(*  Title:      HOL/Auth/n_flash_lemma_on_inv__150.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__150 imports n_flash_base
begin
section{*All lemmas on causal relation between inv__150 and some rule r*}
lemma n_PI_Remote_GetVsinv__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_Get  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_PI_Remote_GetX  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Nak  dst)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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: "(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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__0  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__1  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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_Get_Put_DirtyVsinv__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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_Get_NakVsinv__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_Get_PutVsinv__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_Nak__part__0Vsinv__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1  src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_8_NODE_GetVsinv__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_9__part__0Vsinv__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>pp~=p__Inv4)\<or>(src~=p__Inv4\<and>pp=p__Inv4)\<or>(src~=p__Inv4\<and>pp~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Local_GetX_PutX_11Vsinv__150:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4)\<or>(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__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__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<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__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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_GetX_PutXVsinv__150:
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__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(src=p__Inv4\<and>dst~=p__Inv4)\<or>(src~=p__Inv4\<and>dst=p__Inv4)\<or>(src~=p__Inv4\<and>dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(src=p__Inv4\<and>dst~=p__Inv4)"
  have "?P3 s"
  apply (cut_tac a1 a2 b1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''Proc'') dst) ''CacheState'')) (Const CACHE_E)) (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''HomeHeadPtr'')) (Const true))))" in exI, auto) done
  then have "invHoldForRule s f r (invariants N)" by auto
}
moreover {
  assume b1: "(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__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
}
ultimately show "invHoldForRule s f r (invariants N)" by satx
qed

lemma n_NI_Remote_PutVsinv__150:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Put  dst)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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: "(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__150:
assumes a1: "(\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_PutX  dst)" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "(dst=p__Inv4)\<or>(dst~=p__Inv4)" apply (cut_tac a1 a2, auto) done
moreover {
  assume b1: "(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: "(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_FAckVsinv__150:
assumes a1: "(r=n_NI_FAck  )" and
a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a2 obtain p__Inv4 where a2:"p__Inv4\<le>N\<and>f=inv__150  p__Inv4" apply fastforce done
have "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const true)) s))\<or>((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const true))) s))" by auto
  moreover {
    assume c1: "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const true)) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''HomeProc'')) (Const true)) (eqn (IVar (Field (Field (Ident ''Sta'') ''ShWbMsg'') ''Cmd'')) (Const SHWB_FAck))))" in exI, auto) done
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const true))) s))"
    have "?P2 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__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_PutX_Home  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "r=n_PI_Local_GetX_PutX__part__0  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_WbVsinv__150:
  assumes a1: "r=n_NI_Wb  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_StoreVsinv__150:
  assumes a1: "\<exists> src data. src\<le>N\<and>data\<le>N\<and>r=n_Store  src data" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_3Vsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_3 N src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_1Vsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_1 N src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__1  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__0  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_ReplaceVsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_Replace  src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_Store_HomeVsinv__150:
  assumes a1: "\<exists> data. data\<le>N\<and>r=n_Store_Home  data" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_ReplaceVsinv__150:
  assumes a1: "r=n_PI_Local_Replace  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_existsVsinv__150:
  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__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_PutXVsinv__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_PI_Remote_PutX  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Put_Home  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvVsinv__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Inv  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_PutXVsinv__150:
  assumes a1: "r=n_PI_Local_PutX  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_Get_PutVsinv__150:
  assumes a1: "r=n_PI_Local_Get_Put  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_ShWbVsinv__150:
  assumes a1: "r=n_NI_ShWb N " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_PutX_HeadVld__part__0Vsinv__150:
  assumes a1: "r=n_PI_Local_GetX_PutX_HeadVld__part__0 N " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_ReplaceVsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Replace  src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_Nak_Home  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_PutXAcksDoneVsinv__150:
  assumes a1: "r=n_NI_Local_PutXAcksDone  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "r=n_PI_Local_GetX_PutX__part__1  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  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__150:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Nak_Home  dst" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_exists_HomeVsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_exists_Home  src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Replace_HomeVsinv__150:
  assumes a1: "r=n_NI_Replace_Home  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_PutVsinv__150:
  assumes a1: "r=n_NI_Local_Put  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_ClearVsinv__150:
  assumes a1: "r=n_NI_Nak_Clear  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_Get_GetVsinv__150:
  assumes a1: "r=n_PI_Local_Get_Get  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_HomeVsinv__150:
  assumes a1: "r=n_NI_Nak_Home  " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_2Vsinv__150:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_2 N src" and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_PutX_HeadVld__part__1Vsinv__150:
  assumes a1: "r=n_PI_Local_GetX_PutX_HeadVld__part__1 N " and
  a2: "(\<exists> p__Inv4. p__Inv4\<le>N\<and>f=inv__150  p__Inv4)"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

