src/HOL/UNITY/UNITY_tactics.ML
author paulson
Sat Feb 08 16:05:33 2003 +0100 (2003-02-08)
changeset 13812 91713a1915ee
parent 13798 4c1a53627500
child 21669 c68717c16013
permissions -rw-r--r--
converting HOL/UNITY to use unconditional fairness
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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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(*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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(*UNITY*)
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val mk_total_program_def = thm "mk_total_program_def";
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val totalize_act_def = thm "totalize_act_def";
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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_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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val totalize_constrains_iff = thm "totalize_constrains_iff";
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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 totalize_transientI = thm "totalize_transientI";
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val transientE = thm "transientE";
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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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val Always_ConstrainsD = thm "Always_ConstrainsD";
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val Always_Constrains_weaken = thm "Always_Constrains_weaken";
paulson@13797
   274
val Always_Int_distrib = thm "Always_Int_distrib";
paulson@13797
   275
val Always_INT_distrib = thm "Always_INT_distrib";
paulson@13797
   276
val Always_Int_I = thm "Always_Int_I";
paulson@13797
   277
val Always_Compl_Un_eq = thm "Always_Compl_Un_eq";
paulson@13797
   278
val Always_thin = thm "Always_thin";
paulson@13797
   279
paulson@13796
   280
(*FP*)
paulson@13796
   281
val stable_FP_Orig_Int = thm "stable_FP_Orig_Int";
paulson@13796
   282
val FP_Orig_weakest = thm "FP_Orig_weakest";
paulson@13796
   283
val stable_FP_Int = thm "stable_FP_Int";
paulson@13796
   284
val FP_equivalence = thm "FP_equivalence";
paulson@13796
   285
val FP_weakest = thm "FP_weakest";
paulson@13796
   286
val Compl_FP = thm "Compl_FP";
paulson@13796
   287
val Diff_FP = thm "Diff_FP";
paulson@13796
   288
paulson@13796
   289
(*SubstAx*)
paulson@13796
   290
val LeadsTo_eq_leadsTo = thm "LeadsTo_eq_leadsTo";
paulson@13796
   291
val Always_LeadsTo_pre = thm "Always_LeadsTo_pre";
paulson@13796
   292
val Always_LeadsTo_post = thm "Always_LeadsTo_post";
paulson@13796
   293
val Always_LeadsToI = thm "Always_LeadsToI";
paulson@13796
   294
val Always_LeadsToD = thm "Always_LeadsToD";
paulson@13796
   295
val leadsTo_imp_LeadsTo = thm "leadsTo_imp_LeadsTo";
paulson@13796
   296
val LeadsTo_Trans = thm "LeadsTo_Trans";
paulson@13796
   297
val LeadsTo_Union = thm "LeadsTo_Union";
paulson@13796
   298
val LeadsTo_UNIV = thm "LeadsTo_UNIV";
paulson@13796
   299
val LeadsTo_Un_duplicate = thm "LeadsTo_Un_duplicate";
paulson@13796
   300
val LeadsTo_Un_duplicate2 = thm "LeadsTo_Un_duplicate2";
paulson@13796
   301
val LeadsTo_UN = thm "LeadsTo_UN";
paulson@13796
   302
val LeadsTo_Un = thm "LeadsTo_Un";
paulson@13796
   303
val single_LeadsTo_I = thm "single_LeadsTo_I";
paulson@13796
   304
val subset_imp_LeadsTo = thm "subset_imp_LeadsTo";
paulson@13796
   305
val empty_LeadsTo = thm "empty_LeadsTo";
paulson@13796
   306
val LeadsTo_weaken_R = thm "LeadsTo_weaken_R";
paulson@13796
   307
val LeadsTo_weaken_L = thm "LeadsTo_weaken_L";
paulson@13796
   308
val LeadsTo_weaken = thm "LeadsTo_weaken";
paulson@13796
   309
val Always_LeadsTo_weaken = thm "Always_LeadsTo_weaken";
paulson@13796
   310
val LeadsTo_Un_post = thm "LeadsTo_Un_post";
paulson@13796
   311
val LeadsTo_Trans_Un = thm "LeadsTo_Trans_Un";
paulson@13796
   312
val LeadsTo_Un_distrib = thm "LeadsTo_Un_distrib";
paulson@13796
   313
val LeadsTo_UN_distrib = thm "LeadsTo_UN_distrib";
paulson@13796
   314
val LeadsTo_Union_distrib = thm "LeadsTo_Union_distrib";
paulson@13796
   315
val LeadsTo_Basis = thm "LeadsTo_Basis";
paulson@13796
   316
val EnsuresI = thm "EnsuresI";
paulson@13796
   317
val Always_LeadsTo_Basis = thm "Always_LeadsTo_Basis";
paulson@13796
   318
val LeadsTo_Diff = thm "LeadsTo_Diff";
paulson@13796
   319
