm "leadsTo_UN";
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val leadsTo_Un = thm "leadsTo_Un";
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val single_leadsTo_I = thm "single_leadsTo_I";
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val leadsTo_induct = thm "leadsTo_induct";
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val subset_imp_ensures = thm "subset_imp_ensures";
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val subset_imp_leadsTo = thm "subset_imp_leadsTo";
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val leadsTo_refl = thm "leadsTo_refl";
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val empty_leadsTo = thm "empty_leadsTo";
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val leadsTo_UNIV = thm "leadsTo_UNIV";
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val leadsTo_induct_pre = thm "leadsTo_induct_pre";
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val leadsTo_weaken_R = thm "leadsTo_weaken_R";
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val leadsTo_weaken_L = thm "leadsTo_weaken_L";
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val leadsTo_Un_distrib = thm "leadsTo_Un_distrib";
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val leadsTo_UN_distrib = thm "leadsTo_UN_distrib";
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val leadsTo_Union_distrib = thm "leadsTo_Union_distrib";
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val leadsTo_weaken = thm "leadsTo_weaken";
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val leadsTo_Diff = thm "leadsTo_Diff";
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val leadsTo_UN_UN = thm "leadsTo_UN_UN";
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val leadsTo_Un_Un = thm "leadsTo_Un_Un";
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val leadsTo_cancel2 = thm "leadsTo_cancel2";
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val leadsTo_cancel_Diff2 = thm "leadsTo_cancel_Diff2";
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val leadsTo_cancel1 = thm "leadsTo_cancel1";
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val leadsTo_cancel_Diff1 = thm "leadsTo_cancel_Diff1";
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val leadsTo_empty = thm "leadsTo_empty";
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val psp_stable = thm "psp_stable";
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val psp_stable2 = thm "psp_stable2";
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val psp_ensures = thm "psp_ensures";
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val psp = thm "psp";
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val psp2 = thm "psp2";
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val psp_unless = thm "psp_unless";
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val leadsTo_wf_induct = thm "leadsTo_wf_induct";
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val bounded_induct = thm "bounded_induct";
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val lessThan_induct = thm "lessThan_induct";
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val lessThan_bounded_induct = thm "lessThan_bounded_induct";
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val greaterThan_bounded_induct = thm "greaterThan_bounded_induct";
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val wlt_leadsTo = thm "wlt_leadsTo";
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val leadsTo_subset = thm "leadsTo_subset";
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val leadsTo_eq_subset_wlt = thm "leadsTo_eq_subset_wlt";
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val wlt_increasing = thm "wlt_increasing";
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val leadsTo_123 = thm "leadsTo_123";
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val wlt_constrains_wlt = thm "wlt_constrains_wlt";
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val completion = thm "completion";
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val finite_completion = thm "finite_completion";
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val stable_completion = thm "stable_completion";
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val finite_stable_completion = thm "finite_stable_completion";
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(*Constrains*)
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val Increasing_def = thm "Increasing_def";
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val reachable_Init = thm "reachable.Init";
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val reachable_Acts = thm "reachable.Acts";
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val reachable_equiv_traces = thm "reachable_equiv_traces";
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val Init_subset_reachable = thm "Init_subset_reachable";
