Nominal/Ex/Classical.thy
changeset 3183 313e6f2cdd89
parent 2975 c62e26830420
child 3192 14c7d7e29c44
equal deleted inserted replaced
3182:5335c0ea743a 3183:313e6f2cdd89
    81   apply(rule conjI)
    81   apply(rule conjI)
    82   apply(elim conjE)
    82   apply(elim conjE)
    83   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
    83   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
    84   apply(simp add: Abs_fresh_iff)
    84   apply(simp add: Abs_fresh_iff)
    85   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
    85   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
    86   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
    86   apply(simp add: eqvt_at_def)
    87   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
    87   apply(simp add: atom_eqvt fresh_star_Pair perm_supp_eq)
       
    88   apply(clarify)
       
    89   apply(simp add: eqvt_at_def)
       
    90   apply(simp add: atom_eqvt fresh_star_Pair perm_supp_eq)
    88   apply(elim conjE)
    91   apply(elim conjE)
    89   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
    92   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
    90   apply(simp add: Abs_fresh_iff)
    93   apply(simp add: Abs_fresh_iff)
    91   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
    94   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
    92   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
    95   apply(simp add: eqvt_at_def)
    93   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
    96   apply(simp add: atom_eqvt fresh_star_Pair perm_supp_eq)
    94   apply(elim conjE)
    97   apply(simp add: eqvt_at_def)
    95   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
    98   apply(simp add: atom_eqvt fresh_star_Pair perm_supp_eq)
    96   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
    99   apply(elim conjE)
    97   apply(erule Abs_lst1_fcb2)
   100   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
    98   apply(simp add: Abs_fresh_iff)
   101   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
    99   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   102   apply(erule Abs_lst1_fcb2)
   100   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   103   apply(simp add: Abs_fresh_iff)
       
   104   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   105   apply(simp add: eqvt_at_def)
       
   106   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   107   apply(simp add: eqvt_at_def)
   101   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   108   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   102   apply(blast)
   109   apply(blast)
   103   apply(blast)
   110   apply(blast)
   104   apply(elim conjE)
   111   apply(elim conjE)
   105   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   112   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   106   apply(simp add: Abs_fresh_iff)
   113   apply(simp add: Abs_fresh_iff)
   107   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   114   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   108   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   115   apply(simp add: eqvt_at_def)
   109   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   116   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   110   apply(rule conjI)
   117   apply(simp add: eqvt_at_def)
   111   apply(elim conjE)
   118   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   112   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   119   apply(rule conjI)
   113   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   120   apply(elim conjE)
   114   apply(erule Abs_lst1_fcb2)
   121   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   115   apply(simp add: Abs_fresh_iff)
   122   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   116   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   123   apply(erule Abs_lst1_fcb2)
   117   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   124   apply(simp add: Abs_fresh_iff)
       
   125   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   126   apply(simp add: eqvt_at_def)
       
   127   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   128   apply(simp add: eqvt_at_def)
   118   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   129   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   119   apply(blast)
   130   apply(blast)
   120   apply(blast)
   131   apply(blast)
   121   apply(erule conjE)+
   132   apply(erule conjE)+
   122   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   133   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   123   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   134   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   124   apply(erule Abs_lst1_fcb2)
   135   apply(erule Abs_lst1_fcb2)
   125   apply(simp add: Abs_fresh_iff)
   136   apply(simp add: Abs_fresh_iff)
   126   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   137   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   127   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   138   apply(simp add: eqvt_at_def)
       
   139   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   140   apply(simp add: eqvt_at_def)
   128   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   141   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   129   apply(blast)
   142   apply(blast)
   130   apply(blast)
   143   apply(blast)
   131   apply(elim conjE)
   144   apply(elim conjE)
   132   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   145   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   133   apply(simp add: Abs_fresh_iff)
   146   apply(simp add: Abs_fresh_iff)
   134   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   147   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   135   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   148   apply(simp add: eqvt_at_def)
       