val LeadsTo_UN_UN = thm "LeadsTo_UN_UN";
paulson@13796
   320
val LeadsTo_UN_UN_noindex = thm "LeadsTo_UN_UN_noindex";
paulson@13796
   321
val all_LeadsTo_UN_UN = thm "all_LeadsTo_UN_UN";
paulson@13796
   322
val LeadsTo_Un_Un = thm "LeadsTo_Un_Un";
paulson@13796
   323
val LeadsTo_cancel2 = thm "LeadsTo_cancel2";
paulson@13796
   324
val LeadsTo_cancel_Diff2 = thm "LeadsTo_cancel_Diff2";
paulson@13796
   325
val LeadsTo_cancel1 = thm "LeadsTo_cancel1";
paulson@13796
   326
val LeadsTo_cancel_Diff1 = thm "LeadsTo_cancel_Diff1";
paulson@13796
   327
val LeadsTo_empty = thm "LeadsTo_empty";
paulson@13796
   328
val PSP_Stable = thm "PSP_Stable";
paulson@13796
   329
val PSP_Stable2 = thm "PSP_Stable2";
paulson@13796
   330
val PSP = thm "PSP";
paulson@13796
   331
val PSP2 = thm "PSP2";
paulson@13796
   332
val PSP_Unless = thm "PSP_Unless";
paulson@13796
   333
val Stable_transient_Always_LeadsTo = thm "Stable_transient_Always_LeadsTo";
paulson@13796
   334
val LeadsTo_wf_induct = thm "LeadsTo_wf_induct";
paulson@13796
   335
val Bounded_induct = thm "Bounded_induct";
paulson@13796
   336
val LessThan_induct = thm "LessThan_induct";
paulson@13796
   337
val integ_0_le_induct = thm "integ_0_le_induct";
paulson@13796
   338
val LessThan_bounded_induct = thm "LessThan_bounded_induct";
paulson@13796
   339
val GreaterThan_bounded_induct = thm "GreaterThan_bounded_induct";
paulson@13796
   340
val Completion = thm "Completion";
paulson@13796
   341
val Finite_completion = thm "Finite_completion";
paulson@13796
   342
val Stable_completion = thm "Stable_completion";
paulson@13796
   343
val Finite_stable_completion = thm "Finite_stable_completion";
paulson@13796
   344
paulson@13792
   345
(*Union*)
paulson@13792
   346
val Init_SKIP = thm "Init_SKIP";
paulson@13792
   347
val Acts_SKIP = thm "Acts_SKIP";
paulson@13792
   348
val AllowedActs_SKIP = thm "AllowedActs_SKIP";
paulson@13792
   349
val reachable_SKIP = thm "reachable_SKIP";
paulson@13792
   350
val SKIP_in_constrains_iff = thm "SKIP_in_constrains_iff";
paulson@13792
   351
val SKIP_in_Constrains_iff = thm "SKIP_in_Constrains_iff";
paulson@13792
   352
val SKIP_in_stable = thm "SKIP_in_stable";
paulson@13792
   353
val Init_Join = thm "Init_Join";
paulson@13792
   354
val Acts_Join = thm "Acts_Join";
paulson@13792
   355
val AllowedActs_Join = thm "AllowedActs_Join";
paulson@13792
   356
val JN_empty = thm "JN_empty";
paulson@13792
   357
val JN_insert = thm "JN_insert";
paulson@13792
   358
val Init_JN = thm "Init_JN";
paulson@13792
   359
val Acts_JN = thm "Acts_JN";
paulson@13792
   360
val AllowedActs_JN = thm "AllowedActs_JN";
paulson@13792
   361
val JN_cong = thm "JN_cong";
paulson@13792
   362
val Join_commute = thm "Join_commute";
paulson@13792
   363
val Join_assoc = thm "Join_assoc";
paulson@13792
   364
val Join_left_commute = thm "Join_left_commute";
paulson@13792
   365
val Join_SKIP_left = thm "Join_SKIP_left";
paulson@13792
   366
val Join_SKIP_right = thm "Join_SKIP_right";
paulson@13792
   367
val Join_absorb = thm "Join_absorb";
paulson@13792
   368
val Join_left_absorb = thm "Join_left_absorb";
paulson@13792
   369
val Join_ac = thms "Join_ac";
paulson@13792
   370
val JN_absorb = thm "JN_absorb";
paulson@13792
   371
val JN_Un = thm "JN_Un";
paulson@13792
   372
val JN_constant = thm "JN_constant";
paulson@13792
   373
val JN_Join_distrib = thm "JN_Join_distrib";
paulson@13792
   374
val JN_Join_miniscope = thm "JN_Join_miniscope";
paulson@13792
   375
val JN_Join_diff = thm "JN_Join_diff";
paulson@13792
   376
val JN_constrains = thm "JN_constrains";
paulson@13792
   377
val Join_constrains = thm "Join_constrains";
paulson@13792
   378
val Join_unless = thm "Join_unless";
paulson@13792
   379
val Join_constrains_weaken = thm "Join_constrains_weaken";
paulson@13792
   380
val JN_constrains_weaken = thm "JN_constrains_weaken";
paulson@13792
   381
val JN_stable = thm "JN_stable";
paulson@13792
   382
val invariant_JN_I = thm "invariant_JN_I";
paulson@13792
   383
val Join_stable = thm "Join_stable";
paulson@13792
   384
val Join_increasing = thm "Join_increasing";
paulson@13792
   385
val invariant_JoinI = thm "invariant_JoinI";
paulson@13792
   386
val FP_JN = thm "FP_JN";
paulson@13792
   387
val JN_transient = thm "JN_transient";
paulson@13792
   388
val Join_transient = thm "Join_transient";
paulson@13792
   389
val Join_transient_I1 = thm "Join_transient_I1";