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val stable_reachable = thm "stable_reachable";
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val invariant_reachable = thm "invariant_reachable";
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val invariant_includes_reachable = thm "invariant_includes_reachable";
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val constrains_reachable_Int = thm "constrains_reachable_Int";
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val Constrains_eq_constrains = thm "Constrains_eq_constrains";
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val constrains_imp_Constrains = thm "constrains_imp_Constrains";
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val stable_imp_Stable = thm "stable_imp_Stable";
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val ConstrainsI = thm "ConstrainsI";
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val Constrains_empty = thm "Constrains_empty";
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val Constrains_UNIV = thm "Constrains_UNIV";
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val Constrains_weaken_R = thm "Constrains_weaken_R";
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val Constrains_weaken_L = thm "Constrains_weaken_L";
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val Constrains_weaken = thm "Constrains_weaken";
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val Constrains_Un = thm "Constrains_Un";
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val Constrains_UN = thm "Constrains_UN";
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val Constrains_Int = thm "Constrains_Int";
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val Constrains_INT = thm "Constrains_INT";
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val Constrains_imp_subset = thm "Constrains_imp_subset";
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val Constrains_trans = thm "Constrains_trans";
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val Constrains_cancel = thm "Constrains_cancel";
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val Stable_eq = thm "Stable_eq";
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val Stable_eq_stable = thm "Stable_eq_stable";
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val StableI = thm "StableI";
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val StableD = thm "StableD";
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val Stable_Un = thm "Stable_Un";
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val Stable_Int = thm "Stable_Int";
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val Stable_Constrains_Un = thm "Stable_Constrains_Un";
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val Stable_Constrains_Int = thm "Stable_Constrains_Int";
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val Stable_UN = thm "Stable_UN";
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val Stable_INT = thm "Stable_INT";
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val Stable_reachable = thm "Stable_reachable";
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val IncreasingD = thm "IncreasingD";
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val mono_Increasing_o = thm "mono_Increasing_o";
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val strict_IncreasingD = thm "strict_IncreasingD";
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val increasing_imp_Increasing = thm "increasing_imp_Increasing";
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val Increasing_constant = thm "Increasing_constant";
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val Elimination = thm "Elimination";
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val Elimination_sing = thm "Elimination_sing";
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val AlwaysI = thm "AlwaysI";
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val AlwaysD = thm "AlwaysD";
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val AlwaysE = thm "AlwaysE";
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val Always_imp_Stable = thm "Always_imp_Stable";
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val Always_includes_reachable = thm "Always_includes_reachable";
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val invariant_imp_Always = thm "invariant_imp_Always";
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val Always_reachable = thm "Always_reachable";
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val Always_eq_invariant_reachable = thm "Always_eq_invariant_reachable";
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val Always_eq_includes_reachable = thm "Always_eq_includes_reachable";
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val Always_UNIV_eq = thm "Always_UNIV_eq";
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val UNIV_AlwaysI = thm "UNIV_AlwaysI";
