author | paulson <lp15@cam.ac.uk> |
Wed, 26 Apr 2017 15:53:35 +0100 | |
changeset 65583 | 8d53b3bebab4 |
parent 63648 | f9f3006a5579 |
child 67443 | 3abf6a722518 |
permissions | -rw-r--r-- |
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(* Title: HOL/Auth/Event.thy |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Datatype of events; function "spies"; freshness |
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"bad" agents have been broken by the Spy; their private keys and internal |
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stores are visible to him |
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*) |
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section\<open>Theory of Events for Security Protocols\<close> |
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theory Event imports Message begin |
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consts (*Initial states of agents -- parameter of the construction*) |
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initState :: "agent => msg set" |
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datatype |
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event = Says agent agent msg |
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| Gets agent msg |
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| Notes agent msg |
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consts |
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bad :: "agent set" \<comment> \<open>compromised agents\<close> |
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text\<open>Spy has access to his own key for spoof messages, but Server is secure\<close> |
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specification (bad) |
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Spy_in_bad [iff]: "Spy \<in> bad" |
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Server_not_bad [iff]: "Server \<notin> bad" |
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by (rule exI [of _ "{Spy}"], simp) |
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primrec knows :: "agent => event list => msg set" |
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where |
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knows_Nil: "knows A [] = initState A" |
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| knows_Cons: |
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"knows A (ev # evs) = |
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(if A = Spy then |
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(case ev of |
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Says A' B X => insert X (knows Spy evs) |
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| Gets A' X => knows Spy evs |
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| Notes A' X => |
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if A' \<in> bad then insert X (knows Spy evs) else knows Spy evs) |
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else |
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(case ev of |
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Says A' B X => |
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if A'=A then insert X (knows A evs) else knows A evs |
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| Gets A' X => |
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if A'=A then insert X (knows A evs) else knows A evs |
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| Notes A' X => |
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if A'=A then insert X (knows A evs) else knows A evs))" |
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(* |
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Case A=Spy on the Gets event |
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enforces the fact that if a message is received then it must have been sent, |
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therefore the oops case must use Notes |
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*) |
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text\<open>The constant "spies" is retained for compatibility's sake\<close> |
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abbreviation (input) |
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spies :: "event list => msg set" where |
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"spies == knows Spy" |
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(*Set of items that might be visible to somebody: |
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complement of the set of fresh items*) |
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primrec used :: "event list => msg set" |
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where |
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used_Nil: "used [] = (UN B. parts (initState B))" |
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| used_Cons: "used (ev # evs) = |
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(case ev of |
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Says A B X => parts {X} \<union> used evs |
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| Gets A X => used evs |
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| Notes A X => parts {X} \<union> used evs)" |
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\<comment>\<open>The case for @{term Gets} seems anomalous, but @{term Gets} always |
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follows @{term Says} in real protocols. Seems difficult to change. |
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See \<open>Gets_correct\<close> in theory \<open>Guard/Extensions.thy\<close>.\<close> |
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lemma Notes_imp_used [rule_format]: "Notes A X \<in> set evs --> X \<in> used evs" |
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apply (induct_tac evs) |
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apply (auto split: event.split) |
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done |
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lemma Says_imp_used [rule_format]: "Says A B X \<in> set evs --> X \<in> used evs" |
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apply (induct_tac evs) |
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apply (auto split: event.split) |
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done |
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subsection\<open>Function @{term knows}\<close> |
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(*Simplifying |
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parts(insert X (knows Spy evs)) = parts{X} \<union> parts(knows Spy evs). |
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This version won't loop with the simplifier.*) |
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lemmas parts_insert_knows_A = parts_insert [of _ "knows A evs"] for A evs |
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lemma knows_Spy_Says [simp]: |
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"knows Spy (Says A B X # evs) = insert X (knows Spy evs)" |
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by simp |
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text\<open>Letting the Spy see "bad" agents' notes avoids redundant case-splits |