paulson@13792
   390
val Join_transient_I2 = thm "Join_transient_I2";
paulson@13792
   391
val JN_ensures = thm "JN_ensures";
paulson@13792
   392
val Join_ensures = thm "Join_ensures";
paulson@13792
   393
val stable_Join_constrains = thm "stable_Join_constrains";
paulson@13792
   394
val stable_Join_Always1 = thm "stable_Join_Always1";
paulson@13792
   395
val stable_Join_Always2 = thm "stable_Join_Always2";
paulson@13792
   396
val stable_Join_ensures1 = thm "stable_Join_ensures1";
paulson@13792
   397
val stable_Join_ensures2 = thm "stable_Join_ensures2";
paulson@13792
   398
val ok_SKIP1 = thm "ok_SKIP1";
paulson@13792
   399
val ok_SKIP2 = thm "ok_SKIP2";
paulson@13792
   400
val ok_Join_commute = thm "ok_Join_commute";
paulson@13792
   401
val ok_commute = thm "ok_commute";
paulson@13792
   402
val ok_sym = thm "ok_sym";
paulson@13792
   403
val ok_iff_OK = thm "ok_iff_OK";
paulson@13792
   404
val ok_Join_iff1 = thm "ok_Join_iff1";
paulson@13792
   405
val ok_Join_iff2 = thm "ok_Join_iff2";
paulson@13792
   406
val ok_Join_commute_I = thm "ok_Join_commute_I";
paulson@13792
   407
val ok_JN_iff1 = thm "ok_JN_iff1";
paulson@13792
   408
val ok_JN_iff2 = thm "ok_JN_iff2";
paulson@13792
   409
val OK_iff_ok = thm "OK_iff_ok";
paulson@13792
   410
val OK_imp_ok = thm "OK_imp_ok";
paulson@13792
   411
val Allowed_SKIP = thm "Allowed_SKIP";
paulson@13792
   412
val Allowed_Join = thm "Allowed_Join";
paulson@13792
   413
val Allowed_JN = thm "Allowed_JN";
paulson@13792
   414
val ok_iff_Allowed = thm "ok_iff_Allowed";
paulson@13792
   415
val OK_iff_Allowed = thm "OK_iff_Allowed";
paulson@13792
   416
val safety_prop_Acts_iff = thm "safety_prop_Acts_iff";
paulson@13792
   417
val safety_prop_AllowedActs_iff_Allowed = thm "safety_prop_AllowedActs_iff_Allowed";
paulson@13792
   418
val Allowed_eq = thm "Allowed_eq";
paulson@13792
   419
val def_prg_Allowed = thm "def_prg_Allowed";
paulson@13812
   420
val def_total_prg_Allowed = thm "def_total_prg_Allowed";
paulson@13792
   421
val safety_prop_constrains = thm "safety_prop_constrains";
paulson@13792
   422
val safety_prop_stable = thm "safety_prop_stable";
paulson@13792
   423
val safety_prop_Int = thm "safety_prop_Int";
paulson@13792
   424
val safety_prop_INTER1 = thm "safety_prop_INTER1";
paulson@13792
   425
val safety_prop_INTER = thm "safety_prop_INTER";
paulson@13792
   426
val def_UNION_ok_iff = thm "def_UNION_ok_iff";
paulson@13812
   427
val totalize_JN = thm "totalize_JN";
paulson@13792
   428
paulson@13792
   429
(*Comp*)
paulson@13792
   430
val preserves_def = thm "preserves_def";
paulson@13792
   431
val funPair_def = thm "funPair_def";
paulson@13792
   432
val componentI = thm "componentI";
paulson@13792
   433
val component_eq_subset = thm "component_eq_subset";
paulson@13792
   434
val component_SKIP = thm "component_SKIP";
paulson@13792
   435
val component_refl = thm "component_refl";
paulson@13792
   436
val SKIP_minimal = thm "SKIP_minimal";
paulson@13792
   437
val component_Join1 = thm "component_Join1";
paulson@13792
   438
val component_Join2 = thm "component_Join2";
paulson@13792
   439
val Join_absorb1 = thm "Join_absorb1";
paulson@13792
   440
val Join_absorb2 = thm "Join_absorb2";
paulson@13792
   441
val JN_component_iff = thm "JN_component_iff";
paulson@13792
   442
val component_JN = thm "component_JN";
paulson@13792
   443
val component_trans = thm "component_trans";
paulson@13792
   444
val component_antisym = thm "component_antisym";
paulson@13792
   445
val Join_component_iff = thm "Join_component_iff";
paulson@13792
   446
val component_constrains = thm "component_constrains";
paulson@13792
   447
val program_less_le = thm "program_less_le";
paulson@13792
   448
val preservesI = thm "preservesI";
paulson@13792
   449
val preserves_imp_eq = thm "preserves_imp_eq";
paulson@13792
   450
val Join_preserves = thm "Join_preserves";
paulson@13792
   451
val JN_preserves = thm "JN_preserves";
paulson@13792
   452
val SKIP_preserves = thm "SKIP_preserves";
paulson@13792
   453
val funPair_apply = thm "funPair_apply";
paulson@13792
   454
val preserves_funPair = thm "preserves_funPair";
paulson@13792
   455
val funPair_o_distrib = thm "funPair_o_distrib";
paulson@13792
   456
val fst_o_funPair = thm "fst_o_funPair";
paulson@13792
   457
val snd_o_funPair = thm "snd_o_funPair";
paulson@13792
   458
val subset_preserves_o = thm "subset_preserves_o";