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val Always_eq_UN_invariant = thm "Always_eq_UN_invariant";
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val Always_weaken = thm "Always_weaken";
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val Always_Constrains_pre = thm "Always_Constrains_pre";
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val Always_Constrains_post = thm "Always_Constrains_post";
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val Always_ConstrainsI = thm "Always_ConstrainsI";
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|
|
270 |
val Always_ConstrainsD = thm "Always_ConstrainsD";
|
|
|
271 |
val Always_Constrains_weaken = thm "Always_Constrains_weaken";
|
|
|
272 |
val Always_Int_distrib = thm "Always_Int_distrib";
|
|
|
273 |
val Always_INT_distrib = thm "Always_INT_distrib";
|
|
|
274 |
val Always_Int_I = thm "Always_Int_I";
|
|
|
275 |
val Always_Compl_Un_eq = thm "Always_Compl_Un_eq";
|
|
|
276 |
val Always_thin = thm "Always_thin";
|
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|
277 |
|
|
13796
|
278 |
(*FP*)
|
|
|
279 |
val stable_FP_Orig_Int = thm "stable_FP_Orig_Int";
|
|
|
280 |
val FP_Orig_weakest = thm "FP_Orig_weakest";
|
|
|
281 |
val stable_FP_Int = thm "stable_FP_Int";
|
|
|
282 |
val FP_equivalence = thm "FP_equivalence";
|
|
|
283 |
val FP_weakest = thm "FP_weakest";
|
|
|
284 |
val Compl_FP = thm "Compl_FP";
|
|
|
285 |
val Diff_FP = thm "Diff_FP";
|
|
|
286 |
|
|
|
287 |
(*SubstAx*)
|
|
|
288 |
val LeadsTo_eq_leadsTo = thm "LeadsTo_eq_leadsTo";
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|
|
289 |
val Always_LeadsTo_pre = thm "Always_LeadsTo_pre";
|
|
|
290 |
val Always_LeadsTo_post = thm "Always_LeadsTo_post";
|
|
|
291 |
val Always_LeadsToI = thm "Always_LeadsToI";
|
|
|
292 |
val Always_LeadsToD = thm "Always_LeadsToD";
|
|
|
293 |
val leadsTo_imp_LeadsTo = thm "leadsTo_imp_LeadsTo";
|
|
|
294 |
val LeadsTo_Trans = thm "LeadsTo_Trans";
|
|
|
295 |
val LeadsTo_Union = thm "LeadsTo_Union";
|
|
|
296 |
val LeadsTo_UNIV = thm "LeadsTo_UNIV";
|
|
|
297 |
val LeadsTo_Un_duplicate = thm "LeadsTo_Un_duplicate";
|
|
|
298 |
val LeadsTo_Un_duplicate2 = thm "LeadsTo_Un_duplicate2";
|
|
|
299 |
val LeadsTo_UN = thm "LeadsTo_UN";
|
|
|
300 |
val LeadsTo_Un = thm "LeadsTo_Un";
|
|
|
301 |
val single_LeadsTo_I = thm "single_LeadsTo_I";
|
|
|
302 |
val subset_imp_LeadsTo = thm "subset_imp_LeadsTo";
|
|
|
303 |
val empty_LeadsTo = thm "empty_LeadsTo";
|
|
|
304 |
val LeadsTo_weaken_R = thm "LeadsTo_weaken_R";
|
|
|
305 |
val LeadsTo_weaken_L = thm "LeadsTo_weaken_L";
|
|
|
306 |
val LeadsTo_weaken = thm "LeadsTo_weaken";
|
|
|
307 |
val Always_LeadsTo_weaken = thm "Always_LeadsTo_weaken";
|
|
|
308 |
val LeadsTo_Un_post = thm "LeadsTo_Un_post";
|
|
|
309 |
val LeadsTo_Trans_Un = thm "LeadsTo_Trans_Un";
|
|
|
310 |
val LeadsTo_Un_distrib = thm "LeadsTo_Un_distrib";
|
|
|
311 |
val LeadsTo_UN_distrib = thm "LeadsTo_UN_distrib";
|
|
|
312 |
val LeadsTo_Union_distrib = thm "LeadsTo_Union_distrib";
|
|
|
313 |
val LeadsTo_Basis = thm "LeadsTo_Basis";
|
|
|
314 |
val EnsuresI = thm "EnsuresI";
|
|
|
315 |
val Always_LeadsTo_Basis = thm "Always_LeadsTo_Basis";
|
|
|
316 |
val LeadsTo_Diff = thm "LeadsTo_Diff";
|
|
|
317 |
val LeadsTo_UN_UN = thm "LeadsTo_UN_UN";
|
|
|
318 |
val LeadsTo_UN_UN_noindex = thm "LeadsTo_UN_UN_noindex";
|
|
|
319 |
val all_LeadsTo_UN_UN = thm "all_LeadsTo_UN_UN";
|
|
|
320 |
val LeadsTo_Un_Un = thm "LeadsTo_Un_Un";
|
|
|
321 |
val LeadsTo_cancel2 = thm "LeadsTo_cancel2";
|
|
|
322 |
val LeadsTo_cancel_Diff2 = thm "LeadsTo_cancel_Diff2";
|
|
|
323 |
val LeadsTo_cancel1 = thm "LeadsTo_cancel1";
|
|
|
324 |
val LeadsTo_cancel_Diff1 = thm "LeadsTo_cancel_Diff1";
|
|
|
325 |
val LeadsTo_empty = thm "LeadsTo_empty";
|
|
|
326 |
val PSP_Stable = thm "PSP_Stable";
|
|
|
327 |
val PSP_Stable2 = thm "PSP_Stable2";
|
|
|
328 |
val PSP = thm "PSP";
|
|
|
329 |
val PSP2 = thm "PSP2";
|
|
|
330 |
val PSP_Unless = thm "PSP_Unless";
|
|
|
331 |
val Stable_transient_Always_LeadsTo = thm "Stable_transient_Always_LeadsTo";
|
|
|
332 |
val LeadsTo_wf_induct = thm "LeadsTo_wf_induct";
|
|
|
333 |
val Bounded_induct = thm "Bounded_induct";
|
|
|
334 |
val LessThan_induct = thm "LessThan_induct";
|
|
|
335 |
val integ_0_le_induct = thm "integ_0_le_induct";
|
|
|
336 |
val LessThan_bounded_induct = thm "LessThan_bounded_induct";
|
|
|
337 |
val GreaterThan_bounded_induct = thm "GreaterThan_bounded_induct";
|
|
|
338 |
val Completion = thm "Completion";
|
|
|
339 |
val Finite_completion = thm "Finite_completion";
|
|
|
340 |
val Stable_completion = thm "Stable_completion";
|
|
|
341 |
val Finite_stable_completion = thm "Finite_stable_completion";
|
|
|
342 |
|
|
13792
|
343 |
(*Union*)
|
|
|
344 |
val Init_SKIP = thm "Init_SKIP";
|
|
|
345 |
val Acts_SKIP = thm "Acts_SKIP";
|
|
|
346 |
val AllowedActs_SKIP = thm "AllowedActs_SKIP";
|
|
|
347 |
val reachable_SKIP = thm "reachable_SKIP";
|
|
|
348 |
