theory Sepref_Misc
imports
  "../Refine_Monadic_Add"
  PO_Normalizer
  "List-Index.List_Index"
  "Refine_Imperative_HOL.Named_Theorems_Rev"
  "HOL-Eisbach.Eisbach"
begin

  hide_const (open) CONSTRAINT

  (* Additions for List_Index *)
  lemma index_of_last_distinct[simp]:
    "distinct l \<Longrightarrow> index l (last l) = length l - 1"
    apply (cases l rule: rev_cases)
    apply (auto simp: index_append)
    done

  lemma index_eqlen_conv[simp]: "index l x = length l \<longleftrightarrow> x\<notin>set l"
    by (auto simp: index_size_conv)

  subsection \<open>Iterated Curry and Uncurry\<close>

  text \<open>Uncurry0\<close>
  definition "uncurry0 c \<equiv> \<lambda>_::unit. c"
  definition curry0 :: "(unit \<Rightarrow> 'a) \<Rightarrow> 'a" where "curry0 f = f ()"
  lemma uncurry0_apply[simp]: "uncurry0 c x = c" by (simp add: uncurry0_def)

  lemma curry_uncurry0_id[simp]: "curry0 (uncurry0 f) = f" by (simp add: curry0_def)
  lemma uncurry_curry0_id[simp]: "uncurry0 (curry0 g) = g" by (auto simp: curry0_def)
  lemma param_uncurry0[param]: "(uncurry0,uncurry0) \<in> A \<rightarrow> (unit_rel\<rightarrow>A)" by auto

  text \<open>Abbreviations for higher-order uncurries\<close>
  abbreviation "uncurry2 f \<equiv> uncurry (uncurry f)"
  abbreviation "curry2 f \<equiv> curry (curry f)"
  abbreviation "uncurry3 f \<equiv> uncurry (uncurry2 f)"
  abbreviation "curry3 f \<equiv> curry (curry2 f)"
  abbreviation "uncurry4 f \<equiv> uncurry (uncurry3 f)"
  abbreviation "curry4 f \<equiv> curry (curry3 f)"
  abbreviation "uncurry5 f \<equiv> uncurry (uncurry4 f)"
  abbreviation "curry5 f \<equiv> curry (curry4 f)"
  abbreviation "uncurry6 f \<equiv> uncurry (uncurry5 f)"
  abbreviation "curry6 f \<equiv> curry (curry5 f)"
  abbreviation "uncurry7 f \<equiv> uncurry (uncurry6 f)"
  abbreviation "curry7 f \<equiv> curry (curry6 f)"
  abbreviation "uncurry8 f \<equiv> uncurry (uncurry7 f)"
  abbreviation "curry8 f \<equiv> curry (curry7 f)"
  abbreviation "uncurry9 f \<equiv> uncurry (uncurry8 f)"
  abbreviation "curry9 f \<equiv> curry (curry8 f)"

  lemma fold_partial_uncurry: "uncurry (\<lambda>(ps, cf). f ps cf) = uncurry2 f" by auto

  lemma curry_shl:
    "\<And>g f. (g \<equiv> curry f) \<equiv> (uncurry g \<equiv> f)"
    "\<And>g f. (g \<equiv> curry0 f) \<equiv> (uncurry0 g \<equiv> f)"
    by (atomize (full); auto)+

  lemma curry_shr:
    "\<And>f g. (curry f \<equiv> g) \<equiv> (f \<equiv> uncurry g)"
    "\<And>f g. (curry0 f \<equiv> g) \<equiv> (f \<equiv> uncurry0 g)"
    by (atomize (full); auto)+

  lemmas uncurry_shl = curry_shr[symmetric]
  lemmas uncurry_shr = curry_shl[symmetric]

end


theory flash103Bra  imports flash103Rev

  begin
lemma onInv103:

   assumes

     b1:"r \<in> rules N" and b2:"invf=inv103 "
   shows  "invHoldForRule' s invf r (invariants   N)"
   proof -
have c1:"ex1P N (% iRule1 .  r=NI_Local_GetX_PutX1 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_GetX  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Replace  iRule1 )\<or>ex0P N (  r=NI_ShWb N )\<or>ex0P N (  r=PI_Local_GetX_GetX2 )\<or>ex0P N (  r=NI_Local_PutXAcksDone )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX7 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak2  iRule1 )\<or>ex0P N (  r=NI_ReplaceHomeShrVld )\<or>ex1P N (% iRule1 .  r=NI_Remote_Put  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX5 N  iRule1 )\<or>ex0P N (  r=NI_Wb )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Get  iRule1 )\<or>ex0P N (  r=PI_Local_Replace )\<or>ex1P N (% iRule1 .  r=NI_ReplaceShrVld  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Local_GetX_PutX8 N  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_InvAck_2 N  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_Get_Nak2  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=PI_Remote_Replace  iRule1 )\<or>ex0P N (  r=NI_Nak_Home )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put2  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_InvAck_1  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX11 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX6 N  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_Get_Put2  iRule1  iRule2 )\<or>ex0P N (  r=PI_Local_Get_Put )\<or>ex0P N (  r=PI_Local_GetX_PutX1 N )\<or>ex1P N (% iRule1 .  r=NI_InvAck_1_Home  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_Get_Nak1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak2  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX10_home N  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_Get  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak3  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Local_GetX_PutX10 N  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX2 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_Get_Put1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_PutX  iRule1 )\<or>ex1P N (% iRule1 .  r=Store  iRule1 )\<or>ex0P N (  r=NI_FAck )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX3 N  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX3 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_GetX_PutX  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX8_home N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put1 N  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_GetX1 )\<or>ex0P N (  r=StoreHome )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_GetX_Nak  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Inv  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_PutX  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX4 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX4 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Nak  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX2 N )\<or>ex0P N (  r=NI_Local_Put )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak1  iRule1 )\<or>ex0P N (  r=NI_Nak_Clear )\<or>ex0P N (  r=PI_Local_PutX )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak3  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_GetX_Nak_Home  iRule1 )\<or>ex0P N (  r=PI_Local_Get_Get )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX9 N  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_GetX  iRule1 )\<or>ex0P N (  r=NI_ReplaceHome )\<or>ex1P N (% iRule1 .  r=NI_Remote_GetX_PutX_Home  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put3  iRule1 )"

        apply(cut_tac  b1)
        apply auto
        done      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX1 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX1 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX1 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_GetX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_GetX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_GetX  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_GetXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Replace  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Replace  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Replace  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_ReplaceVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ShWb N )
"

         from c1 have c2:" r= NI_ShWb N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_ShWb N ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_ShWbVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_GetX2 )
"

         from c1 have c2:" r= PI_Local_GetX_GetX2 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_GetX2 ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_GetX2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= NI_Local_PutXAcksDone )
"

         from c1 have c2:" r= NI_Local_PutXAcksDone "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_PutXAcksDone ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_Local_PutXAcksDoneVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX7 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX7 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX7 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX7VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Nak2  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Nak2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ReplaceHomeShrVld )
"

         from c1 have c2:" r= NI_ReplaceHomeShrVld "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_ReplaceHomeShrVld ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_ReplaceHomeShrVldVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Put  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Put  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_Put  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_PutVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX5 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX5 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX5 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX5VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Wb )
"

         from c1 have c2:" r= NI_Wb "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_Wb ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_WbVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Get  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Get  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Get  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_GetVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Replace )
"

         from c1 have c2:" r= PI_Local_Replace "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_Replace ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_ReplaceVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_ReplaceShrVld  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_ReplaceShrVld  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_ReplaceShrVld  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_ReplaceShrVldVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Local_GetX_PutX8 N  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Local_GetX_PutX8 N  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX8 N  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX8VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_InvAck_2 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_InvAck_2 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_InvAck_2 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_InvAck_2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_Get_Nak2  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_Get_Nak2  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_Get_Nak2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_Replace  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_Replace  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (PI_Remote_Replace  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis PI_Remote_ReplaceVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Nak_Home )
"

         from c1 have c2:" r= NI_Nak_Home "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_Nak_Home ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_Nak_HomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Put2  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Put2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_InvAck_1  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_InvAck_1  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_InvAck_1  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_InvAck_1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX11 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX11 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX11 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX11VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX6 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX6 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX6 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX6VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_Get_Put2  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_Get_Put2  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_Get_Put2  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_Get_Put2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Get_Put )
"

         from c1 have c2:" r= PI_Local_Get_Put "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_Get_Put ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_Get_PutVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX1 N )
"

