theory flash19Rev imports flashPub
begin
section{*Main defintions*}
lemma NI_FAckVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_FAck ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_InvVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Inv  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_InvAck_1VsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_InvAck_1  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3 a4 a5 a6,auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_InvAck_1_HomeVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_InvAck_1_Home  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_InvAck_2VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_InvAck_2 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_Local_GetX_GetXVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_GetX  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( eqn ( IVar ( Global ''NakcMsg_Cmd'') )  ( Const NAKC_Nakc ))    ( eqn ( IVar ( Global ''Dir_Pending'') )  ( Const false ))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_Nak1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_Nak1  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_Nak2VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_Nak2  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_Nak3VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_Nak3  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX1 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX2VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX2 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX3VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX3 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX4VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX4 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX5VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX5 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX6VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX6 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX7VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX7 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX8VsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX8 N  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P1 s \<or> ?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX8_homeVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX8_home N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX9VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX9 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX10VsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX10 N  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P1 s \<or> ?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX10_homeVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX10_home N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_GetX_PutX11VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_GetX_PutX11 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_GetVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Get  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_Get ))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Nak1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Nak1  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Nak2VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Nak2  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Nak3VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Nak3  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Put1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Put1 N  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Put2VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Put2  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_Get_Put3VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Get_Put3  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Local_PutVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_Put ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_Local_PutXAcksDoneVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Local_PutXAcksDone ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_NakVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Nak  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Nak_ClearVsInv19:
  (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Nak_Clear ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -
  fix s

      have "?P1 s"

        apply(cut_tac  a1  a2  a3 , auto)

        done

        then  show "?P1 s\<or> ?P2 s\<or> ?P3 s"

       by blast

 qed
lemma NI_Nak_HomeVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Nak_Home ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed

lemma lemmaOnPtrAtGetX[intro]:
  assumes  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "
    and a5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX )) s" and
    a6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2)) s " and
    a7:"\<forall>f. f \<in> (invariants   N) \<longrightarrow> formEval f s "
 shows  "formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
 proof(rule ccontr)
  assume b0:"\<not>formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
  have b1:"formEval (inv2 iInv1 iInv2) s"
    apply(cut_tac a7)

    apply(drule_tac x="inv2  iInv1 iInv2" in spec)
    apply(cut_tac a7 a2 a3 a4,simp)
    done
 with b0 a5 a6 show False
  by auto
qed

lemma lemmaOnPtrAtGet[intro]:
  assumes  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "
    and a5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_Get )) s" and
    a6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2)) s " and
    a7:"\<forall>f. f \<in> (invariants   N) \<longrightarrow> formEval f s "
 shows  "formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
 proof(rule ccontr)
  assume b0:"\<not>formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
  have b1:"formEval (inv3 iInv1 iInv2) s"
    apply(cut_tac a7)

    apply(drule_tac x="inv3  iInv1 iInv2" in spec)
    apply(cut_tac a7 a2 a3 a4,simp)
    done
 with b0 a5 a6 show False
  by auto
qed

lemma lemmaOnPtr1[intro]:
  assumes  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "
    and a5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_Get )) s" and
    a6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2)) s " and
    a7:"\<forall>f. f \<in> (invariants   N) \<longrightarrow> formEval f s " and
    b2:"iInv1' \<le> N" and  b3:"iInv2' \<le> N" and  b4:"iInv1'~=iInv2'  "
    and b5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1') )  ( Const UNI_Get )) s" and
    b6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1') )   (Const iInv2')) s " and
    b7:"iInv2\<noteq>iInv2'"
 shows False
 proof -
  have c1:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
    by(metis a2 a3 a4 a5 a6 a7 lemmaOnPtrAtGet)
  have c2:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2') )  s"
    by(metis b2 b3 b4 b5 b6 a7 lemmaOnPtrAtGet)
 with c1 b7  show False
  by auto
qed