val SKIP_in_constrains_iff = thm "SKIP_in_constrains_iff";
|
|
|
349 |
val SKIP_in_Constrains_iff = thm "SKIP_in_Constrains_iff";
|
|
|
350 |
val SKIP_in_stable = thm "SKIP_in_stable";
|
|
|
351 |
val Init_Join = thm "Init_Join";
|
|
|
352 |
val Acts_Join = thm "Acts_Join";
|
|
|
353 |
val AllowedActs_Join = thm "AllowedActs_Join";
|
|
|
354 |
val JN_empty = thm "JN_empty";
|
|
|
355 |
val JN_insert = thm "JN_insert";
|
|
|
356 |
val Init_JN = thm "Init_JN";
|
|
|
357 |
val Acts_JN = thm "Acts_JN";
|
|
|
358 |
val AllowedActs_JN = thm "AllowedActs_JN";
|
|
|
359 |
val JN_cong = thm "JN_cong";
|
|
|
360 |
val Join_commute = thm "Join_commute";
|
|
|
361 |
val Join_assoc = thm "Join_assoc";
|
|
|
362 |
val Join_left_commute = thm "Join_left_commute";
|
|
|
363 |
val Join_SKIP_left = thm "Join_SKIP_left";
|
|
|
364 |
val Join_SKIP_right = thm "Join_SKIP_right";
|
|
|
365 |
val Join_absorb = thm "Join_absorb";
|
|
|
366 |
val Join_left_absorb = thm "Join_left_absorb";
|
|
|
367 |
val Join_ac = thms "Join_ac";
|
|
|
368 |
val JN_absorb = thm "JN_absorb";
|
|
|
369 |
val JN_Un = thm "JN_Un";
|
|
|
370 |
val JN_constant = thm "JN_constant";
|
|
|
371 |
val JN_Join_distrib = thm "JN_Join_distrib";
|
|
|
372 |
val JN_Join_miniscope = thm "JN_Join_miniscope";
|
|
|
373 |
val JN_Join_diff = thm "JN_Join_diff";
|
|
|
374 |
val JN_constrains = thm "JN_constrains";
|
|
|
375 |
val Join_constrains = thm "Join_constrains";
|
|
|
376 |
val Join_unless = thm "Join_unless";
|
|
|
377 |
val Join_constrains_weaken = thm "Join_constrains_weaken";
|
|
|
378 |
val JN_constrains_weaken = thm "JN_constrains_weaken";
|
|
|
379 |
val JN_stable = thm "JN_stable";
|
|
|
380 |
val invariant_JN_I = thm "invariant_JN_I";
|
|
|
381 |
val Join_stable = thm "Join_stable";
|
|
|
382 |
val Join_increasing = thm "Join_increasing";
|
|
|
383 |
val invariant_JoinI = thm "invariant_JoinI";
|
|
|
384 |
val FP_JN = thm "FP_JN";
|
|
|
385 |
val JN_transient = thm "JN_transient";
|
|
|
386 |
val Join_transient = thm "Join_transient";
|
|
|
387 |
val Join_transient_I1 = thm "Join_transient_I1";
|
|
|
388 |
val Join_transient_I2 = thm "Join_transient_I2";
|
|
|
389 |
val JN_ensures = thm "JN_ensures";
|
|
|
390 |
val Join_ensures = thm "Join_ensures";
|
|
|
391 |
val stable_Join_constrains = thm "stable_Join_constrains";
|
|
|
392 |
val stable_Join_Always1 = thm "stable_Join_Always1";
|
|
|
393 |
val stable_Join_Always2 = thm "stable_Join_Always2";
|
|
|
394 |
val stable_Join_ensures1 = thm "stable_Join_ensures1";
|
|
|
395 |
val stable_Join_ensures2 = thm "stable_Join_ensures2";
|
|
|
396 |
val ok_SKIP1 = thm "ok_SKIP1";
|
|
|
397 |
val ok_SKIP2 = thm "ok_SKIP2";
|
|
|
398 |
val ok_Join_commute = thm "ok_Join_commute";
|
|
|
399 |
val ok_commute = thm "ok_commute";
|
|
|
400 |
val ok_sym = thm "ok_sym";
|
|
|
401 |
val ok_iff_OK = thm "ok_iff_OK";
|
|
|
402 |
val ok_Join_iff1 = thm "ok_Join_iff1";
|
|
|
403 |
val ok_Join_iff2 = thm "ok_Join_iff2";
|
|
|
404 |
val ok_Join_commute_I = thm "ok_Join_commute_I";
|
|
|
405 |
val ok_JN_iff1 = thm "ok_JN_iff1";
|
|
|
406 |
val ok_JN_iff2 = thm "ok_JN_iff2";
|
|
|
407 |
val OK_iff_ok = thm "OK_iff_ok";
|
|
|
408 |
val OK_imp_ok = thm "OK_imp_ok";
|
|
|
409 |
val Allowed_SKIP = thm "Allowed_SKIP";
|
|
|
410 |
val Allowed_Join = thm "Allowed_Join";
|
|
|
411 |
val Allowed_JN = thm "Allowed_JN";
|
|
|
412 |
val ok_iff_Allowed = thm "ok_iff_Allowed";
|
|
|
413 |
val OK_iff_Allowed = thm "OK_iff_Allowed";
|
|
|
414 |
val safety_prop_Acts_iff = thm "safety_prop_Acts_iff";
|
|
|
415 |
val safety_prop_AllowedActs_iff_Allowed = thm "safety_prop_AllowedActs_iff_Allowed";
|
|
|
416 |
val Allowed_eq = thm "Allowed_eq";
|
|
|
417 |
val def_prg_Allowed = thm "def_prg_Allowed";
|
|
|
418 |
val safety_prop_constrains = thm "safety_prop_constrains";
|
|
|
419 |
val safety_prop_stable = thm "safety_prop_stable";
|
|
|
420 |
val safety_prop_Int = thm "safety_prop_Int";
|
|
|
421 |
val safety_prop_INTER1 = thm "safety_prop_INTER1";
|
|
|
422 |
val safety_prop_INTER = thm "safety_prop_INTER";
|
|
|
423 |
val def_UNION_ok_iff = thm "def_UNION_ok_iff";
|
|
|
424 |
|
|
|
425 |
(*Comp*)
|
|
|
426 |
val preserves_def = thm "preserves_def";
|
|
|
427 |
val funPair_def = thm "funPair_def";
|
|
|
428 |
val componentI = thm "componentI";
|
|
|
429 |
val component_eq_subset = thm "component_eq_subset";
|
|
|
430 |
val component_SKIP = thm "component_SKIP";
|
|
|
431 |
val component_refl = thm "component_refl";
|
|
|
432 |
val SKIP_minimal = thm "SKIP_minimal";
|
|
|
433 |
val component_Join1 = thm "component_Join1";
|
|
|
434 |
val component_Join2 = thm "component_Join2";
|
|
|
435 |
val Join_absorb1 = thm "Join_absorb1";
|
|
|
436 |
val Join_absorb2 = thm "Join_absorb2";
|
|
|
437 |
val JN_component_iff = thm "JN_component_iff";
|
|
|
438 |
val component_JN = thm "component_JN";
|
|
|
439 |
val component_trans = thm "component_trans";
|
|
|
440 |
val component_antisym = thm "component_antisym";