   149   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   150   apply(simp add: eqvt_at_def)
   136   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   151   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   137   apply(elim conjE)
   152   apply(elim conjE)
   138   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   153   apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2)
   139   apply(simp add: Abs_fresh_iff)
   154   apply(simp add: Abs_fresh_iff)
   140   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   155   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   141   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   156   apply(simp add: eqvt_at_def)
   142   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   157   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   143   apply(elim conjE)
   158   apply(simp add: eqvt_at_def)
   144   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   159   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   145   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   160   apply(elim conjE)
   146   apply(erule Abs_lst1_fcb2)
   161   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   147   apply(simp add: Abs_fresh_iff)
   162   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   148   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   163   apply(erule Abs_lst1_fcb2)
   149   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   164   apply(simp add: Abs_fresh_iff)
   150   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   165   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   151   apply(blast)
   166   apply(simp add: eqvt_at_def)
   152   apply(blast)
   167   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   153   apply(erule conjE)+
   168   apply(simp add: eqvt_at_def)
   154   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   169   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   155   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   170   apply(blast)
   156   apply(erule Abs_lst1_fcb2)
   171   apply(blast)
   157   apply(simp add: Abs_fresh_iff)
   172   apply(erule conjE)+
   158   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   173   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   159   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   174   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   160   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   175   apply(erule Abs_lst1_fcb2)
   161   apply(blast)
   176   apply(simp add: Abs_fresh_iff)
   162   apply(blast)
   177   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   163   apply(rule conjI)
   178   apply(simp add: eqvt_at_def)
   164   apply(erule conjE)+
   179   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   165   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   180   apply(simp add: eqvt_at_def)
   166   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   181   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   167   apply(erule Abs_lst1_fcb2)
   182   apply(blast)
   168   apply(simp add: Abs_fresh_iff)
   183   apply(blast)
   169   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   184   apply(rule conjI)
   170   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   185   apply(erule conjE)+
       
   186   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
       
   187   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
       
   188   apply(erule Abs_lst1_fcb2)
       
   189   apply(simp add: Abs_fresh_iff)
       
   190   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   191   apply(simp add: eqvt_at_def)
       
   192   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   193   apply(simp add: eqvt_at_def)
   171   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   194   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   172   apply(blast)
   195   apply(blast)
   173   apply(blast)
   196   apply(blast)
   174   apply(erule conjE)+
   197   apply(erule conjE)+
   175   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   198   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   176   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   199   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   177   apply(erule Abs_lst1_fcb2)
   200   apply(erule Abs_lst1_fcb2)
   178   apply(simp add: Abs_fresh_iff)
   201   apply(simp add: Abs_fresh_iff)
   179   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   202   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   180   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   203   apply(simp add: eqvt_at_def)
       
   204   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   205   apply(simp add: eqvt_at_def)
   181   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   206   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   182   apply(blast)
   207   apply(blast)
   183   apply(blast)
   208   apply(blast)
   184   defer
   209   defer
   185   apply(erule conjE)+
   210   apply(erule conjE)+
   187   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   212   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   188   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   213   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   189   apply(erule Abs_lst1_fcb2)
   214   apply(erule Abs_lst1_fcb2)
   190   apply(simp add: Abs_fresh_iff)
   215   apply(simp add: Abs_fresh_iff)
   191   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   216   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   192   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   217   apply(simp add: eqvt_at_def)
       
   218   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   219   apply(simp add: eqvt_at_def)
   193   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   220   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   194   apply(blast)
   221   apply(blast)
   195   apply(blast)  
   222   apply(blast)  
   196   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   223   apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)")
   197   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   224   apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)")
   198   apply(erule Abs_lst1_fcb2)
   225   apply(erule Abs_lst1_fcb2)
   199   apply(simp add: Abs_fresh_iff)
   226   apply(simp add: Abs_fresh_iff)
   200   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   227   apply(simp add: eqvt_at_def)
   201   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   228   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   229   apply(simp add: eqvt_at_def)
       
   230   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   231   apply(simp add: eqvt_at_def)
   202   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   232   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   203   apply(blast)
   233   apply(blast)
   204   apply(blast)
   234   apply(blast)
   205   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   235   apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)")
   206   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   236   apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)")
   208   apply(erule Abs_lst_fcb2)
   238   apply(erule Abs_lst_fcb2)
   209   apply(simp add: Abs_fresh_star)
   239   apply(simp add: Abs_fresh_star)
   210   apply(simp add: Abs_fresh_star)
   240   apply(simp add: Abs_fresh_star)
   211   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   241   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   212   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   242   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   213   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   243   apply(simp add: eqvt_at_def)
       