lemma lemmaOnPtr2[intro]:
  assumes  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "
    and a5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX )) s" and
    a6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2)) s " and
    a7:"\<forall>f. f \<in> (invariants   N) \<longrightarrow> formEval f s " and
    b2:"iInv1' \<le> N" and  b3:"iInv2' \<le> N" and  b4:"iInv1'~=iInv2'  "
    and b5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1') )  ( Const UNI_GetX )) s" and
    b6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1') )   (Const iInv2')) s " and
    b7:"iInv2\<noteq>iInv2'"
 shows False
 proof -
  have c1:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
    by(metis a2 a3 a4 a5 a6 a7 lemmaOnPtrAtGetX)
  have c2:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2') )  s"
    by(metis b2 b3 b4 b5 b6 a7 lemmaOnPtrAtGetX)
 with c1 b7  show False
  by auto
qed

lemma lemmaOnPtr3[intro]:
  assumes  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "
    and a5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_Get )) s" and
    a6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2)) s " and
    a7:"\<forall>f. f \<in> (invariants   N) \<longrightarrow> formEval f s " and
    b2:"iInv1' \<le> N" and  b3:"iInv2' \<le> N" and  b4:"iInv1'~=iInv2'  "
    and b5:"formEval ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1') )  ( Const UNI_GetX )) s" and
    b6:"formEval   ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1') )   (Const iInv2')) s " and
    b7:"iInv2\<noteq>iInv2'"
 shows False
 proof -
  have c1:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2) )  s"
    by(metis a2 a3 a4 a5 a6 a7 lemmaOnPtrAtGet)
  have c2:"formEval ( eqn ( IVar ( Global ''Dir_HeadPtr'') )   (Const iInv2') )  s"
    by(metis b2 b3 b4 b5 b6 a7 lemmaOnPtrAtGetX)
 with c1 b7  show False
  by auto
qed

  lemma NI_Remote_GetX_NakVsInv19Aux:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule'' s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

      have "invHoldForRule3'  s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv2) )   (Const iInv1))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv2) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done
      then have "?P3 s" by(rule weak3)

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "invHoldForRule3'  s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv2) )   (Const iRule2))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv2) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

      then have "?P3 s" by(rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

       have "invHoldForRule3'  s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iRule1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iRule1) )   (Const iInv1))  ) ) " in exI,auto)

        done

        then have "?P3 s" by(rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

      have "invHoldForRule3'  s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iRule1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iRule1) )   (Const iInv2))  ) ) " in exI,auto)

        done

        then have "?P3 s" by(rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                   have "?P3 s"
                  proof( unfold invHoldForRule3''_def,simp only:Let_def,( rule impI)+,                   rule ccontr)
                    assume c1:"\<forall>f'. f' \<in> invariants N \<longrightarrow> formEval f' s" and c2:"formEval (pre (NI_Remote_GetX_Nak iRule1 iRule2)) s "
                    and c3:"\<not> formEval (substFormByStatement (inv19 iInv1 iInv2) (act (NI_Remote_GetX_Nak iRule1 iRule2))) s"
                   have d1:" formEval (eqn (IVar (Para ''UniMsg_Cmd'' iInv1)) (Const UNI_GetX)) s" by(cut_tac b1 c2 c3, auto)
                   have d2:"formEval (eqn (IVar (Para ''UniMsg_Cmd'' iRule1)) (Const UNI_GetX)) s" by(cut_tac b1 c2 c3, auto)
                   have d3:"formEval (eqn (IVar (Para ''UniMsg_proc'' iInv1)) (Const iInv2)) s"  by(cut_tac b1 c2 c3, auto)
                   have d4:"formEval (eqn (IVar (Para ''UniMsg_proc'' iRule1)) (Const iRule2)) s"  by(cut_tac b1 c2 c3, auto)
                    show False thm lemmaOnPtr2
                    apply(cut_tac a1 a2 a3 a4 a5 a6 b1 c1 c2 c3 d1 d2 d3 d4,blast )
                    done
                   qed