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on whether @{term "A=Spy"} and whether @{term "A\<in>bad"}\<close> |
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lemma knows_Spy_Notes [simp]: |
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"knows Spy (Notes A X # evs) = |
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(if A:bad then insert X (knows Spy evs) else knows Spy evs)" |
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by simp |
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lemma knows_Spy_Gets [simp]: "knows Spy (Gets A X # evs) = knows Spy evs" |
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by simp |
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lemma knows_Spy_subset_knows_Spy_Says: |
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"knows Spy evs \<subseteq> knows Spy (Says A B X # evs)" |
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by (simp add: subset_insertI) |
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lemma knows_Spy_subset_knows_Spy_Notes: |
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"knows Spy evs \<subseteq> knows Spy (Notes A X # evs)" |
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by force |
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lemma knows_Spy_subset_knows_Spy_Gets: |
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"knows Spy evs \<subseteq> knows Spy (Gets A X # evs)" |
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by (simp add: subset_insertI) |
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text\<open>Spy sees what is sent on the traffic\<close> |
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lemma Says_imp_knows_Spy [rule_format]: |
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"Says A B X \<in> set evs --> X \<in> knows Spy evs" |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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done |
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lemma Notes_imp_knows_Spy [rule_format]: |
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"Notes A X \<in> set evs --> A: bad --> X \<in> knows Spy evs" |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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done |
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text\<open>Elimination rules: derive contradictions from old Says events containing |
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items known to be fresh\<close> |
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lemmas Says_imp_parts_knows_Spy = |
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Says_imp_knows_Spy [THEN parts.Inj, elim_format] |
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lemmas knows_Spy_partsEs = |
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Says_imp_parts_knows_Spy parts.Body [elim_format] |
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lemmas Says_imp_analz_Spy = Says_imp_knows_Spy [THEN analz.Inj] |
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text\<open>Compatibility for the old "spies" function\<close> |
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lemmas spies_partsEs = knows_Spy_partsEs |
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lemmas Says_imp_spies = Says_imp_knows_Spy |
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lemmas parts_insert_spies = parts_insert_knows_A [of _ Spy] |
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subsection\<open>Knowledge of Agents\<close> |
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lemma knows_subset_knows_Says: "knows A evs \<subseteq> knows A (Says A' B X # evs)" |
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by (simp add: subset_insertI) |
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lemma knows_subset_knows_Notes: "knows A evs \<subseteq> knows A (Notes A' X # evs)" |
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by (simp add: subset_insertI) |
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lemma knows_subset_knows_Gets: "knows A evs \<subseteq> knows A (Gets A' X # evs)" |
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by (simp add: subset_insertI) |
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text\<open>Agents know what they say\<close> |
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lemma Says_imp_knows [rule_format]: "Says A B X \<in> set evs --> X \<in> knows A evs" |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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apply blast |
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done |
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text\<open>Agents know what they note\<close> |
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lemma Notes_imp_knows [rule_format]: "Notes A X \<in> set evs --> X \<in> knows A evs" |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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apply blast |
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done |
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text\<open>Agents know what they receive\<close> |
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lemma Gets_imp_knows_agents [rule_format]: |
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"A \<noteq> Spy --> Gets A X \<in> set evs --> X \<in> knows A evs" |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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done |
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text\<open>What agents DIFFERENT FROM Spy know |
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was either said, or noted, or got, or known initially\<close> |
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lemma knows_imp_Says_Gets_Notes_initState [rule_format]: |
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"[| X \<in> knows A evs; A \<noteq> Spy |] ==> EX B. |
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Says A B X \<in> set evs | Gets A X \<in> set evs | Notes A X \<in> set evs | X \<in> initState A" |
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apply (erule rev_mp) |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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apply blast |
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done |
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text\<open>What the Spy knows -- for the time being -- |
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was either said or noted, or known initially\<close> |
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lemma knows_Spy_imp_Says_Notes_initState [rule_format]: |
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"[| X \<in> knows Spy evs |] ==> EX A B. |
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Says A B X \<in> set evs | Notes A X \<in> set evs | X \<in> initState Spy" |
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apply (erule rev_mp) |
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apply (induct_tac "evs") |
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apply (simp_all (no_asm_simp) split: event.split) |
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apply blast |
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done |
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lemma parts_knows_Spy_subset_used: "parts (knows Spy evs) \<subseteq> used evs" |