|
|
|
441 |
val Join_component_iff = thm "Join_component_iff";
|
|
|
442 |
val component_constrains = thm "component_constrains";
|
|
|
443 |
val program_less_le = thm "program_less_le";
|
|
|
444 |
val preservesI = thm "preservesI";
|
|
|
445 |
val preserves_imp_eq = thm "preserves_imp_eq";
|
|
|
446 |
val Join_preserves = thm "Join_preserves";
|
|
|
447 |
val JN_preserves = thm "JN_preserves";
|
|
|
448 |
val SKIP_preserves = thm "SKIP_preserves";
|
|
|
449 |
val funPair_apply = thm "funPair_apply";
|
|
|
450 |
val preserves_funPair = thm "preserves_funPair";
|
|
|
451 |
val funPair_o_distrib = thm "funPair_o_distrib";
|
|
|
452 |
val fst_o_funPair = thm "fst_o_funPair";
|
|
|
453 |
val snd_o_funPair = thm "snd_o_funPair";
|
|
|
454 |
val subset_preserves_o = thm "subset_preserves_o";
|
|
|
455 |
val preserves_subset_stable = thm "preserves_subset_stable";
|
|
|
456 |
val preserves_subset_increasing = thm "preserves_subset_increasing";
|
|
|
457 |
val preserves_id_subset_stable = thm "preserves_id_subset_stable";
|
|
|
458 |
val safety_prop_preserves = thm "safety_prop_preserves";
|
|
|
459 |
val stable_localTo_stable2 = thm "stable_localTo_stable2";
|
|
|
460 |
val Increasing_preserves_Stable = thm "Increasing_preserves_Stable";
|
|
|
461 |
val component_of_imp_component = thm "component_of_imp_component";
|
|
|
462 |
val component_of_refl = thm "component_of_refl";
|
|
|
463 |
val component_of_SKIP = thm "component_of_SKIP";
|
|
|
464 |
val component_of_trans = thm "component_of_trans";
|
|
|
465 |
val strict_component_of_eq = thm "strict_component_of_eq";
|
|
|
466 |
val localize_Init_eq = thm "localize_Init_eq";
|
|
|
467 |
val localize_Acts_eq = thm "localize_Acts_eq";
|
|
|
468 |
val localize_AllowedActs_eq = thm "localize_AllowedActs_eq";
|
|
|
469 |
|
|
|
470 |
(*Guar*)
|
|
|
471 |
val guar_def = thm "guar_def";
|
|
|
472 |
val OK_insert_iff = thm "OK_insert_iff";
|
|
|
473 |
val ex1 = thm "ex1";
|
|
|
474 |
val ex2 = thm "ex2";
|
|
|
475 |
val ex_prop_finite = thm "ex_prop_finite";
|
|
|
476 |
val ex_prop_equiv = thm "ex_prop_equiv";
|
|
|
477 |
val uv1 = thm "uv1";
|
|
|
478 |
val uv2 = thm "uv2";
|
|
|
479 |
val uv_prop_finite = thm "uv_prop_finite";
|
|
|
480 |
val guaranteesI = thm "guaranteesI";
|
|
|
481 |
val guaranteesD = thm "guaranteesD";
|
|
|
482 |
val component_guaranteesD = thm "component_guaranteesD";
|
|
|
483 |
val guarantees_weaken = thm "guarantees_weaken";
|
|
|
484 |
val subset_imp_guarantees_UNIV = thm "subset_imp_guarantees_UNIV";
|
|
|
485 |
val subset_imp_guarantees = thm "subset_imp_guarantees";
|
|
|
486 |
val ex_prop_imp = thm "ex_prop_imp";
|
|
|
487 |
val guarantees_imp = thm "guarantees_imp";
|
|
|
488 |
val ex_prop_equiv2 = thm "ex_prop_equiv2";
|
|
|
489 |
val guarantees_UN_left = thm "guarantees_UN_left";
|
|
|
490 |
val guarantees_Un_left = thm "guarantees_Un_left";
|
|
|
491 |
val guarantees_INT_right = thm "guarantees_INT_right";
|
|
|
492 |
val guarantees_Int_right = thm "guarantees_Int_right";
|
|
|
493 |
val guarantees_Int_right_I = thm "guarantees_Int_right_I";
|
|
|
494 |
val guarantees_INT_right_iff = thm "guarantees_INT_right_iff";
|
|
|
495 |
val shunting = thm "shunting";
|
|
|
496 |
val contrapositive = thm "contrapositive";
|
|
|
497 |
val combining1 = thm "combining1";
|
|
|
498 |
val combining2 = thm "combining2";
|
|
|
499 |
val all_guarantees = thm "all_guarantees";
|
|
|
500 |
val ex_guarantees = thm "ex_guarantees";
|
|
|
501 |
val guarantees_Join_Int = thm "guarantees_Join_Int";
|
|
|
502 |
val guarantees_Join_Un = thm "guarantees_Join_Un";
|
|
|
503 |
val guarantees_JN_INT = thm "guarantees_JN_INT";
|
|
|
504 |
val guarantees_JN_UN = thm "guarantees_JN_UN";
|
|
|
505 |
val guarantees_Join_I1 = thm "guarantees_Join_I1";
|
|
|
506 |
val guarantees_Join_I2 = thm "guarantees_Join_I2";
|
|
|
507 |
val guarantees_JN_I = thm "guarantees_JN_I";
|
|
|
508 |
val Join_welldef_D1 = thm "Join_welldef_D1";
|
|
|
509 |
val Join_welldef_D2 = thm "Join_welldef_D2";
|
|
|
510 |
val refines_refl = thm "refines_refl";
|
|
|
511 |
val ex_refinement_thm = thm "ex_refinement_thm";
|
|
|
512 |
val uv_refinement_thm = thm "uv_refinement_thm";
|
|
|
513 |
val guarantees_equiv = thm "guarantees_equiv";
|
|
|
514 |
val wg_weakest = thm "wg_weakest";
|
|
|
515 |
val wg_guarantees = thm "wg_guarantees";
|
|
|
516 |
val wg_equiv = thm "wg_equiv";
|
|
|
517 |
val component_of_wg = thm "component_of_wg";
|
|
|
518 |
val wg_finite = thm "wg_finite";
|
|
|
519 |
val wg_ex_prop = thm "wg_ex_prop";
|
|
|
520 |
val wx_subset = thm "wx_subset";
|
|
|
521 |
val wx_ex_prop = thm "wx_ex_prop";
|
|
|
522 |
val wx_weakest = thm "wx_weakest";
|
|
|
523 |
val wx'_ex_prop = thm "wx'_ex_prop";
|
|
|
524 |
val wx_equiv = thm "wx_equiv";
|
|
|
525 |
val guarantees_wx_eq = thm "guarantees_wx_eq";
|
|
|
526 |
val stable_guarantees_Always = thm "stable_guarantees_Always";
|
|
|
527 |
val leadsTo_Basis = thm "leadsTo_Basis";
