src/HOL/Auth/NS_Public.ML

 AddDs [impOfSubs Fake_parts_insert];
 
 AddIffs [Spy_in_bad];
 
 (*A "possibility property": there are traces that reach the end*)
-goal thy 
+Goal 
  "!!A B. A ~= B ==> EX NB. EX evs: ns_public.               \
 \                     Says A B (Crypt (pubK B) (Nonce NB)) : set evs";
 by (REPEAT (resolve_tac [exI,bexI] 1));
 by (rtac (ns_public.Nil RS ns_public.NS1 RS ns_public.NS2 RS ns_public.NS3) 2);
 by possibility_tac;

 
 
 (**** Inductive proofs about ns_public ****)
 
 (*Nobody sends themselves messages*)
-goal thy "!!evs. evs : ns_public ==> ALL A X. Says A A X ~: set evs";
+Goal "!!evs. evs : ns_public ==> ALL A X. Says A A X ~: set evs";
 by (etac ns_public.induct 1);
 by Auto_tac;
 qed_spec_mp "not_Says_to_self";
 Addsimps [not_Says_to_self];
 AddSEs   [not_Says_to_self RSN (2, rev_notE)];

 
 (** Theorems of the form X ~: parts (spies evs) imply that NOBODY
     sends messages containing X! **)
 
 (*Spy never sees another agent's private key! (unless it's bad at start)*)
-goal thy 
+Goal 
  "!!A. evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)";
 by (parts_induct_tac 1);
 by (Blast_tac 1);
 qed "Spy_see_priK";
 Addsimps [Spy_see_priK];
 
-goal thy 
+Goal 
  "!!A. evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)";
 by Auto_tac;
 qed "Spy_analz_priK";
 Addsimps [Spy_analz_priK];
 

 
 (**** Authenticity properties obtained from NS2 ****)
 
 (*It is impossible to re-use a nonce in both NS1 and NS2, provided the nonce
   is secret.  (Honest users generate fresh nonces.)*)
-goal thy 
+Goal 
  "!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
 \           Nonce NA ~: analz (spies evs);   evs : ns_public |]       \
 \ ==> Crypt (pubK C) {|NA', Nonce NA, Agent D|} ~: parts (spies evs)";
 by (etac rev_mp 1);
 by (etac rev_mp 1);

 (*Adding it to the claset slows down proofs...*)
 val nonce_NS1_NS2_E = no_nonce_NS1_NS2 RSN (2, rev_notE);
 
 
 (*Unicity for NS1: nonce NA identifies agents A and B*)
-goal thy 
+Goal 
  "!!evs. [| Nonce NA ~: analz (spies evs);  evs : ns_public |]      \
 \ ==> EX A' B'. ALL A B.                                            \
 \      Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs) --> \
 \      A=A' & B=B'";
 by (etac rev_mp 1);

 (*Fake*)
 by (Clarify_tac 1);
 by (Blast_tac 1);
 val lemma = result();
 
-goal thy 
+Goal 
  "!!evs. [| Crypt(pubK B)  {|Nonce NA, Agent A|}  : parts(spies evs); \
 \           Crypt(pubK B') {|Nonce NA, Agent A'|} : parts(spies evs); \
 \           Nonce NA ~: analz (spies evs);                            \
 \           evs : ns_public |]                                        \
 \        ==> A=A' & B=B'";

     etac ns_public.induct i   THEN
     ALLGOALS Asm_simp_tac;
 
 
 (*Secrecy: Spy does not see the nonce sent in msg NS1 if A and B are secure*)
-goal thy 
+Goal 
  "!!evs. [| Says A B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs;   \
 \           A ~: bad;  B ~: bad;  evs : ns_public |]                    \
 \        ==>  Nonce NA ~: analz (spies evs)";
 by (etac rev_mp 1);
 by (analz_induct_tac 1);

 qed "Spy_not_see_NA";
 
 
 (*Authentication for A: if she receives message 2 and has used NA
   to start a run, then B has sent message 2.*)
-goal thy 
+Goal 
  "!!evs. [| Says A  B (Crypt(pubK B) {|Nonce NA, Agent A|}) : set evs;  \
 \           Says B' A (Crypt(pubK A) {|Nonce NA, Nonce NB, Agent B|})   \
 \             : set evs;                                                \
 \           A ~: bad;  B ~: bad;  evs : ns_public |]                    \
 \        ==> Says B A (Crypt(pubK A) {|Nonce NA, Nonce NB, Agent B|})   \

 by (blast_tac (claset() addDs [Spy_not_see_NA]) 1);
 qed "A_trusts_NS2";
 
 
 (*If the encrypted message appears then it originated with Alice in NS1*)
-goal thy 
+Goal 
  "!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
 \           Nonce NA ~: analz (spies evs);                            \
 \           evs : ns_public |]                                        \
 \   ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs";
 by (etac rev_mp 1);

 (**** Authenticity properties obtained from NS2 ****)
 
 (*Unicity for NS2: nonce NB identifies nonce NA and agents A, B 
   [unicity of B makes Lowe's fix work]
   [proof closely follows that for unique_NA] *)
-goal thy 
+Goal 
  "!!evs. [| Nonce NB ~: analz (spies evs);  evs : ns_public |]            \
 \ ==> EX A' NA' B'. ALL A NA B.                                           \
 \      Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|} : parts (spies evs) \
 \         -->  A=A' & NA=NA' & B=B'";
 by (etac rev_mp 1);

 (*Fake*)
 by (Clarify_tac 1);
 by (Blast_tac 1);
 val lemma = result();
 
-goal thy 
+Goal 
  "!!evs. [| Crypt(pubK A)  {|Nonce NA, Nonce NB, Agent B|}   \
 \             : parts(spies evs);                            \
 \           Crypt(pubK A') {|Nonce NA', Nonce NB, Agent B'|} \
 \             : parts(spies evs);                            \
 \           Nonce NB ~: analz (spies evs);                   \

 
 AddDs [unique_NB];
 
 
 (*Secrecy: Spy does not see the nonce sent in msg NS2 if A and B are secure*)
-goal thy 
+Goal 
  "!!evs. [| Says B A (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \
 \             : set evs;                                              \
 \           A ~: bad;  B ~: bad;  evs : ns_public |]                \
 \ ==> Nonce NB ~: analz (spies evs)";
 by (etac rev_mp 1);

 AddDs [Spy_not_see_NB];
 
 
 (*Authentication for B: if he receives message 3 and has used NB
   in message 2, then A has sent message 3.*)
-goal thy 
+Goal 
  "!!evs. [| Says B A  (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \
 \             : set evs;                                               \
 \           Says A' B (Crypt (pubK B) (Nonce NB)): set evs;            \
 \           A ~: bad;  B ~: bad;  evs : ns_public |]                   \
 \        ==> Says A B (Crypt (pubK B) (Nonce NB)) : set evs";

     read_instantiate [("X","Crypt ?K {|?XX,?YY,?ZZ|}")] Says_imp_spies;
 
 
 (*If B receives NS3 and the nonce NB agrees with the nonce he joined with
   NA, then A initiated the run using NA.  SAME proof as B_trusts_NS3!*)
-goal thy 
+Goal 
  "!!evs. [| Says B A  (Crypt (pubK A) {|Nonce NA, Nonce NB, Agent B|}) \
 \             : set evs;                                               \
 \           Says A' B (Crypt (pubK B) (Nonce NB)): set evs;            \
 \           A ~: bad;  B ~: bad;  evs : ns_public |]                 \
 \    ==> Says A B (Crypt (pubK B) {|Nonce NA, Agent A|}) : set evs";