(*  Title:      HOL/Auth/n_g2kAbsAfter_lemma_inv__60_on_rules.thy
    Author:     Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
    Copyright    2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
*)

header{*The n_g2kAbsAfter Protocol Case Study*}

theory n_g2kAbsAfter_lemma_inv__60_on_rules imports n_g2kAbsAfter_lemma_on_inv__60
begin
section{*All lemmas on causal relation between inv__60*}
lemma lemma_inv__60_on_rules:
  assumes b1: "r \<in> rules N" and b2: "(f=inv__60  )"
  shows "invHoldForRule s f r (invariants N)"
  proof -
  have c1: "(\<exists> d. d\<le>N\<and>r=n_n_Store_i1  d)\<or>
    (\<exists> d. d\<le>N\<and>r=n_n_AStore_i1  d)\<or>
    (r=n_n_SendReqS_j1  )\<or>
    (r=n_n_SendReqEI_i1  )\<or>
    (r=n_n_SendReqES_i1  )\<or>
    (r=n_n_RecvReq_i1  )\<or>
    (r=n_n_SendInvE_i1  )\<or>
    (r=n_n_SendInvS_i1  )\<or>
    (r=n_n_SendInvAck_i1  )\<or>
    (r=n_n_RecvInvAck_i1  )\<or>
    (r=n_n_SendGntS_i1  )\<or>
    (r=n_n_SendGntE_i1  )\<or>
    (r=n_n_RecvGntS_i1  )\<or>
    (r=n_n_RecvGntE_i1  )\<or>
    (r=n_n_ASendReqIS_j1  )\<or>
    (r=n_n_ASendReqSE_j1  )\<or>
    (r=n_n_ASendReqEI_i1  )\<or>
    (r=n_n_ASendReqES_i1  )\<or>
    (r=n_n_SendReqEE_i1  )\<or>
    (r=n_n_ARecvReq_i1  )\<or>
    (r=n_n_ASendInvE_i1  )\<or>
    (r=n_n_ASendInvS_i1  )\<or>
    (r=n_n_ASendInvAck_i1  )\<or>
    (r=n_n_ARecvInvAck_i1  )\<or>
    (r=n_n_ASendGntS_i1  )\<or>
    (r=n_n_ASendGntE_i1  )\<or>
    (r=n_n_ARecvGntS_i1  )\<or>
    (r=n_n_ARecvGntE_i1  )"
  apply (cut_tac b1, auto) done
    moreover {
      assume d1: "(\<exists> d. d\<le>N\<and>r=n_n_Store_i1  d)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_Store_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(\<exists> d. d\<le>N\<and>r=n_n_AStore_i1  d)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_AStore_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendReqS_j1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendReqS_j1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendReqEI_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendReqEI_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendReqES_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendReqES_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_RecvReq_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_RecvReq_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendInvE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendInvE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendInvS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendInvS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendInvAck_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendInvAck_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_RecvInvAck_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_RecvInvAck_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendGntS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendGntS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendGntE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendGntE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_RecvGntS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_RecvGntS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_RecvGntE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_RecvGntE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendReqIS_j1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendReqIS_j1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendReqSE_j1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendReqSE_j1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendReqEI_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendReqEI_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendReqES_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendReqES_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_SendReqEE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_SendReqEE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ARecvReq_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ARecvReq_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendInvE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendInvE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendInvS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendInvS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendInvAck_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendInvAck_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ARecvInvAck_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ARecvInvAck_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendGntS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendGntS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ASendGntE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ASendGntE_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ARecvGntS_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ARecvGntS_i1Vsinv__60) done
    }

    moreover {
      assume d1: "(r=n_n_ARecvGntE_i1  )"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_n_ARecvGntE_i1Vsinv__60) done
    }

  ultimately show "invHoldForRule s f r (invariants N)"
  by satx
qed

end


(*  Title:      HOL/Auth/n_germanSimp_lemma_inv__49_on_rules.thy
    Author:     Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
    Copyright    2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
*)

header{*The n_germanSimp Protocol Case Study*}

theory n_germanSimp_lemma_inv__49_on_rules imports n_germanSimp_lemma_on_inv__49
begin
section{*All lemmas on causal relation between inv__49*}
lemma lemma_inv__49_on_rules:
  assumes b1: "r \<in> rules N" and b2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__49  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  proof -
  have c1: "(\<exists> i d. i\<le>N\<and>d\<le>N\<and>r=n_Store  i d)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvReqS N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvReqE__part__0 N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvReqE__part__1 N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInv__part__0  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInv__part__1  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInvAck  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvInvAck  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendGntS  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendGntE N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvGntS  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvGntE  i)"
  apply (cut_tac b1, auto) done
    moreover {
      assume d1: "(\<exists> i d. i\<le>N\<and>d\<le>N\<and>r=n_Store  i d)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_StoreVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvReqS N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvReqSVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvReqE__part__0 N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvReqE__part__0Vsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvReqE__part__1 N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvReqE__part__1Vsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInv__part__0  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInv__part__0Vsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInv__part__1  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInv__part__1Vsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInvAck  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInvAckVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvInvAck  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvInvAckVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendGntS  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendGntSVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendGntE N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendGntEVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvGntS  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvGntSVsinv__49) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvGntE  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvGntEVsinv__49) done
    }