paulson@13792
   459
val preserves_subset_stable = thm "preserves_subset_stable";
paulson@13792
   460
val preserves_subset_increasing = thm "preserves_subset_increasing";
paulson@13792
   461
val preserves_id_subset_stable = thm "preserves_id_subset_stable";
paulson@13792
   462
val safety_prop_preserves = thm "safety_prop_preserves";
paulson@13792
   463
val stable_localTo_stable2 = thm "stable_localTo_stable2";
paulson@13792
   464
val Increasing_preserves_Stable = thm "Increasing_preserves_Stable";
paulson@13792
   465
val component_of_imp_component = thm "component_of_imp_component";
paulson@13792
   466
val component_of_refl = thm "component_of_refl";
paulson@13792
   467
val component_of_SKIP = thm "component_of_SKIP";
paulson@13792
   468
val component_of_trans = thm "component_of_trans";
paulson@13792
   469
val strict_component_of_eq = thm "strict_component_of_eq";
paulson@13792
   470
val localize_Init_eq = thm "localize_Init_eq";
paulson@13792
   471
val localize_Acts_eq = thm "localize_Acts_eq";
paulson@13792
   472
val localize_AllowedActs_eq = thm "localize_AllowedActs_eq";
paulson@13792
   473
paulson@13792
   474
(*Guar*)
paulson@13792
   475
val guar_def = thm "guar_def";
paulson@13792
   476
val OK_insert_iff = thm "OK_insert_iff";
paulson@13792
   477
val ex1 = thm "ex1";
paulson@13792
   478
val ex2 = thm "ex2";
paulson@13792
   479
val ex_prop_finite = thm "ex_prop_finite";
paulson@13792
   480
val ex_prop_equiv = thm "ex_prop_equiv";
paulson@13792
   481
val uv1 = thm "uv1";
paulson@13792
   482
val uv2 = thm "uv2";
paulson@13792
   483
val uv_prop_finite = thm "uv_prop_finite";
paulson@13792
   484
val guaranteesI = thm "guaranteesI";
paulson@13792
   485
val guaranteesD = thm "guaranteesD";
paulson@13792
   486
val component_guaranteesD = thm "component_guaranteesD";
paulson@13792
   487
val guarantees_weaken = thm "guarantees_weaken";
paulson@13792
   488
val subset_imp_guarantees_UNIV = thm "subset_imp_guarantees_UNIV";
paulson@13792
   489
val subset_imp_guarantees = thm "subset_imp_guarantees";
paulson@13792
   490
val ex_prop_imp = thm "ex_prop_imp";
paulson@13792
   491
val guarantees_imp = thm "guarantees_imp";
paulson@13792
   492
val ex_prop_equiv2 = thm "ex_prop_equiv2";
paulson@13792
   493
val guarantees_UN_left = thm "guarantees_UN_left";
paulson@13792
   494
val guarantees_Un_left = thm "guarantees_Un_left";
paulson@13792
   495
val guarantees_INT_right = thm "guarantees_INT_right";
paulson@13792
   496
val guarantees_Int_right = thm "guarantees_Int_right";
paulson@13792
   497
val guarantees_Int_right_I = thm "guarantees_Int_right_I";
paulson@13792
   498
val guarantees_INT_right_iff = thm "guarantees_INT_right_iff";
paulson@13792
   499
val shunting = thm "shunting";
paulson@13792
   500
val contrapositive = thm "contrapositive";
paulson@13792
   501
val combining1 = thm "combining1";
paulson@13792
   502
val combining2 = thm "combining2";
paulson@13792
   503
val all_guarantees = thm "all_guarantees";
paulson@13792
   504
val ex_guarantees = thm "ex_guarantees";
paulson@13792
   505
val guarantees_Join_Int = thm "guarantees_Join_Int";
paulson@13792
   506
val guarantees_Join_Un = thm "guarantees_Join_Un";
paulson@13792
   507
val guarantees_JN_INT = thm "guarantees_JN_INT";
paulson@13792
   508
val guarantees_JN_UN = thm "guarantees_JN_UN";
paulson@13792
   509
val guarantees_Join_I1 = thm "guarantees_Join_I1";
paulson@13792
   510
val guarantees_Join_I2 = thm "guarantees_Join_I2";
paulson@13792
   511
val guarantees_JN_I = thm "guarantees_JN_I";
paulson@13792
   512
val Join_welldef_D1 = thm "Join_welldef_D1";
paulson@13792
   513
val Join_welldef_D2 = thm "Join_welldef_D2";
paulson@13792
   514
val refines_refl = thm "refines_refl";
paulson@13792
   515
val ex_refinement_thm = thm "ex_refinement_thm";
paulson@13792
   516
val uv_refinement_thm = thm "uv_refinement_thm";
paulson@13792
   517
val guarantees_equiv = thm "guarantees_equiv";
paulson@13792
   518
val wg_weakest = thm "wg_weakest";
paulson@13792
   519
val wg_guarantees = thm "wg_guarantees";
paulson@13792
   520
val wg_equiv = thm "wg_equiv";
paulson@13792
   521
val component_of_wg = thm "component_of_wg";
paulson@13792
   522
val wg_finite = thm "wg_finite";
paulson@13792
   523
val wg_ex_prop = thm "wg_ex_prop";
paulson@13792
   524
val wx_subset = thm "wx_subset";
paulson@13792
   525
val wx_ex_prop = thm "wx_ex_prop";
paulson@13792
