(*  Title:      HOL/Auth/n_german_lemma_inv__7_on_rules.thy
    Author:     Yongjian Li and Kaiqiang Duan, State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
    Copyright    2016 State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences
*)

header{*The n_german Protocol Case Study*}

theory n_german_lemma_inv__7_on_rules imports n_german_lemma_on_inv__7
begin
section{*All lemmas on causal relation between inv__7*}
lemma lemma_inv__7_on_rules:
  assumes b1: "r \<in> rules N" and b2: "(\<exists> p__Inv2. p__Inv2\<le>N\<and>f=inv__7  p__Inv2)"
  shows "invHoldForRule s f r (invariants N)"
  proof -
  have c1: "(\<exists> i d. i\<le>N\<and>d\<le>N\<and>r=n_Store  i d)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendReqS  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendReqE__part__0  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendReqE__part__1  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvReqS N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvReqE N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInv__part__0  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInv__part__1  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendInvAck  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvInvAck  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendGntS  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_SendGntE N i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvGntS  i)\<or>
    (\<exists> i. i\<le>N\<and>r=n_RecvGntE  i)"
  apply (cut_tac b1, auto) done
    moreover {
      assume d1: "(\<exists> i d. i\<le>N\<and>d\<le>N\<and>r=n_Store  i d)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_StoreVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendReqS  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendReqSVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendReqE__part__0  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendReqE__part__0Vsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendReqE__part__1  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendReqE__part__1Vsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvReqS N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvReqSVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvReqE N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvReqEVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInv__part__0  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInv__part__0Vsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInv__part__1  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInv__part__1Vsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendInvAck  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendInvAckVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvInvAck  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvInvAckVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendGntS  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendGntSVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_SendGntE N i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_SendGntEVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvGntS  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvGntSVsinv__7) done
    }

    moreover {
      assume d1: "(\<exists> i. i\<le>N\<and>r=n_RecvGntE  i)"
      have "invHoldForRule s f r (invariants N)"
      apply (cut_tac b2 d1, metis n_RecvGntEVsinv__7) done
    }

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

end