  ultimately show "invHoldForRule s f r (invariants N)"
  by satx
qed

end


(*  Title:      HOL/Auth/n_flash_lemma_on_inv__147.thy
    Author:     Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
    Copyright    2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
*)

header{*The n_flash Protocol Case Study*}

theory n_flash_lemma_on_inv__147 imports n_flash_base
begin
section{*All lemmas on causal relation between inv__147 and some rule r*}
lemma n_PI_Remote_GetVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_Get  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_PI_Remote_Get  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_PI_Remote_GetXVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_GetX  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_PI_Remote_GetX  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_NakVsinv__147:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Nak  dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Nak  dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst=p__Inv3)\<or>(dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Nak__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Nak__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Nak__part__2Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Get__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__0  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Get__part__0  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Get__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__1  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Get__part__1  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Put_HeadVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P3 s"
  apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv3) ''Cmd'')) (Const UNI_PutX)) (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false))))" in exI, auto) done
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_PutVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_Get_Put_DirtyVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_Get_NakVsinv__147:
assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Nak  src dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Nak  src dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst=p__Inv3)\<or>(src=p__Inv3\<and>dst=p__Inv4)\<or>(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)\<or>(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_Get_PutVsinv__147:
assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Put  src dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_Get_Put  src dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst=p__Inv3)\<or>(src=p__Inv3\<and>dst=p__Inv4)\<or>(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)\<or>(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_Nak__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_Nak__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_Nak__part__2Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_GetX__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_GetX__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_2Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_3Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_4Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_5Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_6Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_7__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_7__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__0 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__0 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__1 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__1 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_8_HomeVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_8_Home_NODE_GetVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_8Vsinv__147:
assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8 N src pp)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8 N src pp" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp=p__Inv3)\<or>(src=p__Inv3\<and>pp=p__Inv4)\<or>(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)\<or>(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_8_NODE_GetVsinv__147:
assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8_NODE_Get N src pp)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_8_NODE_Get N src pp" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp=p__Inv3)\<or>(src=p__Inv3\<and>pp=p__Inv4)\<or>(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)\<or>(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_9__part__0Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_9__part__1Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_10_HomeVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_10Vsinv__147:
assumes a1: "(\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_10 N src pp)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src pp where a1:"src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_Local_GetX_PutX_10 N src pp" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp=p__Inv3)\<or>(src=p__Inv3\<and>pp=p__Inv4)\<or>(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)\<or>(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>pp~=p__Inv3\<and>pp~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_11Vsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_GetX_NakVsinv__147:
assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_Nak  src dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_Nak  src dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst=p__Inv3)\<or>(src=p__Inv3\<and>dst=p__Inv4)\<or>(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)\<or>(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_GetX_PutXVsinv__147:
assumes a1: "(\<exists> src dst. src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_PutX  src dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src dst where a1:"src\<le>N\<and>dst\<le>N\<and>src~=dst\<and>r=n_NI_Remote_GetX_PutX  src dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst=p__Inv3)\<or>(src=p__Inv3\<and>dst=p__Inv4)\<or>(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)\<or>(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst=p__Inv4)"
  have "?P3 s"
  apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''Proc'') p__Inv4) ''CacheState'')) (Const CACHE_E))))" in exI, auto) done
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src=p__Inv3\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P3 s"
  apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''Proc'') dst) ''CacheState'')) (Const CACHE_E))))" in exI, auto) done
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4\<and>dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_PutVsinv__147:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Put  dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Remote_Put  dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst=p__Inv3)\<or>(dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_PutXVsinv__147:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_PutX  dst)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain dst where a1:"dst\<le>N\<and>r=n_NI_Remote_PutX  dst" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst=p__Inv3)\<or>(dst~=p__Inv3\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(dst=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst=p__Inv3)"