   244   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   245   apply(simp add: eqvt_at_def)
   214   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   246   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   215   apply(blast)
   247   apply(blast)
   216   apply(blast)
   248   apply(blast)
   217   done
   249   done
   218 
   250 
   252   apply(rule conjI)
   284   apply(rule conjI)
   253   apply(elim conjE)
   285   apply(elim conjE)
   254   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   286   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   255   apply(simp add: Abs_fresh_iff)
   287   apply(simp add: Abs_fresh_iff)
   256   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   288   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   257   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   289   apply(simp add: eqvt_at_def)
       
   290   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   291   apply(simp add: eqvt_at_def)
   258   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   292   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   259   apply(elim conjE)
   293   apply(elim conjE)
   260   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   294   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   261   apply(simp add: Abs_fresh_iff)
   295   apply(simp add: Abs_fresh_iff)
   262   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   296   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   263   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   297   apply(simp add: eqvt_at_def)
       
   298   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   299   apply(simp add: eqvt_at_def)
   264   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   300   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   265   apply(elim conjE)
   301   apply(elim conjE)
   266   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   302   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   267   apply(simp add: Abs_fresh_iff)
   303   apply(simp add: Abs_fresh_iff)
   268   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   304   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   269   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   305   apply(simp add: eqvt_at_def)
   270   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   306   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   271   apply(elim conjE)
   307   apply(simp add: eqvt_at_def)
   272   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   308   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   273   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   309   apply(elim conjE)
   274   apply(erule Abs_lst1_fcb2)
   310   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   275   apply(simp add: Abs_fresh_iff)
   311   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   276   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   312   apply(erule Abs_lst1_fcb2)
   277   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   313   apply(simp add: Abs_fresh_iff)
   278   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   314   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   279   apply(blast)
   315   apply(simp add: eqvt_at_def)
   280   apply(blast)
   316   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   281   apply(elim conjE)
   317   apply(simp add: eqvt_at_def)
   282   apply(rule conjI)
   318   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   283   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   319   apply(blast)
   284   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   320   apply(blast)
   285   apply(erule Abs_lst1_fcb2)
   321   apply(elim conjE)
   286   apply(simp add: Abs_fresh_iff)
   322   apply(rule conjI)
   287   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   323   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   288   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   324   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
       
   325   apply(erule Abs_lst1_fcb2)
       
   326   apply(simp add: Abs_fresh_iff)
       
   327   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   328   apply(simp add: eqvt_at_def)
       
   329   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   330   apply(simp add: eqvt_at_def)
   289   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   331   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   290   apply(blast)
   332   apply(blast)
   291   apply(blast)
   333   apply(blast)
   292   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   334   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   293   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   335   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   294   apply(erule Abs_lst1_fcb2)
   336   apply(erule Abs_lst1_fcb2)
   295   apply(simp add: Abs_fresh_iff)
   337   apply(simp add: Abs_fresh_iff)
   296   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   338   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   297   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   339   apply(simp add: eqvt_at_def)
   298   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   340   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   299   apply(blast)
   341   apply(simp add: eqvt_at_def)
   300   apply(blast)
   342   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   301   apply(elim conjE)
   343   apply(blast)
   302   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   344   apply(blast)
   303   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   345   apply(elim conjE)
   304   apply(erule Abs_lst1_fcb2)
   346   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   305   apply(simp add: Abs_fresh_iff)
   347   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   306   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   348   apply(erule Abs_lst1_fcb2)
   307   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   349   apply(simp add: Abs_fresh_iff)
       
   350   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   351   apply(simp add: eqvt_at_def)
       
   352   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   353   apply(simp add: eqvt_at_def)
   308   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   354   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   309   apply(blast)
   355   apply(blast)
   310   apply(blast)
   356   apply(blast)
   311   apply(elim conjE)+
   357   apply(elim conjE)+
   312   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   358   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   313   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   359   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   314   apply(erule Abs_lst1_fcb2)
   360   apply(erule Abs_lst1_fcb2)
   315   apply(simp add: Abs_fresh_iff)
   361   apply(simp add: Abs_fresh_iff)
   316   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   362   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   317   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   363   apply(simp add: eqvt_at_def)
       
