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|    440  |    440  | 
|    441 abbreviation |    441 abbreviation | 
|    442   spies_max :: "event list => msg set" where |    442   spies_max :: "event list => msg set" where | 
|    443   "spies_max evs == knows_max Spy evs" |    443   "spies_max evs == knows_max Spy evs" | 
|    444  |    444  | 
|    445 subsubsection\<open>basic facts about @{term knows_max}\<close> |    445 subsubsection\<open>basic facts about \<^term>\<open>knows_max\<close>\<close> | 
|    446  |    446  | 
|    447 lemma spies_max_spies [iff]: "spies_max evs = spies evs" |    447 lemma spies_max_spies [iff]: "spies_max evs = spies evs" | 
|    448 by (induct evs, auto simp: knows_max_def split: event.splits) |    448 by (induct evs, auto simp: knows_max_def split: event.splits) | 
|    449  |    449  | 
|    450 lemma knows_max'_Cons: "knows_max' A (ev#evs) |    450 lemma knows_max'_Cons: "knows_max' A (ev#evs) |