   526
val wx_weakest = thm "wx_weakest";
paulson@13792
   527
val wx'_ex_prop = thm "wx'_ex_prop";
paulson@13792
   528
val wx_equiv = thm "wx_equiv";
paulson@13792
   529
val guarantees_wx_eq = thm "guarantees_wx_eq";
paulson@13792
   530
val stable_guarantees_Always = thm "stable_guarantees_Always";
paulson@13792
   531
val leadsTo_Basis = thm "leadsTo_Basis";
paulson@13792
   532
val constrains_guarantees_leadsTo = thm "constrains_guarantees_leadsTo";
paulson@13792
   533
paulson@13790
   534
(*Extend*)
paulson@13790
   535
val Restrict_iff = thm "Restrict_iff";
paulson@13790
   536
val Restrict_UNIV = thm "Restrict_UNIV";
paulson@13790
   537
val Restrict_empty = thm "Restrict_empty";
paulson@13790
   538
val Restrict_Int = thm "Restrict_Int";
paulson@13790
   539
val Restrict_triv = thm "Restrict_triv";
paulson@13790
   540
val Restrict_subset = thm "Restrict_subset";
paulson@13790
   541
val Restrict_eq_mono = thm "Restrict_eq_mono";
paulson@13790
   542
val Restrict_imageI = thm "Restrict_imageI";
paulson@13790
   543
val Domain_Restrict = thm "Domain_Restrict";
paulson@13790
   544
val Image_Restrict = thm "Image_Restrict";
paulson@13790
   545
val insert_Id_image_Acts = thm "insert_Id_image_Acts";
paulson@13790
   546
val good_mapI = thm "good_mapI";
paulson@13790
   547
val good_map_is_surj = thm "good_map_is_surj";
paulson@13790
   548
val fst_inv_equalityI = thm "fst_inv_equalityI";
paulson@13790
   549
val project_set_iff = thm "project_set_iff";
paulson@13790
   550
val extend_set_mono = thm "extend_set_mono";
paulson@13790
   551
val extend_set_empty = thm "extend_set_empty";
paulson@13790
   552
val project_set_Int_subset = thm "project_set_Int_subset";
paulson@13790
   553
val Init_extend = thm "Init_extend";
paulson@13790
   554
val Init_project = thm "Init_project";
paulson@13790
   555
val Acts_project = thm "Acts_project";
paulson@13790
   556
val project_set_UNIV = thm "project_set_UNIV";
paulson@13790
   557
val project_set_Union = thm "project_set_Union";
paulson@13790
   558
val project_act_mono = thm "project_act_mono";
paulson@13790
   559
val project_constrains_project_set = thm "project_constrains_project_set";
paulson@13790
   560
val project_stable_project_set = thm "project_stable_project_set";
paulson@13790
   561
paulson@13790
   562
paulson@13790
   563
(*Rename*)
paulson@13790
   564
val good_map_bij = thm "good_map_bij";
paulson@13790
   565
val fst_o_inv_eq_inv = thm "fst_o_inv_eq_inv";
paulson@13790
   566
val mem_rename_set_iff = thm "mem_rename_set_iff";
paulson@13790
   567
val extend_set_eq_image = thm "extend_set_eq_image";
paulson@13790
   568
val Init_rename = thm "Init_rename";
paulson@13790
   569
val extend_set_inv = thm "extend_set_inv";
paulson@13790
   570
val bij_extend_act_eq_project_act = thm "bij_extend_act_eq_project_act";
paulson@13790
   571
val bij_extend_act = thm "bij_extend_act";
paulson@13790
   572
val bij_project_act = thm "bij_project_act";
paulson@13790
   573
val bij_inv_project_act_eq = thm "bij_inv_project_act_eq";
paulson@13790
   574
val Acts_project = thm "Acts_project";
paulson@13790
   575
val extend_inv = thm "extend_inv";
paulson@13790
   576
val rename_inv_rename = thm "rename_inv_rename";
paulson@13790
   577
val rename_rename_inv = thm "rename_rename_inv";
paulson@13790
   578
val rename_inv_eq = thm "rename_inv_eq";
paulson@13790
   579
val bij_extend = thm "bij_extend";
paulson@13790
   580
val bij_project = thm "bij_project";
paulson@13790
   581
val inv_project_eq = thm "inv_project_eq";
paulson@13790
   582
val Allowed_rename = thm "Allowed_rename";
paulson@13790
   583
val bij_rename = thm "bij_rename";
paulson@13790
   584
val surj_rename = thm "surj_rename";
paulson@13790
   585
val inj_rename_imp_inj = thm "inj_rename_imp_inj";
paulson@13790
   586
val surj_rename_imp_surj = thm "surj_rename_imp_surj";
paulson@13790
   587
val bij_rename_imp_bij = thm "bij_rename_imp_bij";
paulson@13790
   588
val bij_rename_iff = thm "bij_rename_iff";
paulson@13790
   589
val rename_SKIP = thm "rename_SKIP";
paulson@13790
   590
val rename_Join = thm "rename_Join";
paulson@13790
   591
val rename_JN = thm "rename_JN";
paulson@13790
   592
val rename_constrains = thm "rename_constrains";
paulson@13790
   593
val rename_stable = thm "rename_stable";
paulson@13790
   594
val rename_invariant = thm "rename_invariant";
paulson@13790
   595