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Remote_GetX_Nak_HomeVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak_Home  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed

  lemma NI_Remote_GetX_NakVsInv19 :
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_Nak  iRule1  iRule2 ) (invariants   N)"
by (metis NI_Remote_GetX_NakVsInv19Aux a2 a3 a4 a5 a6 local.a1 strengthEn)

lemma NI_Remote_GetX_PutXVsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_PutX  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P1 s \<or> ?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Remote_GetX_PutX_HomeVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_GetX_PutX_Home  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_Remote_Get_Nak1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak1  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

      have "?P3 s"

        apply(   cut_tac  a1  a2  a3  a4  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_Cmd'' Home) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Remote_Get_Nak2VsInv19Aux:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule'' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

      have "invHoldForRule3' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv2) )   (Const iInv1))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv2) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P3 s" by( rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "invHoldForRule3' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv2) )   (Const iRule2))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv2) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

       then  have "?P3 s" by( rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

      have "invHoldForRule3' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iRule1) )   (Const iInv1))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iRule1) )  ( Const UNI_Get ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  ) ) " in exI,auto)

        done

        then  have "?P3 s" by( rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

      have "invHoldForRule3' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)"

        apply(   cut_tac  a1  a2  a3  a4  a5  a6  b1 , simp)

        apply(rule_tac x=" (neg ( andForm ( andForm ( andForm ( eqn ( IVar ( Para ''UniMsg_Cmd'' iRule1) )  ( Const UNI_Get ))    ( eqn ( IVar ( Para ''UniMsg_proc'' iInv1) )   (Const iInv2))  )    ( eqn ( IVar ( Para ''UniMsg_Cmd'' iInv1) )  ( Const UNI_GetX ))  )    ( eqn ( IVar ( Para ''UniMsg_proc'' iRule1) )   (Const iInv2))  ) ) " in exI,auto)

        done

        then  have "?P3 s" by( rule weak3)
       then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                   have "?P3 s"
                  proof( unfold invHoldForRule3''_def,simp only:Let_def,( rule impI)+,                   rule ccontr)
                    assume c1:"\<forall>f'. f' \<in> invariants N \<longrightarrow> formEval f' s" and c2:"formEval (pre (NI_Remote_Get_Nak2 iRule1 iRule2)) s "
                    and c3:"\<not> formEval (substFormByStatement (inv19 iInv1 iInv2) (act (NI_Remote_Get_Nak2 iRule1 iRule2))) s"
                   have d1:" formEval (eqn (IVar (Para ''UniMsg_Cmd'' iInv1)) (Const UNI_GetX)) s" by(cut_tac b1 c2 c3, auto)
                   have d2:"formEval (eqn (IVar (Para ''UniMsg_Cmd'' iRule1)) (Const UNI_Get)) s" by(cut_tac b1 c2 c3, auto)
                   have d3:"formEval (eqn (IVar (Para ''UniMsg_proc'' iInv1)) (Const iInv2)) s"  by(cut_tac b1 c2 c3, auto)
                   have d4:"formEval (eqn (IVar (Para ''UniMsg_proc'' iRule1)) (Const iRule2)) s"  by(cut_tac b1 c2 c3, auto)
                    show False thm lemmaOnPtr2
                    apply(cut_tac a1 a2 a3 a4 a5 a6 b1 c1 c2 c3 d1 d2 d3 d4,blast )
                    done
                   qed

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed

 lemma NI_Remote_Get_Nak2VsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Nak2  iRule1  iRule2 ) (invariants   N)"
by (metis NI_Remote_Get_Nak2VsInv19Aux a2 a3 a4 a5 a6 local.a1 strengthEn)

lemma NI_Remote_Get_Put1VsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Put1  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_Remote_Get_Put2VsInv19:
    (*Rule2VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iRule2 \<le> N" and  a3:"iInv1 \<le> N" and  a4:"iInv2 \<le> N" and  a5:"iInv1~=iInv2  " and  a6:"iRule1~=iRule2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_Get_Put2  iRule1  iRule2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1\<and>iRule2=iInv2)   \<or>(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>(iRule1=iInv2\<and>iRule2=iInv1)   \<or>(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  a5  a6  , auto)
moreover
                {assume b1:"(iRule1=iInv1\<and>iRule2=iInv2)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv1\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv1)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>iRule2=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 )\<and>(iRule2~=iInv1 \<and>iRule2~=iInv2 ))"