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apply (induct_tac "evs", force) |
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apply (simp add: parts_insert_knows_A knows_Cons add: event.split, blast) |
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done |
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lemmas usedI = parts_knows_Spy_subset_used [THEN subsetD, intro] |
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lemma initState_into_used: "X \<in> parts (initState B) ==> X \<in> used evs" |
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apply (induct_tac "evs") |
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apply (simp_all add: parts_insert_knows_A split: event.split, blast) |
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done |
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lemma used_Says [simp]: "used (Says A B X # evs) = parts{X} \<union> used evs" |
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by simp |
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lemma used_Notes [simp]: "used (Notes A X # evs) = parts{X} \<union> used evs" |
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by simp |
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lemma used_Gets [simp]: "used (Gets A X # evs) = used evs" |
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by simp |
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lemma used_nil_subset: "used [] \<subseteq> used evs" |
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apply simp |
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apply (blast intro: initState_into_used) |
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done |
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text\<open>NOTE REMOVAL--laws above are cleaner, as they don't involve "case"\<close> |
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declare knows_Cons [simp del] |
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used_Nil [simp del] used_Cons [simp del] |
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text\<open>For proving theorems of the form @{term "X \<notin> analz (knows Spy evs) --> P"} |
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New events added by induction to "evs" are discarded. Provided |
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this information isn't needed, the proof will be much shorter, since |
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it will omit complicated reasoning about @{term analz}.\<close> |
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lemmas analz_mono_contra = |
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knows_Spy_subset_knows_Spy_Says [THEN analz_mono, THEN contra_subsetD] |
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knows_Spy_subset_knows_Spy_Notes [THEN analz_mono, THEN contra_subsetD] |
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knows_Spy_subset_knows_Spy_Gets [THEN analz_mono, THEN contra_subsetD] |
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lemma knows_subset_knows_Cons: "knows A evs \<subseteq> knows A (e # evs)" |
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by (cases e, auto simp: knows_Cons) |
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lemma initState_subset_knows: "initState A \<subseteq> knows A evs" |
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apply (induct_tac evs, simp) |
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apply (blast intro: knows_subset_knows_Cons [THEN subsetD]) |
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done |
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text\<open>For proving \<open>new_keys_not_used\<close>\<close> |
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lemma keysFor_parts_insert: |
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"[| K \<in> keysFor (parts (insert X G)); X \<in> synth (analz H) |] |
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==> K \<in> keysFor (parts (G \<union> H)) | Key (invKey K) \<in> parts H" |
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by (force |
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dest!: parts_insert_subset_Un [THEN keysFor_mono, THEN [2] rev_subsetD] |
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analz_subset_parts [THEN keysFor_mono, THEN [2] rev_subsetD] |
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intro: analz_subset_parts [THEN subsetD] parts_mono [THEN [2] rev_subsetD]) |
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lemmas analz_impI = impI [where P = "Y \<notin> analz (knows Spy evs)"] for Y evs |
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ML |
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\<open> |
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fun analz_mono_contra_tac ctxt = |
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resolve_tac ctxt @{thms analz_impI} THEN' |
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REPEAT1 o (dresolve_tac ctxt @{thms analz_mono_contra}) |
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THEN' (mp_tac ctxt) |
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\<close> |
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method_setup analz_mono_contra = \<open> |
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Scan.succeed (fn ctxt => SIMPLE_METHOD (REPEAT_FIRST (analz_mono_contra_tac ctxt)))\<close> |
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"for proving theorems of the form X \<notin> analz (knows Spy evs) --> P" |
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subsubsection\<open>Useful for case analysis on whether a hash is a spoof or not\<close> |
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lemmas syan_impI = impI [where P = "Y \<notin> synth (analz (knows Spy evs))"] for Y evs |
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ML |
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\<open> |
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fun synth_analz_mono_contra_tac ctxt = |
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resolve_tac ctxt @{thms syan_impI} THEN' |
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REPEAT1 o |
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(dresolve_tac ctxt |
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[@{thm knows_Spy_subset_knows_Spy_Says} RS @{thm synth_analz_mono} RS @{thm contra_subsetD}, |
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@{thm knows_Spy_subset_knows_Spy_Notes} RS @{thm synth_analz_mono} RS @{thm contra_subsetD}, |
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@{thm knows_Spy_subset_knows_Spy_Gets} RS @{thm synth_analz_mono} RS @{thm contra_subsetD}]) |
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THEN' |
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mp_tac ctxt |
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\<close> |
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method_setup synth_analz_mono_contra = \<open> |
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Scan.succeed (fn ctxt => SIMPLE_METHOD (REPEAT_FIRST (synth_analz_mono_contra_tac ctxt)))\<close> |
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"for proving theorems of the form X \<notin> synth (analz (knows Spy evs)) --> P" |
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end |