val rename_increasing = thm "rename_increasing";
paulson@13790
   596
val reachable_rename_eq = thm "reachable_rename_eq";
paulson@13790
   597
val rename_Constrains = thm "rename_Constrains";
paulson@13790
   598
val rename_Stable = thm "rename_Stable";
paulson@13790
   599
val rename_Always = thm "rename_Always";
paulson@13790
   600
val rename_Increasing = thm "rename_Increasing";
paulson@13790
   601
val rename_transient = thm "rename_transient";
paulson@13790
   602
val rename_ensures = thm "rename_ensures";
paulson@13790
   603
val rename_leadsTo = thm "rename_leadsTo";
paulson@13790
   604
val rename_LeadsTo = thm "rename_LeadsTo";
paulson@13790
   605
val rename_rename_guarantees_eq = thm "rename_rename_guarantees_eq";
paulson@13790
   606
val rename_guarantees_eq_rename_inv = thm "rename_guarantees_eq_rename_inv";
paulson@13790
   607
val rename_preserves = thm "rename_preserves";
paulson@13790
   608
val ok_rename_iff = thm "ok_rename_iff";
paulson@13790
   609
val OK_rename_iff = thm "OK_rename_iff";
paulson@13790
   610
val bij_eq_rename = thm "bij_eq_rename";
paulson@13790
   611
val rename_image_constrains = thm "rename_image_constrains";
paulson@13790
   612
val rename_image_stable = thm "rename_image_stable";
paulson@13790
   613
val rename_image_increasing = thm "rename_image_increasing";
paulson@13790
   614
val rename_image_invariant = thm "rename_image_invariant";
paulson@13790
   615
val rename_image_Constrains = thm "rename_image_Constrains";
paulson@13790
   616
val rename_image_preserves = thm "rename_image_preserves";
paulson@13790
   617
val rename_image_Stable = thm "rename_image_Stable";
paulson@13790
   618
val rename_image_Increasing = thm "rename_image_Increasing";
paulson@13790
   619
val rename_image_Always = thm "rename_image_Always";
paulson@13790
   620
val rename_image_leadsTo = thm "rename_image_leadsTo";
paulson@13790
   621
val rename_image_LeadsTo = thm "rename_image_LeadsTo";
paulson@13790
   622
paulson@13790
   623
paulson@13786
   624
paulson@13786
   625
(*Lift_prog*)
paulson@13786
   626
val sub_def = thm "sub_def";
paulson@13786
   627
val lift_map_def = thm "lift_map_def";
paulson@13786
   628
val drop_map_def = thm "drop_map_def";
paulson@13786
   629
val insert_map_inverse = thm "insert_map_inverse";
paulson@13786
   630
val insert_map_delete_map_eq = thm "insert_map_delete_map_eq";
paulson@13786
   631
val insert_map_inject1 = thm "insert_map_inject1";
paulson@13786
   632
val insert_map_inject2 = thm "insert_map_inject2";
paulson@13786
   633
val insert_map_inject = thm "insert_map_inject";
paulson@13786
   634
val insert_map_inject = thm "insert_map_inject";
paulson@13786
   635
val lift_map_eq_iff = thm "lift_map_eq_iff";
paulson@13786
   636
val drop_map_lift_map_eq = thm "drop_map_lift_map_eq";
paulson@13786
   637
val inj_lift_map = thm "inj_lift_map";
paulson@13786
   638
val lift_map_drop_map_eq = thm "lift_map_drop_map_eq";
paulson@13786
   639
val drop_map_inject = thm "drop_map_inject";
paulson@13786
   640
val surj_lift_map = thm "surj_lift_map";
paulson@13786
   641
val bij_lift_map = thm "bij_lift_map";
paulson@13786
   642
val inv_lift_map_eq = thm "inv_lift_map_eq";
paulson@13786
   643
val inv_drop_map_eq = thm "inv_drop_map_eq";
paulson@13786
   644
val bij_drop_map = thm "bij_drop_map";
paulson@13786
   645
val sub_apply = thm "sub_apply";
paulson@13786
   646
val lift_set_empty = thm "lift_set_empty";
paulson@13786
   647
val lift_set_iff = thm "lift_set_iff";
paulson@13786
   648
val lift_set_iff2 = thm "lift_set_iff2";
paulson@13786
   649
val lift_set_mono = thm "lift_set_mono";
paulson@13786
   650
val lift_set_Un_distrib = thm "lift_set_Un_distrib";
paulson@13786
   651
val lift_set_Diff_distrib = thm "lift_set_Diff_distrib";
paulson@13786
   652
val bij_lift = thm "bij_lift";
paulson@13786
   653
val lift_SKIP = thm "lift_SKIP";
paulson@13786
   654
val lift_Join = thm "lift_Join";
paulson@13786
   655
val lift_JN = thm "lift_JN";
paulson@13786
   656
val lift_constrains = thm "lift_constrains";
paulson@13786
   657
val lift_stable = thm "lift_stable";
paulson@13786
   658
val lift_invariant = thm "lift_invariant";
paulson@13786
   659
val lift_Constrains = thm "lift_Constrains";
paulson@13786
   660
val lift_Stable = thm "lift_Stable";
paulson@13786
   661
val lift_Always = thm "lift_Always";
paulson@13786
   662
val lift_transient = thm "lift_transient";
paulson@13786