                  have "?P1 s \<or> ?P2 s"

  apply(cut_tac  a1  a2  a3  a4  a5  a6  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Remote_PutVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_Put  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_Remote_PutXVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Remote_PutX  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma NI_ReplaceVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Replace  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_ReplaceHomeVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_ReplaceHome ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_ReplaceHomeShrVldVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_ReplaceHomeShrVld ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_ReplaceShrVldVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_ReplaceShrVld  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma NI_ShWbVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_ShWb N ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma NI_WbVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (NI_Wb ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_GetX1VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_GetX1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_GetX2VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_GetX2 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_PutX1VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_PutX1 N ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_PutX2VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_PutX2 N ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_PutX3VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_PutX3 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_GetX_PutX4VsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_GetX_PutX4 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_Get_GetVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_Get_Get ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_Get_PutVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_Get_Put ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_PutXVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_PutX ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Local_ReplaceVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Local_Replace ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  lemma PI_Remote_GetVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Remote_Get  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma PI_Remote_GetXVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Remote_GetX  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have allCases:"(iRule1=iInv1)   \<or>(iRule1=iInv2)   \<or>((iRule1~=iInv1 \<and>iRule1~=iInv2 ))   "
	                      by( cut_tac  a1  a2  a3  a4  , auto)
moreover
                {assume b1:"(iRule1=iInv1)"

      have "?P1 s"

        apply(cut_tac  a1  a2  a3  a4  b1 , auto)

        done

        then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

       by blast

	                }
moreover
                {assume b1:"(iRule1=iInv2)"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
moreover
                {assume b1:"((iRule1~=iInv1 \<and>iRule1~=iInv2 ))"

                  have "?P2 s"

  apply(cut_tac  a1  a2  a3  a4  b1 , auto intro!:forallVars1 simp  add :invHoldForRule2'_def varsOfVar_def)

  done

  then  have "?P1 s\<or> ?P2 s \<or> ?P3 s"

        by blast

	                }
   ultimately show "?P1 s\<or> ?P2 s\<or> ?P3 s"

	                         by metis

 qed
lemma PI_Remote_PutXVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Remote_PutX  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma PI_Remote_ReplaceVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (PI_Remote_Replace  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma StoreVsInv19:
    (*Rule1VsPInv2*)
  assumes   a1:"iRule1 \<le> N" and  a2:"iInv1 \<le> N" and  a3:"iInv2 \<le> N" and  a4:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (Store  iRule1 ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

    by (cut_tac  a1  a2  a3  a4 , auto)
 lemma StoreHomeVsInv19:
    (*Rule0VsPInv2*)
  assumes   a1:"iInv1 \<le> N" and  a2:"iInv2 \<le> N" and  a3:"iInv1~=iInv2  "

  shows  "invHoldForRule' s (inv19  iInv1  iInv2 ) (StoreHome ) (invariants   N)" (is " ?P1 s\<or>?P2 s\<or>?P3 s")

  proof -

     have "?P2 s"

     by (cut_tac a1 a2 a3, auto  )
   then show "?P1 s\<or>?P2 s\<or>?P3 s"
      by auto
 qed
  end


(*
 * Copyright 2014, NICTA
 *
 * This software may be distributed and modified according to the terms of
 * the BSD 2-Clause license. Note that NO WARRANTY is provided.
 * See "LICENSE_BSD2.txt" for details.
 *
 * @TAG(NICTA_BSD)
 *)

theory Simple
imports
  "../../AutoCorres"
  GCD
begin

(* Parse the input file. *)
install_C_file "simple.c"

(* Abstract the input file. *)
autocorres [ ts_force pure = max, ts_force nondet = gcd, unsigned_word_abs = gcd ] "simple.c"