end


(*  Title:      HOL/Auth/n_germanSymIndex_on_inis.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_germanSymIndex Protocol Case Study*}

theory n_germanSymIndex_on_inis imports n_germanSymIndex_on_ini
begin
lemma on_inis:
  assumes b1: "f \<in> (invariants N)" and b2: "ini \<in> {andList (allInitSpecs N)}" and b3: "formEval ini s"
  shows "formEval f s"
  proof -
  have c1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__1  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__2  p__Inv0 p__Inv2)\<or>
    (f=inv__3  )\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__4  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__5  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__6  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__7  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__8  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__9  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__10  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__11  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__12  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__13  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__14  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__15  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__16  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__17  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__18  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__19  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__20  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__21  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__22  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__23  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__24  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__25  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__26  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__27  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__28  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__29  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__30  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__31  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__32  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__33  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__34  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__35  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__36  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__37  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__38  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__39  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__40  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__41  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__42  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__43  p__Inv2)\<or>
    (\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__44  p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__45  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__46  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__47  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__48  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__49  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__50  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__51  p__Inv0 p__Inv2)\<or>
    (\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__52  p__Inv0 p__Inv2)"
  apply (cut_tac b1, simp) done
    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__1  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__1)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__2  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__2)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(f=inv__3  )"
      have "formEval f s"
      apply (rule iniImply_inv__3)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__4  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__4)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__5  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__5)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__6  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__6)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__7  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__7)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__8  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__8)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__9  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__9)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__10  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__10)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__11  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__11)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__12  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__12)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__13  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__13)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__14  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__14)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__15  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__15)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__16  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__16)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__17  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__17)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__18  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__18)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__19  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__19)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__20  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__20)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__21  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__21)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__22  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__22)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__23  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__23)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__24  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__24)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__25  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__25)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__26  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__26)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__27  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__27)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__28  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__28)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__29  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__29)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__30  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__30)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__31  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__31)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__32  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__32)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__33  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__33)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__34  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__34)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__35  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__35)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__36  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__36)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__37  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__37)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__38  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__38)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__39  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__39)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__40  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__40)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__41  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__41)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__42  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__42)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__43  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__43)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__44  p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__44)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__45  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__45)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__46  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__46)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__47  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__47)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__48  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__48)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__49  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__49)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__50  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__50)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__51  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__51)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

    moreover {
      assume d1: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__52  p__Inv0 p__Inv2)"
      have "formEval f s"
      apply (rule iniImply_inv__52)
      apply (cut_tac d1, assumption)
      apply (cut_tac b2 b3, blast) done
    }

  ultimately show "formEval f s"
  by satx
qed

end


(*  Title:      HOL/Auth/flash_data_cub_lemma_on_inv__10.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 flash_data_cub Protocol Case Study*}

