(*  Title:      HOL/Auth/n_german_lemma_inv__53_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__53_on_rules imports n_german_lemma_on_inv__53
begin
section{*All lemmas on causal relation between inv__53*}
lemma lemma_inv__53_on_rules:
  assumes b1: "r \<in> rules N" and b2: "(\<exists> p__Inv0 p__Inv2. p__Inv0\<le>N\<and>p__Inv2\<le>N\<and>p__Inv0~=p__Inv2\<and>f=inv__53  p__Inv0 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) 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__53) done
    }

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

end