   364   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   365   apply(simp add: eqvt_at_def)
   318   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   366   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   319   apply(blast)
   367   apply(blast)
   320   apply(blast)
   368   apply(blast)
   321   apply(elim conjE)+
   369   apply(elim conjE)+
   322   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   370   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   323   apply(simp add: Abs_fresh_iff)
   371   apply(simp add: Abs_fresh_iff)
   324   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   372   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   325   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   373   apply(simp add: eqvt_at_def)
       
   374   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   375   apply(simp add: eqvt_at_def)
   326   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   376   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   327   apply(elim conjE)
   377   apply(elim conjE)
   328   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   378   apply(erule_tac c="(ua,va)" in Abs_lst1_fcb2)
   329   apply(simp add: Abs_fresh_iff)
   379   apply(simp add: Abs_fresh_iff)
   330   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   380   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   331   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   381   apply(simp add: eqvt_at_def)
   332   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   382   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   333   apply(elim conjE)
   383   apply(simp add: eqvt_at_def)
   334   apply(rule conjI)
   384   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   335   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   385   apply(elim conjE)
   336   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   386   apply(rule conjI)
   337   apply(erule Abs_lst1_fcb2)
   387   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   338   apply(simp add: Abs_fresh_iff)
   388   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   339   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   389   apply(erule Abs_lst1_fcb2)
   340   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   390   apply(simp add: Abs_fresh_iff)
       
   391   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   392   apply(simp add: eqvt_at_def)
       
   393   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   394   apply(simp add: eqvt_at_def)
   341   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   395   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   342   apply(blast)
   396   apply(blast)
   343   apply(blast)
   397   apply(blast)
   344   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   398   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   345   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   399   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   346   apply(erule Abs_lst1_fcb2)
   400   apply(erule Abs_lst1_fcb2)
   347   apply(simp add: Abs_fresh_iff)
   401   apply(simp add: Abs_fresh_iff)
   348   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   402   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   349   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   403   apply(simp add: eqvt_at_def)
       
   404   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   405   apply(simp add: eqvt_at_def)
   350   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   406   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   351   apply(blast)
   407   apply(blast)
   352   apply(blast)
   408   apply(blast)
   353   apply(erule conjE)+
   409   apply(erule conjE)+
   354   apply(erule Abs_lst_fcb2)
   410   apply(erule Abs_lst_fcb2)
   355   apply(simp add: Abs_fresh_star)
   411   apply(simp add: Abs_fresh_star)
   356   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   412   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   357   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   413   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   358   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   414   apply(simp add: eqvt_at_def)
   359   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   415   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   360   apply(erule conjE)+
   416   apply(simp add: eqvt_at_def)
   361   apply(rule conjI)
   417   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   362   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   418   apply(erule conjE)+
   363   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   419   apply(rule conjI)
   364   apply(erule Abs_lst1_fcb2)
   420   apply(subgoal_tac "eqvt_at nrename_sumC (M, ua, va)")
   365   apply(simp add: Abs_fresh_iff)
   421   apply(subgoal_tac "eqvt_at nrename_sumC (Ma, ua, va)")
   366   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   422   apply(erule Abs_lst1_fcb2)
   367   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   423   apply(simp add: Abs_fresh_iff)
       
   424   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
       
   425   apply(simp add: eqvt_at_def)
       
   426   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   427   apply(simp add: eqvt_at_def)
   368   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   428   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   369   apply(blast)
   429   apply(blast)
   370   apply(blast)
   430   apply(blast)
   371   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   431   apply(subgoal_tac "eqvt_at nrename_sumC (N, ua, va)")
   372   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   432   apply(subgoal_tac "eqvt_at nrename_sumC (Na, ua, va)")
   373   apply(erule Abs_lst1_fcb2)
   433   apply(erule Abs_lst1_fcb2)
   374   apply(simp add: Abs_fresh_iff)
   434   apply(simp add: Abs_fresh_iff)
   375   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   435   apply(simp add: fresh_at_base fresh_star_def fresh_Pair)
   376   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   436   apply(simp add: eqvt_at_def)
       
   437   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
       
   438   apply(simp add: eqvt_at_def)
   377   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   439   apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq)
   378   apply(blast)
   440   apply(blast)
   379   apply(blast)
   441   apply(blast)
   380   done
   442   done
   381 
   443