|
|
|
528 |
val constrains_guarantees_leadsTo = thm "constrains_guarantees_leadsTo";
|
|
|
529 |
|
|
13790
|
530 |
(*Extend*)
|
|
|
531 |
val Restrict_iff = thm "Restrict_iff";
|
|
|
532 |
val Restrict_UNIV = thm "Restrict_UNIV";
|
|
|
533 |
val Restrict_empty = thm "Restrict_empty";
|
|
|
534 |
val Restrict_Int = thm "Restrict_Int";
|
|
|
535 |
val Restrict_triv = thm "Restrict_triv";
|
|
|
536 |
val Restrict_subset = thm "Restrict_subset";
|
|
|
537 |
val Restrict_eq_mono = thm "Restrict_eq_mono";
|
|
|
538 |
val Restrict_imageI = thm "Restrict_imageI";
|
|
|
539 |
val Domain_Restrict = thm "Domain_Restrict";
|
|
|
540 |
val Image_Restrict = thm "Image_Restrict";
|
|
|
541 |
val insert_Id_image_Acts = thm "insert_Id_image_Acts";
|
|
|
542 |
val good_mapI = thm "good_mapI";
|
|
|
543 |
val good_map_is_surj = thm "good_map_is_surj";
|
|
|
544 |
val fst_inv_equalityI = thm "fst_inv_equalityI";
|
|
|
545 |
val project_set_iff = thm "project_set_iff";
|
|
|
546 |
val extend_set_mono = thm "extend_set_mono";
|
|
|
547 |
val extend_set_empty = thm "extend_set_empty";
|
|
|
548 |
val project_set_Int_subset = thm "project_set_Int_subset";
|
|
|
549 |
val Init_extend = thm "Init_extend";
|
|
|
550 |
val Init_project = thm "Init_project";
|
|
|
551 |
val Acts_project = thm "Acts_project";
|
|
|
552 |
val project_set_UNIV = thm "project_set_UNIV";
|
|
|
553 |
val project_set_Union = thm "project_set_Union";
|
|
|
554 |
val project_act_mono = thm "project_act_mono";
|
|
|
555 |
val project_constrains_project_set = thm "project_constrains_project_set";
|
|
|
556 |
val project_stable_project_set = thm "project_stable_project_set";
|
|
|
557 |
|
|
|
558 |
|
|
|
559 |
(*Rename*)
|
|
|
560 |
val good_map_bij = thm "good_map_bij";
|
|
|
561 |
val fst_o_inv_eq_inv = thm "fst_o_inv_eq_inv";
|
|
|
562 |
val mem_rename_set_iff = thm "mem_rename_set_iff";
|
|
|
563 |
val extend_set_eq_image = thm "extend_set_eq_image";
|
|
|
564 |
val Init_rename = thm "Init_rename";
|
|
|
565 |
val extend_set_inv = thm "extend_set_inv";
|
|
|
566 |
val bij_extend_act_eq_project_act = thm "bij_extend_act_eq_project_act";
|
|
|
567 |
val bij_extend_act = thm "bij_extend_act";
|
|
|
568 |
val bij_project_act = thm "bij_project_act";
|
|
|
569 |
val bij_inv_project_act_eq = thm "bij_inv_project_act_eq";
|
|
|
570 |
val Acts_project = thm "Acts_project";
|
|
|
571 |
val extend_inv = thm "extend_inv";
|
|
|
572 |
val rename_inv_rename = thm "rename_inv_rename";
|
|
|
573 |
val rename_rename_inv = thm "rename_rename_inv";
|
|
|
574 |
val rename_inv_eq = thm "rename_inv_eq";
|
|
|
575 |
val bij_extend = thm "bij_extend";
|
|
|
576 |
val bij_project = thm "bij_project";
|
|
|
577 |
val inv_project_eq = thm "inv_project_eq";
|
|
|
578 |
val Allowed_rename = thm "Allowed_rename";
|
|
|
579 |
val bij_rename = thm "bij_rename";
|
|
|
580 |
val surj_rename = thm "surj_rename";
|
|
|
581 |
val inj_rename_imp_inj = thm "inj_rename_imp_inj";
|
|
|
582 |
val surj_rename_imp_surj = thm "surj_rename_imp_surj";
|
|
|
583 |
val bij_rename_imp_bij = thm "bij_rename_imp_bij";
|
|
|
584 |
val bij_rename_iff = thm "bij_rename_iff";
|
|
|
585 |
val rename_SKIP = thm "rename_SKIP";
|
|
|
586 |
val rename_Join = thm "rename_Join";
|
|
|
587 |
val rename_JN = thm "rename_JN";
|
|
|
588 |
val rename_constrains = thm "rename_constrains";
|
|
|
589 |
val rename_stable = thm "rename_stable";
|
|
|
590 |
val rename_invariant = thm "rename_invariant";
|
|
|
591 |
val rename_increasing = thm "rename_increasing";
|
|
|
592 |
val reachable_rename_eq = thm "reachable_rename_eq";
|
|
|
593 |
val rename_Constrains = thm "rename_Constrains";
|
|
|
594 |
val rename_Stable = thm "rename_Stable";
|
|
|
595 |
val rename_Always = thm "rename_Always";
|
|
|
596 |
val rename_Increasing = thm "rename_Increasing";
|
|
|
597 |
val rename_transient = thm "rename_transient";
|
|
|
598 |
val rename_ensures = thm "rename_ensures";
|
|
|
599 |
val rename_leadsTo = thm "rename_leadsTo";
|
|
|
600 |
val rename_LeadsTo = thm "rename_LeadsTo";
|
|
|
601 |
val rename_rename_guarantees_eq = thm "rename_rename_guarantees_eq";
|
|
|
602 |
val rename_guarantees_eq_rename_inv = thm "rename_guarantees_eq_rename_inv";
|
|
|
603 |
val rename_preserves = thm "rename_preserves";
|
|
|
604 |
val ok_rename_iff = thm "ok_rename_iff";
|
|
|
605 |
val OK_rename_iff = thm "OK_rename_iff";
|
|
|
606 |
val bij_eq_rename = thm "bij_eq_rename";
|
|
|
607 |
val rename_image_constrains = thm "rename_image_constrains";
|
|
|
608 |
val rename_image_stable = thm "rename_image_stable";
|
|
|
609 |
val rename_image_increasing = thm "rename_image_increasing";
|
|
|
610 |
val rename_image_invariant = thm "rename_image_invariant";
|
|
|
611 |
val rename_image_Constrains = thm "rename_image_Constrains";
|
|
|
612 |
val rename_image_preserves = thm "rename_image_preserves";
|
|
|
613 |
val rename_image_Stable = thm "rename_image_Stable";
|
|
|
614 |