         from c1 have c2:" r= PI_Local_GetX_PutX1 N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_PutX1 N ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_PutX1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_InvAck_1_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_InvAck_1_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_InvAck_1_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_InvAck_1_HomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Get_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Get_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_Get_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_Get_Nak1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Nak1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_Nak2  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_Nak2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX10_home N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX10_home N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX10_home N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX10_homeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_Get  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_Get  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (PI_Remote_Get  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis PI_Remote_GetVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_Nak3  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_Nak3VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Local_GetX_PutX10 N  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Local_GetX_PutX10 N  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX10 N  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX10VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX2 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX2 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX2 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Get_Put1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Get_Put1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_Get_Put1  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_Get_Put1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_PutX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_PutX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_PutX  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_PutXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= Store  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= Store  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (Store  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis StoreVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_FAck )
"

         from c1 have c2:" r= NI_FAck "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_FAck ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_FAckVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX3 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX3 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX3 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX3VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX3 )
"

         from c1 have c2:" r= PI_Local_GetX_PutX3 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_PutX3 ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_PutX3VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_GetX_PutX  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_GetX_PutX  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_GetX_PutX  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_GetX_PutXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX8_home N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX8_home N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX8_home N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX8_homeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put1 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put1 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Put1 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Put1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_GetX1 )
"

         from c1 have c2:" r= PI_Local_GetX_GetX1 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_GetX1 ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_GetX1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= StoreHome )
"

         from c1 have c2:" r= StoreHome "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (StoreHome ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis StoreHomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_GetX_Nak  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_GetX_Nak  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_GetX_NakVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Inv  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Inv  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Inv  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_InvVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_PutX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_PutX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (PI_Remote_PutX  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis PI_Remote_PutXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX4 )
"

         from c1 have c2:" r= PI_Local_GetX_PutX4 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_PutX4 ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_PutX4VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX4 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX4 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX4 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX4VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Nak  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Nak  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Nak  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_NakVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX2 N )
"

         from c1 have c2:" r= PI_Local_GetX_PutX2 N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_GetX_PutX2 N ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_GetX_PutX2VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= NI_Local_Put )
"

         from c1 have c2:" r= NI_Local_Put "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Put ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_Local_PutVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_Nak1VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Nak_Clear )
"

         from c1 have c2:" r= NI_Nak_Clear "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_Nak_Clear ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_Nak_ClearVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_PutX )
"

         from c1 have c2:" r= PI_Local_PutX "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_PutX ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_PutXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Nak3  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Nak3VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_GetX_Nak_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_GetX_Nak_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_GetX_Nak_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_GetX_Nak_HomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Get_Get )
"

         from c1 have c2:" r= PI_Local_Get_Get "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (PI_Local_Get_Get ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis PI_Local_Get_GetVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX9 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX9 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_GetX_PutX9 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_GetX_PutX9VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_GetX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_GetX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (PI_Remote_GetX  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis PI_Remote_GetXVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ReplaceHome )
"

         from c1 have c2:" r= NI_ReplaceHome "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv103 ) (NI_ReplaceHome ) (invariants N) "
            apply(cut_tac    b2 c2 )
            by (metis NI_ReplaceHomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_GetX_PutX_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_GetX_PutX_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Remote_GetX_PutX_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Remote_GetX_PutX_HomeVsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv103 ) (NI_Local_Get_Put3  iRule1 ) (invariants N) "
            apply(cut_tac  c2  )
            by (metis NI_Local_Get_Put3VsInv103 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }ultimately show "invHoldForRule' s invf r (invariants N) "
          by blast
     qed
end


theory flash6Bra  imports flash6Rev

  begin
lemma onInv6:

   assumes  a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  " and

     b1:"r \<in> rules N" and b2:"invf=inv6  iInv1  iInv2 "
   shows  "invHoldForRule' s invf r (invariants   N)"
   proof -
have c1:"ex1P N (% iRule1 .  r=NI_Local_GetX_PutX1 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_GetX  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Replace  iRule1 )\<or>ex0P N (  r=NI_ShWb N )\<or>ex0P N (  r=PI_Local_GetX_GetX2 )\<or>ex0P N (  r=NI_Local_PutXAcksDone )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX7 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak2  iRule1 )\<or>ex0P N (  r=NI_ReplaceHomeShrVld )\<or>ex1P N (% iRule1 .  r=NI_Remote_Put  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX5 N  iRule1 )\<or>ex0P N (  r=NI_Wb )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Get  iRule1 )\<or>ex0P N (  r=PI_Local_Replace )\<or>ex1P N (% iRule1 .  r=NI_ReplaceShrVld  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Local_GetX_PutX8 N  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_InvAck_2 N  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_Get_Nak2  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=PI_Remote_Replace  iRule1 )\<or>ex0P N (  r=NI_Nak_Home )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put2  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_InvAck_1  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX11 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX6 N  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_Get_Put2  iRule1  iRule2 )\<or>ex0P N (  r=PI_Local_Get_Put )\<or>ex0P N (  r=PI_Local_GetX_PutX1 N )\<or>ex1P N (% iRule1 .  r=NI_InvAck_1_Home  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_Get_Nak1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak2  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX10_home N  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_Get  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak3  iRule1 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Local_GetX_PutX10 N  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX2 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_Get_Put1  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_PutX  iRule1 )\<or>ex1P N (% iRule1 .  r=Store  iRule1 )\<or>ex0P N (  r=NI_FAck )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX3 N  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX3 )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_GetX_PutX  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX8_home N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put1 N  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_GetX1 )\<or>ex0P N (  r=StoreHome )\<or>ex2P N (% iRule1  iRule2 .  r=NI_Remote_GetX_Nak  iRule1  iRule2 )\<or>ex1P N (% iRule1 .  r=NI_Inv  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_PutX  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX4 )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX4 N  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Nak  iRule1 )\<or>ex0P N (  r=PI_Local_GetX_PutX2 N )\<or>ex0P N (  r=NI_Local_Put )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_Nak1  iRule1 )\<or>ex0P N (  r=NI_Nak_Clear )\<or>ex0P N (  r=PI_Local_PutX )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Nak3  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Remote_GetX_Nak_Home  iRule1 )\<or>ex0P N (  r=PI_Local_Get_Get )\<or>ex1P N (% iRule1 .  r=NI_Local_GetX_PutX9 N  iRule1 )\<or>ex1P N (% iRule1 .  r=PI_Remote_GetX  iRule1 )\<or>ex0P N (  r=NI_ReplaceHome )\<or>ex1P N (% iRule1 .  r=NI_Remote_GetX_PutX_Home  iRule1 )\<or>ex1P N (% iRule1 .  r=NI_Local_Get_Put3  iRule1 )"

        apply(cut_tac  b1)
        apply auto
        done      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX1 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX1 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX1 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_GetX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_GetX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_GetX  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_GetXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Replace  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Replace  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Replace  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_ReplaceVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ShWb N )
"

         from c1 have c2:" r= NI_ShWb N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_ShWb N ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_ShWbVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_GetX2 )
"

         from c1 have c2:" r= PI_Local_GetX_GetX2 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_GetX2 ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_GetX2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= NI_Local_PutXAcksDone )
"

         from c1 have c2:" r= NI_Local_PutXAcksDone "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_PutXAcksDone ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_Local_PutXAcksDoneVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX7 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX7 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX7 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX7VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Nak2  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Nak2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ReplaceHomeShrVld )
"

         from c1 have c2:" r= NI_ReplaceHomeShrVld "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_ReplaceHomeShrVld ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_ReplaceHomeShrVldVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Put  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Put  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_Put  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_PutVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX5 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX5 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX5 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX5VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Wb )
"

         from c1 have c2:" r= NI_Wb "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Wb ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_WbVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Get  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Get  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Get  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_GetVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Replace )
"

         from c1 have c2:" r= PI_Local_Replace "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_Replace ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_ReplaceVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_ReplaceShrVld  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_ReplaceShrVld  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_ReplaceShrVld  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_ReplaceShrVldVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Local_GetX_PutX8 N  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Local_GetX_PutX8 N  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX8 N  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX8VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_InvAck_2 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_InvAck_2 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_InvAck_2 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_InvAck_2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_Get_Nak2  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_Get_Nak2  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_Get_Nak2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_Replace  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_Replace  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Remote_Replace  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis PI_Remote_ReplaceVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Nak_Home )
"

         from c1 have c2:" r= NI_Nak_Home "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Nak_Home ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_Nak_HomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Put2  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Put2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_InvAck_1  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_InvAck_1  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_InvAck_1  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_InvAck_1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX11 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX11 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX11 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX11VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX6 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX6 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX6 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX6VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_Get_Put2  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_Get_Put2  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_Get_Put2  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_Get_Put2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Get_Put )
"

         from c1 have c2:" r= PI_Local_Get_Put "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_Get_Put ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_Get_PutVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX1 N )
"