(* Generated theorems and proofs. *)
thm simple.max'_def simple.max'_ac_corres
thm simple.gcd'_def simple.gcd'_ac_corres

context simple begin

(* Show generated "max'" function matches in-built "max". *)
lemma "max' a b = max a b"
  unfolding max'_def max_def
  by (rule refl)

(* Show "gcd'" calculates the gcd. *)
lemma gcd_wp [wp]:
    "\<lbrace> P (gcd a b) \<rbrace> gcd' a b \<lbrace> P \<rbrace>!"
  (* Unfold definition of "gcd'". *)
  apply (unfold gcd'_def)

  (* Annoate the loop with an invariant and measure. *)
  apply (subst whileLoop_add_inv [where
     I="\<lambda>(a', b') s. gcd a b = gcd a' b' \<and> P (gcd a b) s"
     and M="\<lambda>((a', b'), s). a'"])

  (* Solve using weakest-precondition. *)
  apply wp
    apply clarsimp
    apply (metis gcd_commute_nat gcd_red_nat)
   apply clarsimp
  apply clarsimp
  done

lemma monad_to_gets:
    "\<lbrakk> \<And>P. \<lbrace> P \<rbrace> f \<lbrace> \<lambda>r s. P s \<and> r = v s \<rbrace>!; empty_fail f \<rbrakk> \<Longrightarrow> f = gets v"
  apply atomize
  apply (monad_eq simp: validNF_def valid_def no_fail_def empty_fail_def)
  apply (rule conjI)
   apply clarsimp
   apply (drule_tac x="\<lambda>s'. s = s'" in spec)
   apply clarsimp
   apply force
  apply clarsimp
  apply (drule_tac x="\<lambda>s'. s' = t" in spec)
  apply clarsimp
  apply force
  done

lemma gcd_to_return [simp]:
    "gcd' a b = return (gcd a b)"
  apply (subst monad_to_gets [where v="\<lambda>_. gcd a b"])
    apply (wp gcd_wp)
    apply simp
   apply (clarsimp simp: gcd'_def)
   apply (rule empty_fail_bind)
    apply (rule empty_fail_whileLoop)
    apply (clarsimp simp: split_def)
   apply (clarsimp simp: split_def)
  apply (clarsimp simp: split_def)
  done

end

end


(*
 * Copyright 2014, General Dynamics C4 Systems
 *
 * This software may be distributed and modified according to the terms of
 * the GNU General Public License version 2. Note that NO WARRANTY is provided.
 * See "LICENSE_GPLv2.txt" for details.
 *
 * @TAG(GD_GPL)
 *)

(*
    Properties of machine operations.
*)

theory Machine_R
imports Bits_R
begin

definition "irq_state_independent_H (P :: kernel_state \<Rightarrow> bool)\<equiv>
              \<forall>(f :: nat \<Rightarrow> nat) (s :: kernel_state). P s \<longrightarrow> P (s\<lparr>ksMachineState := ksMachineState s
                                \<lparr>irq_state := f (irq_state (ksMachineState s))\<rparr>\<rparr>)"

lemma irq_state_independent_HI[intro!, simp]:
  "\<lbrakk>\<And>s f. P (s\<lparr>ksMachineState := ksMachineState s
              \<lparr>irq_state := f (irq_state (ksMachineState s))\<rparr>\<rparr>) = P s\<rbrakk>
   \<Longrightarrow> irq_state_independent_H P"
  by (simp add: irq_state_independent_H_def)

lemma irq_state_independent_H_conjI[intro!]:
  "\<lbrakk>irq_state_independent_H P; irq_state_independent_H Q\<rbrakk>
   \<Longrightarrow> irq_state_independent_H (P and Q)"
  "\<lbrakk>irq_state_independent_H P; irq_state_independent_H Q\<rbrakk>
   \<Longrightarrow> irq_state_independent_H (\<lambda>s. P s \<and> Q s)"
  by (simp add: irq_state_independent_H_def)+