val rename_image_Increasing = thm "rename_image_Increasing";
|
|
|
615 |
val rename_image_Always = thm "rename_image_Always";
|
|
|
616 |
val rename_image_leadsTo = thm "rename_image_leadsTo";
|
|
|
617 |
val rename_image_LeadsTo = thm "rename_image_LeadsTo";
|
|
|
618 |
|
|
|
619 |
|
|
13786
|
620 |
|
|
|
621 |
(*Lift_prog*)
|
|
|
622 |
val sub_def = thm "sub_def";
|
|
|
623 |
val lift_map_def = thm "lift_map_def";
|
|
|
624 |
val drop_map_def = thm "drop_map_def";
|
|
|
625 |
val insert_map_inverse = thm "insert_map_inverse";
|
|
|
626 |
val insert_map_delete_map_eq = thm "insert_map_delete_map_eq";
|
|
|
627 |
val insert_map_inject1 = thm "insert_map_inject1";
|
|
|
628 |
val insert_map_inject2 = thm "insert_map_inject2";
|
|
|
629 |
val insert_map_inject = thm "insert_map_inject";
|
|
|
630 |
val insert_map_inject = thm "insert_map_inject";
|
|
|
631 |
val lift_map_eq_iff = thm "lift_map_eq_iff";
|
|
|
632 |
val drop_map_lift_map_eq = thm "drop_map_lift_map_eq";
|
|
|
633 |
val inj_lift_map = thm "inj_lift_map";
|
|
|
634 |
val lift_map_drop_map_eq = thm "lift_map_drop_map_eq";
|
|
|
635 |
val drop_map_inject = thm "drop_map_inject";
|
|
|
636 |
val surj_lift_map = thm "surj_lift_map";
|
|
|
637 |
val bij_lift_map = thm "bij_lift_map";
|
|
|
638 |
val inv_lift_map_eq = thm "inv_lift_map_eq";
|
|
|
639 |
val inv_drop_map_eq = thm "inv_drop_map_eq";
|
|
|
640 |
val bij_drop_map = thm "bij_drop_map";
|
|
|
641 |
val sub_apply = thm "sub_apply";
|
|
|
642 |
val lift_set_empty = thm "lift_set_empty";
|
|
|
643 |
val lift_set_iff = thm "lift_set_iff";
|
|
|
644 |
val lift_set_iff2 = thm "lift_set_iff2";
|
|
|
645 |
val lift_set_mono = thm "lift_set_mono";
|
|
|
646 |
val lift_set_Un_distrib = thm "lift_set_Un_distrib";
|
|
|
647 |
val lift_set_Diff_distrib = thm "lift_set_Diff_distrib";
|
|
|
648 |
val bij_lift = thm "bij_lift";
|
|
|
649 |
val lift_SKIP = thm "lift_SKIP";
|
|
|
650 |
val lift_Join = thm "lift_Join";
|
|
|
651 |
val lift_JN = thm "lift_JN";
|
|
|
652 |
val lift_constrains = thm "lift_constrains";
|
|
|
653 |
val lift_stable = thm "lift_stable";
|
|
|
654 |
val lift_invariant = thm "lift_invariant";
|
|
|
655 |
val lift_Constrains = thm "lift_Constrains";
|
|
|
656 |
val lift_Stable = thm "lift_Stable";
|
|
|
657 |
val lift_Always = thm "lift_Always";
|
|
|
658 |
val lift_transient = thm "lift_transient";
|
|
|
659 |
val lift_ensures = thm "lift_ensures";
|
|
|
660 |
val lift_leadsTo = thm "lift_leadsTo";
|
|
|
661 |
val lift_LeadsTo = thm "lift_LeadsTo";
|
|
|
662 |
val lift_lift_guarantees_eq = thm "lift_lift_guarantees_eq";
|
|
|
663 |
val lift_guarantees_eq_lift_inv = thm "lift_guarantees_eq_lift_inv";
|
|
|
664 |
val lift_preserves_snd_I = thm "lift_preserves_snd_I";
|
|
|
665 |
val delete_map_eqE = thm "delete_map_eqE";
|
|
|
666 |
val delete_map_eqE = thm "delete_map_eqE";
|
|
|
667 |
val delete_map_neq_apply = thm "delete_map_neq_apply";
|
|
|
668 |
val vimage_o_fst_eq = thm "vimage_o_fst_eq";
|
|
|
669 |
val vimage_sub_eq_lift_set = thm "vimage_sub_eq_lift_set";
|
|
|
670 |
val mem_lift_act_iff = thm "mem_lift_act_iff";
|
|
|
671 |
val preserves_snd_lift_stable = thm "preserves_snd_lift_stable";
|
|
|
672 |
val constrains_imp_lift_constrains = thm "constrains_imp_lift_constrains";
|
|
|
673 |
val insert_map_upd_same = thm "insert_map_upd_same";
|
|
|
674 |
val insert_map_upd = thm "insert_map_upd";
|
|
|
675 |
val insert_map_eq_diff = thm "insert_map_eq_diff";
|
|
|
676 |
val lift_map_eq_diff = thm "lift_map_eq_diff";
|
|
|
677 |
val lift_transient_eq_disj = thm "lift_transient_eq_disj";
|
|
|
678 |
val lift_map_image_Times = thm "lift_map_image_Times";
|
|
|
679 |
val lift_preserves_eq = thm "lift_preserves_eq";
|
|
|
680 |
val lift_preserves_sub = thm "lift_preserves_sub";
|
|
|
681 |
val o_equiv_assoc = thm "o_equiv_assoc";
|
|
|
682 |
val o_equiv_apply = thm "o_equiv_apply";
|
|
|
683 |
val fst_o_lift_map = thm "fst_o_lift_map";
|
|
|
684 |
val snd_o_lift_map = thm "snd_o_lift_map";
|
|
|
685 |
val extend_act_extend_act = thm "extend_act_extend_act";
|
|
|
686 |
val project_act_project_act = thm "project_act_project_act";
|
|
|
687 |
val project_act_extend_act = thm "project_act_extend_act";
|
|
|
688 |
val act_in_UNION_preserves_fst = thm "act_in_UNION_preserves_fst";
|
|
|
689 |
val UNION_OK_lift_I = thm "UNION_OK_lift_I";
|
|
|
690 |
val OK_lift_I = thm "OK_lift_I";
|
|
|
691 |
val Allowed_lift = thm "Allowed_lift";
|
|
|
692 |
val lift_image_preserves = thm "lift_image_preserves";
|
|
|
693 |
|
|
|
694 |
|
|
|
695 |
(*PPROD*)
|
|
|
696 |
val Init_PLam = thm "Init_PLam";
|
|
|
697 |
val PLam_empty = thm "PLam_empty";
|
|
|
698 |
val PLam_SKIP = thm "PLam_SKIP";
|
|
|
699 |
val PLam_insert = thm "PLam_insert";
|
|
|
700 |
val PLam_component_iff = thm "PLam_component_iff";
|
|
|
701 |
val component_PLam = thm "component_PLam";
|
|
|
702 |
val PLam_constrains = thm "PLam_constrains";
|
|
|
703 |
val PLam_stable = thm "PLam_stable";