  have "?P1 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(dst~=p__Inv3\<and>dst~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_ReplaceVsinv__147:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Replace  src)" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src where a1:"src\<le>N\<and>r=n_NI_Replace  src" apply fastforce done
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(src=p__Inv3)\<or>(src~=p__Inv3\<and>src~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4)"
  have "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''ShrVld'')) (Const true)) s))\<or>((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''ShrVld'')) (Const true))) s))" by auto
  moreover {
    assume c1: "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''ShrVld'')) (Const true)) s))"
    have "?P1 s"
    proof(cut_tac a1 a2 b1 c1, auto) qed
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''ShrVld'')) (Const true))) s))"
    have "?P2 s"
    proof(cut_tac a1 a2 b1 c1, auto) qed
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  ultimately have "invHoldForRule s f r (invariants N)" by satx
}
moreover {
  assume b1: "(src=p__Inv3)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(src~=p__Inv3\<and>src~=p__Inv4)"
  have "?P2 s"
  proof(cut_tac a1 a2 b1, auto) qed
  then have "invHoldForRule s f r (invariants N)" by auto
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_PI_Local_GetX_PutX_HeadVld__part__0Vsinv__147:
assumes a1: "(r=n_PI_Local_GetX_PutX_HeadVld__part__0 N )" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_PI_Local_GetX_PutX_HeadVld__part__1Vsinv__147:
assumes a1: "(r=n_PI_Local_GetX_PutX_HeadVld__part__1 N )" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_ShWbVsinv__147:
assumes a1: "(r=n_NI_ShWb N )" and
a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a2 obtain p__Inv3 p__Inv4 where a2:"p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4" apply fastforce done
have "((formEval (andForm (eqn (Const (index p__Inv4)) (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Proc''))) (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''HomeProc'')) (Const false))) s))\<or>((formEval (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)) s))\<or>((formEval (andForm (neg (eqn (Const (index p__Inv4)) (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Proc'')))) (neg (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)))) s))\<or>((formEval (andForm (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''HomeProc'')) (Const false))) (neg (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)))) s))" by auto
  moreover {
    assume c1: "((formEval (andForm (eqn (Const (index p__Inv4)) (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Proc''))) (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''HomeProc'')) (Const false))) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv3) ''Cmd'')) (Const UNI_PutX)) (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Cmd'')) (Const SHWB_ShWb))))" in exI, auto) done
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (andForm (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)) (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''UniMsg'') p__Inv3) ''Cmd'')) (Const UNI_PutX))))" in exI, auto) done
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (andForm (neg (eqn (Const (index p__Inv4)) (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Proc'')))) (neg (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)))) s))"
    have "?P1 s"
    proof(cut_tac a1 a2  c1, auto) qed
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (andForm (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''HomeProc'')) (Const false))) (neg (eqn (IVar (Para (Field (Field (Ident ''Sta'') ''Dir'') ''ShrSet'') p__Inv4)) (Const true)))) s))"
    have "?P1 s"
    proof(cut_tac a1 a2  c1, auto) qed
    then have "invHoldForRule s f r (invariants N)" by auto
  }
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_GetX_PutX_HomeVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_PutX_Home  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_PutX__part__0Vsinv__147:
  assumes a1: "r=n_PI_Local_GetX_PutX__part__0  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_WbVsinv__147:
  assumes a1: "r=n_NI_Wb  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_StoreVsinv__147:
  assumes a1: "\<exists> src data. src\<le>N\<and>data\<le>N\<and>r=n_Store  src data" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_3Vsinv__147:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_3 N src" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_1Vsinv__147:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_1 N src" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_GetX__part__1Vsinv__147:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__1  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_GetX__part__0Vsinv__147:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__0  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_ReplaceVsinv__147:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_Replace  src" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_Store_HomeVsinv__147:
  assumes a1: "\<exists> data. data\<le>N\<and>r=n_Store_Home  data" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_ReplaceVsinv__147:
  assumes a1: "r=n_PI_Local_Replace  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_existsVsinv__147:
  assumes a1: "\<exists> src pp. src\<le>N\<and>pp\<le>N\<and>src~=pp\<and>r=n_NI_InvAck_exists  src pp" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_PutXVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_PI_Remote_PutX  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_Put_HomeVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Put_Home  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Inv  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_PutXVsinv__147:
  assumes a1: "r=n_PI_Local_PutX  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_Get_PutVsinv__147:
  assumes a1: "r=n_PI_Local_Get_Put  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_GetX_Nak_HomeVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_Nak_Home  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_PutXAcksDoneVsinv__147:
  assumes a1: "r=n_NI_Local_PutXAcksDone  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_PutX__part__1Vsinv__147:
  assumes a1: "r=n_PI_Local_GetX_PutX__part__1  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_Nak_HomeVsinv__147:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Nak_Home  dst" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_exists_HomeVsinv__147:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_exists_Home  src" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Replace_HomeVsinv__147:
  assumes a1: "r=n_NI_Replace_Home  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_PutVsinv__147:
  assumes a1: "r=n_NI_Local_Put  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_ClearVsinv__147:
  assumes a1: "r=n_NI_Nak_Clear  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_Get_GetVsinv__147:
  assumes a1: "r=n_PI_Local_Get_Get  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_HomeVsinv__147:
  assumes a1: "r=n_NI_Nak_Home  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_2Vsinv__147:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_2 N src" and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_FAckVsinv__147:
  assumes a1: "r=n_NI_FAck  " and
  a2: "(\<exists> p__Inv3 p__Inv4. p__Inv3\<le>N\<and>p__Inv4\<le>N\<and>p__Inv3~=p__Inv4\<and>f=inv__147  p__Inv3 p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

end