         from c1 have c2:" r= PI_Local_GetX_PutX1 N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_PutX1 N ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_PutX1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_InvAck_1_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_InvAck_1_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_InvAck_1_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_InvAck_1_HomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Get_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Get_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_Get_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_Get_Nak1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Nak1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak2  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak2  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_Nak2  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_Nak2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX10_home N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX10_home N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX10_home N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX10_homeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_Get  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_Get  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Remote_Get  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis PI_Remote_GetVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_Nak3  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_Nak3VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Local_GetX_PutX10 N  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Local_GetX_PutX10 N  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX10 N  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX10VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX2 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX2 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX2 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_Get_Put1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_Get_Put1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_Get_Put1  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_Get_Put1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_PutX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_PutX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_PutX  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_PutXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= Store  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= Store  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (Store  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis StoreVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_FAck )
"

         from c1 have c2:" r= NI_FAck "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_FAck ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_FAckVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX3 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX3 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX3 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX3VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX3 )
"

         from c1 have c2:" r= PI_Local_GetX_PutX3 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_PutX3 ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_PutX3VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_GetX_PutX  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_GetX_PutX  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_GetX_PutX  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_GetX_PutXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX8_home N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX8_home N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX8_home N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX8_homeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put1 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put1 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Put1 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Put1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_GetX1 )
"

         from c1 have c2:" r= PI_Local_GetX_GetX1 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_GetX1 ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_GetX1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= StoreHome )
"

         from c1 have c2:" r= StoreHome "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (StoreHome ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis StoreHomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex2P N (% iRule1  iRule2 .  r= NI_Remote_GetX_Nak  iRule1  iRule2 )
"

         from c1 obtain  iRule1  iRule2  where c2:"  iRule1~=iRule2    \<and>   iRule1 \<le> N \<and>   iRule2 \<le> N \<and>  r= NI_Remote_GetX_Nak  iRule1  iRule2 "
         by (auto simp add: ex2P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_GetX_NakVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Inv  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Inv  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Inv  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_InvVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_PutX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_PutX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Remote_PutX  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis PI_Remote_PutXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX4 )
"

         from c1 have c2:" r= PI_Local_GetX_PutX4 "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_PutX4 ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_PutX4VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX4 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX4 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX4 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX4VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Nak  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Nak  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Nak  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_NakVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_GetX_PutX2 N )
"

         from c1 have c2:" r= PI_Local_GetX_PutX2 N "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_GetX_PutX2 N ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_GetX_PutX2VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= NI_Local_Put )
"

         from c1 have c2:" r= NI_Local_Put "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Put ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_Local_PutVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_Nak1  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_Nak1  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_Nak1  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_Nak1VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_Nak_Clear )
"

         from c1 have c2:" r= NI_Nak_Clear "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Nak_Clear ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_Nak_ClearVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex0P N (  r= PI_Local_PutX )
"

         from c1 have c2:" r= PI_Local_PutX "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_PutX ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_PutXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Nak3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Nak3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Nak3  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Nak3VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_GetX_Nak_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_GetX_Nak_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_GetX_Nak_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_GetX_Nak_HomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= PI_Local_Get_Get )
"

         from c1 have c2:" r= PI_Local_Get_Get "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Local_Get_Get ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis PI_Local_Get_GetVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_GetX_PutX9 N  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_GetX_PutX9 N  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_GetX_PutX9 N  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_GetX_PutX9VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= PI_Remote_GetX  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= PI_Remote_GetX  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (PI_Remote_GetX  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis PI_Remote_GetXVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex0P N (  r= NI_ReplaceHome )
"

         from c1 have c2:" r= NI_ReplaceHome "
         by (auto simp add: ex0P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_ReplaceHome ) (invariants N) "
            apply(cut_tac   a1  a2  a3   b2 c2 )
            by (metis NI_ReplaceHomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
	}      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Remote_GetX_PutX_Home  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Remote_GetX_PutX_Home  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Remote_GetX_PutX_Home  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Remote_GetX_PutX_HomeVsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }      moreover
        {assume c1: "ex1P N (% iRule1 .  r= NI_Local_Get_Put3  iRule1 )
"

         from c1 obtain  iRule1  where c2:"  iRule1 \<le> N \<and>  r= NI_Local_Get_Put3  iRule1 "
         by (auto simp add: ex1P_def)

         have "invHoldForRule' s (inv6  iInv1  iInv2 ) (NI_Local_Get_Put3  iRule1 ) (invariants N) "
            apply(cut_tac  c2   a1  a2  a3 )
            by (metis NI_Local_Get_Put3VsInv6 )
          then have "invHoldForRule' s invf r (invariants N) "
            by(cut_tac c2 b2, metis)
        }ultimately show "invHoldForRule' s invf r (invariants N) "
          by blast
     qed
end