(*  Title:      HOL/Auth/n_german.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 imports n_german_lemma_invs_on_rules n_german_on_inis
begin
lemma main:
assumes a1: "s \<in> reachableSet {andList (allInitSpecs N)} (rules N)"
and a2: "0 < N"
shows "\<forall> f. f \<in> (invariants N) --> formEval f s"
proof (rule consistentLemma)
show "consistent (invariants N) {andList (allInitSpecs N)} (rules N)"
proof (cut_tac a1, unfold consistent_def, rule conjI)
show "\<forall> f ini s. f \<in> (invariants N) --> ini \<in> {andList (allInitSpecs N)} --> formEval ini s --> formEval f s"
proof ((rule allI)+, (rule impI)+)
  fix f ini s
  assume b1: "f \<in> (invariants N)" and b2: "ini \<in> {andList (allInitSpecs N)}" and b3: "formEval ini s"
  have b4: "formEval (andList (allInitSpecs N)) s"
  apply (cut_tac b2 b3, simp) done
  show "formEval f s"
  apply (rule on_inis, cut_tac b1, assumption, cut_tac b2, assumption, cut_tac b3, assumption) done
qed
next show "\<forall> f r s. f \<in> invariants N --> r \<in> rules N --> invHoldForRule s f r (invariants N)"
proof ((rule allI)+, (rule impI)+)
  fix f r s
  assume b1: "f \<in> invariants N" and b2: "r \<in> rules N"
  show "invHoldForRule s f r (invariants N)"
  apply (rule invs_on_rules, cut_tac b1, assumption, cut_tac b2, assumption) done
qed
qed
next show "s \<in> reachableSet {andList (allInitSpecs N)} (rules N)"
  apply (metis a1) done
qed
end