   663
val lift_ensures = thm "lift_ensures";
paulson@13786
   664
val lift_leadsTo = thm "lift_leadsTo";
paulson@13786
   665
val lift_LeadsTo = thm "lift_LeadsTo";
paulson@13786
   666
val lift_lift_guarantees_eq = thm "lift_lift_guarantees_eq";
paulson@13786
   667
val lift_guarantees_eq_lift_inv = thm "lift_guarantees_eq_lift_inv";
paulson@13786
   668
val lift_preserves_snd_I = thm "lift_preserves_snd_I";
paulson@13786
   669
val delete_map_eqE = thm "delete_map_eqE";
paulson@13786
   670
val delete_map_eqE = thm "delete_map_eqE";
paulson@13786
   671
val delete_map_neq_apply = thm "delete_map_neq_apply";
paulson@13786
   672
val vimage_o_fst_eq = thm "vimage_o_fst_eq";
paulson@13786
   673
val vimage_sub_eq_lift_set = thm "vimage_sub_eq_lift_set";
paulson@13786
   674
val mem_lift_act_iff = thm "mem_lift_act_iff";
paulson@13786
   675
val preserves_snd_lift_stable = thm "preserves_snd_lift_stable";
paulson@13786
   676
val constrains_imp_lift_constrains = thm "constrains_imp_lift_constrains";
paulson@13786
   677
val lift_map_image_Times = thm "lift_map_image_Times";
paulson@13786
   678
val lift_preserves_eq = thm "lift_preserves_eq";
paulson@13786
   679
val lift_preserves_sub = thm "lift_preserves_sub";
paulson@13786
   680
val o_equiv_assoc = thm "o_equiv_assoc";
paulson@13786
   681
val o_equiv_apply = thm "o_equiv_apply";
paulson@13786
   682
val fst_o_lift_map = thm "fst_o_lift_map";
paulson@13786
   683
val snd_o_lift_map = thm "snd_o_lift_map";
paulson@13786
   684
val extend_act_extend_act = thm "extend_act_extend_act";
paulson@13786
   685
val project_act_project_act = thm "project_act_project_act";
paulson@13786
   686
val project_act_extend_act = thm "project_act_extend_act";
paulson@13786
   687
val act_in_UNION_preserves_fst = thm "act_in_UNION_preserves_fst";
paulson@13786
   688
val UNION_OK_lift_I = thm "UNION_OK_lift_I";
paulson@13786
   689
val OK_lift_I = thm "OK_lift_I";
paulson@13786
   690
val Allowed_lift = thm "Allowed_lift";
paulson@13786
   691
val lift_image_preserves = thm "lift_image_preserves";
paulson@13786
   692
paulson@13786
   693
paulson@13786
   694
(*PPROD*)
paulson@13786
   695
val Init_PLam = thm "Init_PLam";
paulson@13786
   696
val PLam_empty = thm "PLam_empty";
paulson@13786
   697
val PLam_SKIP = thm "PLam_SKIP";
paulson@13786
   698
val PLam_insert = thm "PLam_insert";
paulson@13786
   699
val PLam_component_iff = thm "PLam_component_iff";
paulson@13786
   700
val component_PLam = thm "component_PLam";
paulson@13786
   701
val PLam_constrains = thm "PLam_constrains";
paulson@13786
   702
val PLam_stable = thm "PLam_stable";
paulson@13786
   703
val PLam_transient = thm "PLam_transient";
paulson@13786
   704
val PLam_ensures = thm "PLam_ensures";
paulson@13786
   705
val PLam_leadsTo_Basis = thm "PLam_leadsTo_Basis";
paulson@13786
   706
val invariant_imp_PLam_invariant = thm "invariant_imp_PLam_invariant";
paulson@13786
   707
val PLam_preserves_fst = thm "PLam_preserves_fst";
paulson@13786
   708
val PLam_preserves_snd = thm "PLam_preserves_snd";
paulson@13786
   709
val guarantees_PLam_I = thm "guarantees_PLam_I";
paulson@13786
   710
val Allowed_PLam = thm "Allowed_PLam";
paulson@13786
   711
val PLam_preserves = thm "PLam_preserves";
paulson@13786
   712
paulson@13796
   713
(*Follows*)
paulson@13796
   714
val mono_Always_o = thm "mono_Always_o";
paulson@13796
   715
val mono_LeadsTo_o = thm "mono_LeadsTo_o";
paulson@13796
   716
val Follows_constant = thm "Follows_constant";
paulson@13796
   717
val mono_Follows_o = thm "mono_Follows_o";
paulson@13796
   718
val mono_Follows_apply = thm "mono_Follows_apply";
paulson@13796
   719
val Follows_trans = thm "Follows_trans";
paulson@13796
   720
val Follows_Increasing1 = thm "Follows_Increasing1";
paulson@13796
   721
val Follows_Increasing2 = thm "Follows_Increasing2";
paulson@13796
   722
val Follows_Bounded = thm "Follows_Bounded";
paulson@13796
   723
val Follows_LeadsTo = thm "Follows_LeadsTo";
paulson@13796
   724
val Follows_LeadsTo_pfixLe = thm "Follows_LeadsTo_pfixLe";
paulson@13796
   725
val Follows_LeadsTo_pfixGe = thm "Follows_LeadsTo_pfixGe";
paulson@13796
   726
val Always_Follows1 = thm "Always_Follows1";
paulson@13796
   727
val Always_Follows2 = thm "Always_Follows2";
paulson@13796
   728
val increasing_Un = thm "increasing_Un";
paulson@13796
   729
val Increasing_Un = thm "Increasing_Un";
paulson@13796
   730