|
|
|
704 |
val PLam_transient = thm "PLam_transient";
|
|
|
705 |
val PLam_ensures = thm "PLam_ensures";
|
|
|
706 |
val PLam_leadsTo_Basis = thm "PLam_leadsTo_Basis";
|
|
|
707 |
val invariant_imp_PLam_invariant = thm "invariant_imp_PLam_invariant";
|
|
|
708 |
val PLam_preserves_fst = thm "PLam_preserves_fst";
|
|
|
709 |
val PLam_preserves_snd = thm "PLam_preserves_snd";
|
|
|
710 |
val guarantees_PLam_I = thm "guarantees_PLam_I";
|
|
|
711 |
val Allowed_PLam = thm "Allowed_PLam";
|
|
|
712 |
val PLam_preserves = thm "PLam_preserves";
|
|
|
713 |
|
|
13796
|
714 |
(*Follows*)
|
|
|
715 |
val mono_Always_o = thm "mono_Always_o";
|
|
|
716 |
val mono_LeadsTo_o = thm "mono_LeadsTo_o";
|
|
|
717 |
val Follows_constant = thm "Follows_constant";
|
|
|
718 |
val mono_Follows_o = thm "mono_Follows_o";
|
|
|
719 |
val mono_Follows_apply = thm "mono_Follows_apply";
|
|
|
720 |
val Follows_trans = thm "Follows_trans";
|
|
|
721 |
val Follows_Increasing1 = thm "Follows_Increasing1";
|
|
|
722 |
val Follows_Increasing2 = thm "Follows_Increasing2";
|
|
|
723 |
val Follows_Bounded = thm "Follows_Bounded";
|
|
|
724 |
val Follows_LeadsTo = thm "Follows_LeadsTo";
|
|
|
725 |
val Follows_LeadsTo_pfixLe = thm "Follows_LeadsTo_pfixLe";
|
|
|
726 |
val Follows_LeadsTo_pfixGe = thm "Follows_LeadsTo_pfixGe";
|
|
|
727 |
val Always_Follows1 = thm "Always_Follows1";
|
|
|
728 |
val Always_Follows2 = thm "Always_Follows2";
|
|
|
729 |
val increasing_Un = thm "increasing_Un";
|
|
|
730 |
val Increasing_Un = thm "Increasing_Un";
|
|
|
731 |
val Always_Un = thm "Always_Un";
|
|
|
732 |
val Follows_Un = thm "Follows_Un";
|
|
|
733 |
val increasing_union = thm "increasing_union";
|
|
|
734 |
val Increasing_union = thm "Increasing_union";
|
|
|
735 |
val Always_union = thm "Always_union";
|
|
|
736 |
val Follows_union = thm "Follows_union";
|
|
|
737 |
val Follows_setsum = thm "Follows_setsum";
|
|
|
738 |
val Increasing_imp_Stable_pfixGe = thm "Increasing_imp_Stable_pfixGe";
|
|
|
739 |
val LeadsTo_le_imp_pfixGe = thm "LeadsTo_le_imp_pfixGe";
|
|
|
740 |
|
|
13786
|
741 |
|
|
13797
|
742 |
(*Lazy unfolding of actions or of sets*)
|
|
|
743 |
fun simp_of_act def = def RS def_act_simp;
|
|
|
744 |
|
|
|
745 |
fun simp_of_set def = def RS def_set_simp;
|
|
|
746 |
|
|
|
747 |
|
|
|
748 |
(*Combines two invariance ASSUMPTIONS into one. USEFUL??*)
|
|
|
749 |
val Always_Int_tac = dtac Always_Int_I THEN' assume_tac THEN' etac Always_thin
|
|
|
750 |
|
|
|
751 |
(*Combines a list of invariance THEOREMS into one.*)
|
|
|
752 |
val Always_Int_rule = foldr1 (fn (th1,th2) => [th1,th2] MRS Always_Int_I)
|
|
|
753 |
|
|
13786
|
754 |
(*proves "co" properties when the program is specified*)
|
|
|
755 |
fun gen_constrains_tac(cs,ss) i =
|
|
|
756 |
SELECT_GOAL
|
|
|
757 |
(EVERY [REPEAT (Always_Int_tac 1),
|
|
|
758 |
REPEAT (etac Always_ConstrainsI 1
|
|
|
759 |
ORELSE
|
|
|
760 |
resolve_tac [StableI, stableI,
|
|
|
761 |
constrains_imp_Constrains] 1),
|
|
|
762 |
rtac constrainsI 1,
|
|
|
763 |
full_simp_tac ss 1,
|
|
|
764 |
REPEAT (FIRSTGOAL (etac disjE)),
|
|
|
765 |
ALLGOALS (clarify_tac cs),
|
|
|
766 |
ALLGOALS (asm_lr_simp_tac ss)]) i;
|
|
|
767 |
|
|
|
768 |
(*proves "ensures/leadsTo" properties when the program is specified*)
|
|
|
769 |
fun gen_ensures_tac(cs,ss) sact =
|
|
|
770 |
SELECT_GOAL
|
|
|
771 |
(EVERY [REPEAT (Always_Int_tac 1),
|
|
|
772 |
etac Always_LeadsTo_Basis 1
|
|
|
773 |
ORELSE (*subgoal may involve LeadsTo, leadsTo or ensures*)
|
|
|
774 |
REPEAT (ares_tac [LeadsTo_Basis, leadsTo_Basis,
|
|
|
775 |
EnsuresI, ensuresI] 1),
|
|
|
776 |
(*now there are two subgoals: co & transient*)
|
|
|
777 |
simp_tac ss 2,
|
|
|
778 |
res_inst_tac [("act", sact)] transientI 2,
|
|
|
779 |
(*simplify the command's domain*)
|
|
|
780 |
simp_tac (ss addsimps [Domain_def]) 3,
|
|
|
781 |
gen_constrains_tac (cs,ss) 1,
|
|
|
782 |
ALLGOALS (clarify_tac cs),
|
|
|
783 |
ALLGOALS (asm_lr_simp_tac ss)]);
|
|
|
784 |
|
|
13797
|
785 |
fun constrains_tac st = gen_constrains_tac (claset(), simpset()) st;
|
|
|
786 |
|
|
13796
|
787 |
fun ensures_tac sact = gen_ensures_tac (claset(), simpset()) sact;
|
|
|
788 |
|
|
13786
|
789 |
|
|
|
790 |
(*Composition equivalences, from Lift_prog*)
|
|
|
791 |
|
|
|
792 |
fun make_o_equivs th =
|
|
|
793 |
[th,
|
|
|
794 |
th RS o_equiv_assoc |> simplify (HOL_ss addsimps [o_assoc]),
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795 |
th RS o_equiv_apply |> simplify (HOL_ss addsimps [o_def, sub_def])];
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796 |
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797 |
Addsimps (make_o_equivs fst_o_funPair @ make_o_equivs snd_o_funPair);
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798 |
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799 |
Addsimps (make_o_equivs fst_o_lift_map @ make_o_equivs snd_o_lift_map);
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