theory flash_data_cub_lemma_on_inv__10 imports flash_data_cub_base
begin
section{*All lemmas on causal relation between inv__10 and some rule r*}
lemma n_StoreVsinv__10:
assumes a1: "(\<exists> src data. src\<le>N\<and>data\<le>N\<and>r=n_Store  src data)" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain src data where a1:"src\<le>N\<and>data\<le>N\<and>r=n_Store  src data" apply fastforce done
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Para (Field (Ident ''Sta'') ''Proc'') src) ''CacheState'')) (Const CACHE_E)) (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Local'')) (Const true))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_Store_HomeVsinv__10:
assumes a1: "(\<exists> data. data\<le>N\<and>r=n_Store_Home  data)" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
from a1 obtain data where a1:"data\<le>N\<and>r=n_Store_Home  data" 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_Get_PutVsinv__10:
assumes a1: "(r=n_PI_Local_Get_Put  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
have "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)) s))\<or>((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true))) s))" by auto
  moreover {
    assume c1: "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)))" in exI, auto) done
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true))) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false)) (neg (eqn (IVar (Field (Ident ''Sta'') ''MemData'')) (IVar (Field (Ident ''Sta'') ''CurrData''))))))" in exI, auto) done
    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__10:
assumes a1: "(r=n_PI_Local_GetX_PutX_HeadVld__part__0 N )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false)) (neg (eqn (IVar (Field (Ident ''Sta'') ''MemData'')) (IVar (Field (Ident ''Sta'') ''CurrData''))))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_PI_Local_GetX_PutX_HeadVld__part__1Vsinv__10:
assumes a1: "(r=n_PI_Local_GetX_PutX_HeadVld__part__1 N )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false)) (neg (eqn (IVar (Field (Ident ''Sta'') ''MemData'')) (IVar (Field (Ident ''Sta'') ''CurrData''))))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_PI_Local_GetX_PutX__part__0Vsinv__10:
assumes a1: "(r=n_PI_Local_GetX_PutX__part__0  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false)) (neg (eqn (IVar (Field (Ident ''Sta'') ''MemData'')) (IVar (Field (Ident ''Sta'') ''CurrData''))))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_PI_Local_GetX_PutX__part__1Vsinv__10:
assumes a1: "(r=n_PI_Local_GetX_PutX__part__1  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Dirty'')) (Const false)) (neg (eqn (IVar (Field (Ident ''Sta'') ''MemData'')) (IVar (Field (Ident ''Sta'') ''CurrData''))))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_PI_Local_PutXVsinv__10:
assumes a1: "(r=n_PI_Local_PutX  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
have "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Pending'')) (Const true)) s))\<or>((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Pending'')) (Const true))) s))" by auto
  moreover {
    assume c1: "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''Dir'') ''Pending'')) (Const true)) s))"
    have "?P2 s"
    proof(cut_tac a1 a2  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'') ''Pending'')) (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_PI_Local_ReplaceVsinv__10:
assumes a1: "(r=n_PI_Local_Replace  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_1Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_1 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_2Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_2 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_3Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_3 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_4Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_4 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_5Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_5 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_6Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_6 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_7__part__0Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__0 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_7__part__1Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7__part__1 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__0Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__0 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_7_NODE_Get__part__1Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_7_NODE_Get__part__1 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_8_HomeVsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_8_Home_NODE_GetVsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_8_Home_NODE_Get N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_8Vsinv__10:
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: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_8_NODE_GetVsinv__10:
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: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_9__part__0Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__0 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_9__part__1Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_9__part__1 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_10_HomeVsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_10_Home N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_10Vsinv__10:
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: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_GetX_PutX_11Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_PutX_11 N src)" and
a2: "(f=inv__10  )"
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
  have "?P1 s"
  proof(cut_tac a1 a2 , auto) qed
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_Local_PutVsinv__10:
assumes a1: "(r=n_NI_Local_Put  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
have "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)) s))\<or>((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true))) s))" by auto
  moreover {
    assume c1: "((formEval (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true)))" in exI, auto) done
    then have "invHoldForRule s f r (invariants N)" by auto
  }
  moreover {
    assume c1: "((formEval (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeProc'') ''InvMarked'')) (Const true))) s))"
    have "?P3 s"
    apply (cut_tac a1 a2  c1, simp, rule_tac x="(neg (andForm (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeUniMsg'') ''Data'')) (IVar (Field (Ident ''Sta'') ''CurrData'')))) (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeUniMsg'') ''Cmd'')) (Const UNI_Put))))" in exI, auto) done
    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_PutXAcksDoneVsinv__10:
assumes a1: "(r=n_NI_Local_PutXAcksDone  )" and
a2: "(f=inv__10  )"
shows "invHoldForRule s f r (invariants N)" (is "?P1 s \<or> ?P2 s \<or> ?P3 s")
proof -
  have "?P3 s"
  apply (cut_tac a1 a2 , simp, rule_tac x="(neg (andForm (neg (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeUniMsg'') ''Data'')) (IVar (Field (Ident ''Sta'') ''CurrData'')))) (eqn (IVar (Field (Field (Ident ''Sta'') ''HomeUniMsg'') ''Cmd'')) (Const UNI_PutX))))" in exI, auto) done
  then show "invHoldForRule s f r (invariants N)" by auto
qed

