src/HOL/Auth/OtwayRees_AN.ML

 
 
 (** For reasoning about the encrypted portion of messages **)
 
 goal thy "!!evs. Says S' B {|X, Crypt(shrK B) X'|} : set evs ==> \
-\                X : analz (sees Spy evs)";
-by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
-qed "OR4_analz_sees_Spy";
+\                X : analz (spies evs)";
+by (blast_tac (!claset addSDs [Says_imp_spies RS analz.Inj]) 1);
+qed "OR4_analz_spies";
 
 goal thy "!!evs. Says Server B {|X, Crypt K' {|NB, a, Agent B, K|}|} \
-\                  : set evs ==> K : parts (sees Spy evs)";
-by (blast_tac (!claset addSEs sees_Spy_partsEs) 1);
-qed "Oops_parts_sees_Spy";
-
-(*OR4_analz_sees_Spy lets us treat those cases using the same 
+\                  : set evs ==> K : parts (spies evs)";
+by (blast_tac (!claset addSEs spies_partsEs) 1);
+qed "Oops_parts_spies";
+
+(*OR4_analz_spies lets us treat those cases using the same 
   argument as for the Fake case.  This is possible for most, but not all,
   proofs, since Fake messages originate from the Spy. *)
 
-bind_thm ("OR4_parts_sees_Spy",
-          OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
-
-(*For proving the easier theorems about X ~: parts (sees Spy evs).*)
+bind_thm ("OR4_parts_spies",
+          OR4_analz_spies RS (impOfSubs analz_subset_parts));
+
+(*For proving the easier theorems about X ~: parts (spies evs).*)
 fun parts_induct_tac i = 
     etac otway.induct i			THEN 
-    forward_tac [Oops_parts_sees_Spy] (i+6) THEN
-    forward_tac [OR4_parts_sees_Spy]  (i+5) THEN
+    forward_tac [Oops_parts_spies] (i+6) THEN
+    forward_tac [OR4_parts_spies]  (i+5) THEN
     prove_simple_subgoals_tac  i;
 
 
-(** Theorems of the form X ~: parts (sees Spy evs) imply that NOBODY
+(** Theorems of the form X ~: parts (spies evs) imply that NOBODY
     sends messages containing X! **)
 
-(*Spy never sees another agent's shared key! (unless it's lost at start)*)
-goal thy 
- "!!evs. evs : otway ==> (Key (shrK A) : parts (sees Spy evs)) = (A : lost)";
+(*Spy never sees another agent's shared key! (unless it's bad at start)*)
+goal thy 
+ "!!evs. evs : otway ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
 by (parts_induct_tac 1);
 by (Fake_parts_insert_tac 1);
 by (Blast_tac 1);
 qed "Spy_see_shrK";
 Addsimps [Spy_see_shrK];
 
 goal thy 
- "!!evs. evs : otway ==> (Key (shrK A) : analz (sees Spy evs)) = (A : lost)";
+ "!!evs. evs : otway ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
 by (auto_tac(!claset addDs [impOfSubs analz_subset_parts], !simpset));
 qed "Spy_analz_shrK";
 Addsimps [Spy_analz_shrK];
 
-goal thy  "!!A. [| Key (shrK A) : parts (sees Spy evs);       \
-\                  evs : otway |] ==> A:lost";
+goal thy  "!!A. [| Key (shrK A) : parts (spies evs); evs : otway |] ==> A:bad";
 by (blast_tac (!claset addDs [Spy_see_shrK]) 1);
 qed "Spy_see_shrK_D";
 
 bind_thm ("Spy_analz_shrK_D", analz_subset_parts RS subsetD RS Spy_see_shrK_D);
 AddSDs [Spy_see_shrK_D, Spy_analz_shrK_D];
 