lemma irq_state_independent_H_disjI[intro]:
  "\<lbrakk>irq_state_independent_H P; irq_state_independent_H Q\<rbrakk>
   \<Longrightarrow> irq_state_independent_H (P or Q)"
  "\<lbrakk>irq_state_independent_H P; irq_state_independent_H Q\<rbrakk>
   \<Longrightarrow> irq_state_independent_H (\<lambda>s. P s \<or> Q s)"
  by (simp add: irq_state_independent_H_def)+

context begin interpretation Arch . (*FIXME: arch_split*)

lemma dmo_getirq_inv[wp]:
  "irq_state_independent_H P \<Longrightarrow> \<lbrace>P\<rbrace> doMachineOp getActiveIRQ \<lbrace>\<lambda>rv. P\<rbrace>"
  apply (simp add: getActiveIRQ_def doMachineOp_def split_def exec_gets
                   select_f_select[simplified liftM_def]
                   select_modify_comm gets_machine_state_modify)
  apply wp
  apply (clarsimp simp: irq_state_independent_H_def in_monad return_def split: if_splits)
  done

lemma getActiveIRQ_masked:
  "\<lbrace>\<lambda>s. valid_irq_masks' table (irq_masks s)\<rbrace> getActiveIRQ
  \<lbrace>\<lambda>rv s. \<forall>irq. rv = Some irq \<longrightarrow> table irq \<noteq> IRQInactive\<rbrace>"
  apply (simp add: getActiveIRQ_def)
  apply wp
  apply (clarsimp simp: valid_irq_masks'_def)
  done

lemma dmo_maskInterrupt:
  "\<lbrace>\<lambda>s. P (ksMachineState_update (irq_masks_update (\<lambda>t. t (irq := m))) s)\<rbrace>
  doMachineOp (maskInterrupt m irq) \<lbrace>\<lambda>_. P\<rbrace>"
  apply (simp add: doMachineOp_def split_def)
  apply wp
  apply (clarsimp simp: maskInterrupt_def in_monad)
  apply (erule rsubst [where P=P])
  apply simp
  done

lemma dmo_maskInterrupt_True:
  "\<lbrace>invs'\<rbrace> doMachineOp (maskInterrupt True irq) \<lbrace>\<lambda>_. invs'\<rbrace>"
  apply (wp dmo_maskInterrupt)
  apply (clarsimp simp: invs'_def valid_state'_def)
  apply (simp add: valid_irq_masks'_def valid_machine_state'_def
                   ct_not_inQ_def ct_idle_or_in_cur_domain'_def tcb_in_cur_domain'_def)
  done

lemma setIRQState_irq_states':
  "\<lbrace>valid_irq_states'\<rbrace>
      setIRQState state irq
   \<lbrace>\<lambda>rv. valid_irq_states'\<rbrace>"
  apply (simp add: setIRQState_def setInterruptState_def getInterruptState_def)
  apply (wp dmo_maskInterrupt)
  apply (simp add: valid_irq_masks'_def)
  done

lemma getActiveIRQ_le_maxIRQ:
  "\<lbrace>irqs_masked' and valid_irq_states'\<rbrace> doMachineOp getActiveIRQ \<lbrace>\<lambda>rv s. \<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ\<rbrace>"
  apply (simp add: doMachineOp_def split_def)
  apply wp
  apply clarsimp
  apply (drule use_valid, rule getActiveIRQ_le_maxIRQ')
   prefer 2
   apply simp
  apply (simp add: irqs_masked'_def valid_irq_states'_def)
  done

(* FIXME: follows already from getActiveIRQ_le_maxIRQ *)
lemma getActiveIRQ_neq_Some0xFF:
  "\<lbrace>\<top>\<rbrace> doMachineOp getActiveIRQ \<lbrace>\<lambda>rv s. rv \<noteq> Some 0x3FF\<rbrace>"
  apply (simp add: doMachineOp_def split_def)
  apply wp
  apply clarsimp
  apply (drule use_valid, rule getActiveIRQ_neq_Some0xFF')
   apply auto
  done

end
end