lemma n_NI_InvAck_1Vsinv__10:
assumes a1: "(\<exists> src. src\<le>N\<and>r=n_NI_InvAck_1 N src)" and
a2: "(f=inv__10  )"
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_InvAck_1 N src" 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_Local_Get_Get__part__1Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__1  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_GetX_PutX_HomeVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_PutX_Home  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_GetVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_Get  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_WbVsinv__10:
  assumes a1: "r=n_NI_Wb  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_GetX_GetX__part__1Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__1  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_3Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_3 N src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_GetX__part__1Vsinv__10:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__1  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_GetX_GetX__part__0Vsinv__10:
  assumes a1: "r=n_PI_Local_GetX_GetX__part__0  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_ReplaceVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_Replace  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_GetX_Nak__part__1Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__1  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Nak__part__1Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__1  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Get__part__0Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Get__part__0  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_existsVsinv__10:
  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: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_GetX_Nak__part__2Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__2  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_PutXVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_PI_Remote_PutX  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_Put_HomeVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Put_Home  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Put_HeadVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Head N src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Inv  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Nak__part__2Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__2  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_GetX_GetX__part__0Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_GetX__part__0  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_ShWbVsinv__10:
  assumes a1: "r=n_NI_ShWb N " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_ReplaceVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Replace  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_GetX_Nak_HomeVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_GetX_Nak_Home  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_GetX_NakVsinv__10:
  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: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_NakVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Nak  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Remote_GetXVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_PI_Remote_GetX  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_Nak_HomeVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Get_Nak_Home  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_PutXVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_PutX  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_PutVsinv__10:
  assumes a1: "\<exists> dst. dst\<le>N\<and>r=n_NI_Remote_Put  dst" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_PutVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_GetX_Nak__part__0Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_GetX_Nak__part__0  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_exists_HomeVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_exists_Home  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Replace_HomeVsinv__10:
  assumes a1: "r=n_NI_Replace_Home  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_GetX_PutXVsinv__10:
  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: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_NakVsinv__10:
  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: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_ClearVsinv__10:
  assumes a1: "r=n_NI_Nak_Clear  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Put_DirtyVsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Put_Dirty  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Local_Get_Nak__part__0Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_Local_Get_Nak__part__0  src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_PI_Local_Get_GetVsinv__10:
  assumes a1: "r=n_PI_Local_Get_Get  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Remote_Get_PutVsinv__10:
  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: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_Nak_HomeVsinv__10:
  assumes a1: "r=n_NI_Nak_Home  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_InvAck_2Vsinv__10:
  assumes a1: "\<exists> src. src\<le>N\<and>r=n_NI_InvAck_2 N src" and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

lemma n_NI_FAckVsinv__10:
  assumes a1: "r=n_NI_FAck  " and
  a2: "(f=inv__10  )"
  shows "invHoldForRule s f r (invariants N)"
  apply (rule noEffectOnRule, cut_tac a1 a2, auto) done

end