 
 (*Nobody can have used non-existent keys!*)
 goal thy "!!evs. evs : otway ==>          \
-\         Key K ~: used evs --> K ~: keysFor (parts (sees Spy evs))";
+\         Key K ~: used evs --> K ~: keysFor (parts (spies evs))";
 by (parts_induct_tac 1);
 (*Fake*)
 by (best_tac
       (!claset addIs [impOfSubs analz_subset_parts]
                addDs [impOfSubs (analz_subset_parts RS keysFor_mono),

 by (Blast_tac 1);
 qed "Says_Server_message_form";
 
 
 (*For proofs involving analz.*)
-val analz_sees_tac = 
-    dtac OR4_analz_sees_Spy 6 THEN
+val analz_spies_tac = 
+    dtac OR4_analz_spies 6 THEN
     forward_tac [Says_Server_message_form] 7 THEN
     assume_tac 7 THEN
     REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7);
 
 
 (****
  The following is to prove theorems of the form
 
-  Key K : analz (insert (Key KAB) (sees Spy evs)) ==>
-  Key K : analz (sees Spy evs)
+  Key K : analz (insert (Key KAB) (spies evs)) ==>
+  Key K : analz (spies evs)
 
  A more general formula must be proved inductively.
 ****)
 
 

 
 (*The equality makes the induction hypothesis easier to apply*)
 goal thy  
  "!!evs. evs : otway ==>                                    \
 \  ALL K KK. KK <= Compl (range shrK) -->                   \
-\            (Key K : analz (Key``KK Un (sees Spy evs))) =  \
-\            (K : KK | Key K : analz (sees Spy evs))";
-by (etac otway.induct 1);
-by analz_sees_tac;
+\            (Key K : analz (Key``KK Un (spies evs))) =  \
+\            (K : KK | Key K : analz (spies evs))";
+by (etac otway.induct 1);
+by analz_spies_tac;
 by (REPEAT_FIRST (resolve_tac [allI, impI]));
 by (REPEAT_FIRST (rtac analz_image_freshK_lemma ));
 by (ALLGOALS (asm_simp_tac analz_image_freshK_ss));
 (*Fake*) 
 by (spy_analz_tac 2);

 qed_spec_mp "analz_image_freshK";
 
 
 goal thy
  "!!evs. [| evs : otway;  KAB ~: range shrK |] ==>          \
-\        Key K : analz (insert (Key KAB) (sees Spy evs)) =  \
-\        (K = KAB | Key K : analz (sees Spy evs))";
+\        Key K : analz (insert (Key KAB) (spies evs)) =  \
+\        (K = KAB | Key K : analz (spies evs))";
 by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
 qed "analz_insert_freshK";
 
 
 (*** The Key K uniquely identifies the Server's  message. **)

 by (ex_strip_tac 2);
 by (Blast_tac 2);
 by (expand_case_tac "K = ?y" 1);
 by (REPEAT (ares_tac [refl,exI,impI,conjI] 2));
 (*...we assume X is a recent message and handle this case by contradiction*)
-by (blast_tac (!claset addSEs sees_Spy_partsEs
+by (blast_tac (!claset addSEs spies_partsEs
                        delrules[conjI] (*prevent splitup into 4 subgoals*)) 1);
 val lemma = result();
 
 
 goal thy 

 
 (**** Authenticity properties relating to NA ****)
 
 (*If the encrypted message appears then it originated with the Server!*)
 goal thy 
- "!!evs. [| A ~: lost;  evs : otway |]                 \
-\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}   \
-\      : parts (sees Spy evs)                          \
+ "!!evs. [| A ~: bad;  evs : otway |]                 \
+\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|} : parts (spies evs) \
 \     --> (EX NB. Says Server B                                          \
 \                  {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},     \
 \                    Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|}    \
 \                  : set evs)";
 by (parts_induct_tac 1);