val Always_Un = thm "Always_Un";
paulson@13796
   731
val Follows_Un = thm "Follows_Un";
paulson@13796
   732
val increasing_union = thm "increasing_union";
paulson@13796
   733
val Increasing_union = thm "Increasing_union";
paulson@13796
   734
val Always_union = thm "Always_union";
paulson@13796
   735
val Follows_union = thm "Follows_union";
paulson@13796
   736
val Follows_setsum = thm "Follows_setsum";
paulson@13796
   737
val Increasing_imp_Stable_pfixGe = thm "Increasing_imp_Stable_pfixGe";
paulson@13796
   738
val LeadsTo_le_imp_pfixGe = thm "LeadsTo_le_imp_pfixGe";
paulson@13796
   739
paulson@13786
   740
paulson@13797
   741
(*Lazy unfolding of actions or of sets*)
paulson@13797
   742
fun simp_of_act def = def RS def_act_simp;
paulson@13797
   743
paulson@13797
   744
fun simp_of_set def = def RS def_set_simp;
paulson@13797
   745
paulson@13797
   746
paulson@13797
   747
(*Combines two invariance ASSUMPTIONS into one.  USEFUL??*)
paulson@13797
   748
val Always_Int_tac = dtac Always_Int_I THEN' assume_tac THEN' etac Always_thin
paulson@13797
   749
paulson@13797
   750
(*Combines a list of invariance THEOREMS into one.*)
paulson@13797
   751
val Always_Int_rule = foldr1 (fn (th1,th2) => [th1,th2] MRS Always_Int_I)
paulson@13797
   752
paulson@13812
   753
(*Proves "co" properties when the program is specified.  Any use of invariants
paulson@13812
   754
  (from weak constrains) must have been done already.*)
paulson@13786
   755
fun gen_constrains_tac(cs,ss) i = 
paulson@13786
   756
   SELECT_GOAL
paulson@13786
   757
      (EVERY [REPEAT (Always_Int_tac 1),
paulson@13812
   758
              (*reduce the fancy safety properties to "constrains"*)
paulson@13786
   759
	      REPEAT (etac Always_ConstrainsI 1
paulson@13786
   760
		      ORELSE
paulson@13786
   761
		      resolve_tac [StableI, stableI,
paulson@13786
   762
				   constrains_imp_Constrains] 1),
paulson@13812
   763
              (*for safety, the totalize operator can be ignored*)
paulson@13812
   764
	      simp_tac (HOL_ss addsimps
paulson@13812
   765
                         [mk_total_program_def, totalize_constrains_iff]) 1,
paulson@13786
   766
	      rtac constrainsI 1,
paulson@13786
   767
	      full_simp_tac ss 1,
paulson@13786
   768
	      REPEAT (FIRSTGOAL (etac disjE)),
paulson@13786
   769
	      ALLGOALS (clarify_tac cs),
paulson@13786
   770
	      ALLGOALS (asm_lr_simp_tac ss)]) i;
paulson@13786
   771
paulson@13786
   772
(*proves "ensures/leadsTo" properties when the program is specified*)
paulson@13786
   773
fun gen_ensures_tac(cs,ss) sact = 
paulson@13786
   774
    SELECT_GOAL
paulson@13786
   775
      (EVERY [REPEAT (Always_Int_tac 1),
paulson@13786
   776
	      etac Always_LeadsTo_Basis 1 
paulson@13786
   777
	          ORELSE   (*subgoal may involve LeadsTo, leadsTo or ensures*)
paulson@13786
   778
		  REPEAT (ares_tac [LeadsTo_Basis, leadsTo_Basis,
paulson@13786
   779
				    EnsuresI, ensuresI] 1),
paulson@13786
   780
	      (*now there are two subgoals: co & transient*)
paulson@13812
   781
	      simp_tac (ss addsimps [mk_total_program_def]) 2,
paulson@13812
   782
	      res_inst_tac [("act", sact)] totalize_transientI 2 
paulson@13812
   783
 	      ORELSE res_inst_tac [("act", sact)] transientI 2,
paulson@13786
   784
                 (*simplify the command's domain*)
paulson@13786
   785
	      simp_tac (ss addsimps [Domain_def]) 3,
paulson@13786
   786
	      gen_constrains_tac (cs,ss) 1,
paulson@13786
   787
	      ALLGOALS (clarify_tac cs),
paulson@13786
   788
	      ALLGOALS (asm_lr_simp_tac ss)]);
paulson@13786
   789
paulson@13797
   790
fun constrains_tac st = gen_constrains_tac (claset(), simpset()) st;
paulson@13797
   791
paulson@13796
   792
fun ensures_tac sact = gen_ensures_tac (claset(), simpset()) sact;
paulson@13796
   793
paulson@13786
   794
paulson@13786
   795
(*Composition equivalences, from Lift_prog*)
paulson@13786
   796
paulson@13786
   797
fun make_o_equivs th =
paulson@13786
   798
    [th,
paulson@13786
   799
     th RS o_equiv_assoc |> simplify (HOL_ss addsimps [o_assoc]),
paulson@13786
   800
     th RS o_equiv_apply |> simplify (HOL_ss addsimps [o_def, sub_def])];
paulson@13786
   801
paulson@13786
   802
Addsimps (make_o_equivs fst_o_funPair @ make_o_equivs snd_o_funPair);
paulson@13786
   803
paulson@13786
   804
Addsimps (make_o_equivs fst_o_lift_map @ make_o_equivs snd_o_lift_map);