 (*Corollary: if A receives B's OR4 message then it originated with the Server.
   Freshness may be inferred from nonce NA.*)
 goal thy 
  "!!evs. [| Says B' A (Crypt (shrK A) {|NA, Agent A, Agent B, Key K|})  \
 \            : set evs;                                                 \
-\           A ~: lost;  evs : otway |]                                  \
+\           A ~: bad;  evs : otway |]                                  \
 \        ==> EX NB. Says Server B                                       \
 \                    {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},  \
 \                      Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \
 \                   : set evs";
 by (blast_tac (!claset addSIs [NA_Crypt_imp_Server_msg]
-                      addEs  sees_Spy_partsEs) 1);
+                      addEs  spies_partsEs) 1);
 qed "A_trusts_OR4";
 
 
 (** Crucial secrecy property: Spy does not see the keys sent in msg OR3
     Does not in itself guarantee security: an attack could violate 
     the premises, e.g. by having A=Spy **)
 
 goal thy 
- "!!evs. [| A ~: lost;  B ~: lost;  evs : otway |]                 \
+ "!!evs. [| A ~: bad;  B ~: bad;  evs : otway |]                 \
 \        ==> Says Server B                                         \
 \             {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},    \
 \               Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|}   \
 \            : set evs -->                                         \
 \            Says B Spy {|NA, NB, Key K|} ~: set evs -->           \
-\            Key K ~: analz (sees Spy evs)";
-by (etac otway.induct 1);
-by analz_sees_tac;
+\            Key K ~: analz (spies evs)";
+by (etac otway.induct 1);
+by analz_spies_tac;
 by (ALLGOALS
     (asm_simp_tac (!simpset addcongs [conj_cong, if_weak_cong] 
                             addsimps [analz_insert_eq, analz_insert_freshK]
                             setloop split_tac [expand_if])));
 (*Oops*)
 by (blast_tac (!claset addSDs [unique_session_keys]) 4);
 (*OR4*) 
 by (Blast_tac 3);
 (*OR3*)
-by (blast_tac (!claset addSEs sees_Spy_partsEs
+by (blast_tac (!claset addSEs spies_partsEs
                        addIs [impOfSubs analz_subset_parts]) 2);
 (*Fake*) 
 by (spy_analz_tac 1);
 val lemma = result() RS mp RS mp RSN(2,rev_notE);
 

  "!!evs. [| Says Server B                                           \
 \              {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},    \
 \                Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|}   \
 \             : set evs;                                            \
 \           Says B Spy {|NA, NB, Key K|} ~: set evs;                \
-\           A ~: lost;  B ~: lost;  evs : otway |]                  \
-\        ==> Key K ~: analz (sees Spy evs)";
+\           A ~: bad;  B ~: bad;  evs : otway |]                  \
+\        ==> Key K ~: analz (spies evs)";
 by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
 by (blast_tac (!claset addSEs [lemma]) 1);
 qed "Spy_not_see_encrypted_key";
 
 
 (**** Authenticity properties relating to NB ****)
 
 (*If the encrypted message appears then it originated with the Server!*)
 goal thy 
- "!!evs. [| B ~: lost;  evs : otway |]                                 \
-\    ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}                \
-\         : parts (sees Spy evs)                                       \
+ "!!evs. [| B ~: bad;  evs : otway |]                                 \
+\    ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|} : parts (spies evs) \
 \        --> (EX NA. Says Server B                                          \
 \                     {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},     \
 \                       Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|}    \
 \                     : set evs)";
 by (parts_induct_tac 1);

 
 
 (*Guarantee for B: if it gets a well-formed certificate then the Server
   has sent the correct message in round 3.*)
 goal thy 
- "!!evs. [| B ~: lost;  evs : otway;                                        \
+ "!!evs. [| B ~: bad;  evs : otway;                                        \
 \           Says S' B {|X, Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \
 \            : set evs |]                                                   \
 \        ==> EX NA. Says Server B                                           \
 \                     {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|},     \
 \                       Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|}    \
 \                     : set evs";
 by (blast_tac (!claset addSIs [NB_Crypt_imp_Server_msg]
-                       addEs  sees_Spy_partsEs) 1);
+                       addEs  spies_partsEs) 1);
 qed "B_trusts_OR3";