src/HOL/Auth/NS_Shared.ML

 AddDs [impOfSubs Fake_parts_insert];
 
 
 (*A "possibility property": there are traces that reach the end*)
 Goal 
- "!!A B. [| A ~= B; A ~= Server; B ~= Server |]       \
+ "[| A ~= B; A ~= Server; B ~= Server |]       \
 \        ==> EX N K. EX evs: ns_shared.               \
 \               Says A B (Crypt K {|Nonce N, Nonce N|}) : set evs";
 by (REPEAT (resolve_tac [exI,bexI] 1));
 by (rtac (ns_shared.Nil RS ns_shared.NS1 RS ns_shared.NS2 RS 
           ns_shared.NS3 RS ns_shared.NS4 RS ns_shared.NS5) 2);
 by possibility_tac;
 result();
 
 Goal 
- "!!A B. [| A ~= B; A ~= Server; B ~= Server |]       \
+ "[| A ~= B; A ~= Server; B ~= Server |]       \
 \        ==> EX evs: ns_shared.          \
 \               Says A B (Crypt ?K {|Nonce ?N, Nonce ?N|}) : set evs";
 by (REPEAT (resolve_tac [exI,bexI] 1));
 by (rtac (ns_shared.Nil RS ns_shared.NS1 RS ns_shared.NS2 RS 
           ns_shared.NS3 RS ns_shared.NS4 RS ns_shared.NS5) 2);
 by possibility_tac;
 
 (**** Inductive proofs about ns_shared ****)
 
 (*Nobody sends themselves messages*)
-Goal "!!evs. evs : ns_shared ==> ALL A X. Says A A X ~: set evs";
+Goal "evs : ns_shared ==> ALL A X. Says A A X ~: set evs";
 by (etac ns_shared.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)];
 
 (*For reasoning about the encrypted portion of message NS3*)
-Goal "!!evs. Says S A (Crypt KA {|N, B, K, X|}) : set evs \
+Goal "Says S A (Crypt KA {|N, B, K, X|}) : set evs \
 \                ==> X : parts (spies evs)";
 by (Blast_tac 1);
 qed "NS3_msg_in_parts_spies";
                               
 Goal
-    "!!evs. Says Server A (Crypt (shrK A) {|NA, B, K, X|}) : set evs \
+    "Says Server A (Crypt (shrK A) {|NA, B, K, X|}) : set evs \
 \           ==> K : parts (spies evs)";
 by (Blast_tac 1);
 qed "Oops_parts_spies";
 
 (*For proving the easier theorems about X ~: parts (spies evs).*)

 (** 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 bad at start)*)
 Goal 
- "!!evs. evs : ns_shared ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
+ "evs : ns_shared ==> (Key (shrK A) : parts (spies evs)) = (A : bad)";
 by (parts_induct_tac 1);
 by (ALLGOALS Blast_tac);
 qed "Spy_see_shrK";
 Addsimps [Spy_see_shrK];
 
 Goal 
- "!!evs. evs : ns_shared ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
+ "evs : ns_shared ==> (Key (shrK A) : analz (spies evs)) = (A : bad)";
 by Auto_tac;
 qed "Spy_analz_shrK";
 Addsimps [Spy_analz_shrK];
 
 AddSDs [Spy_see_shrK RSN (2, rev_iffD1), 
 	Spy_analz_shrK RSN (2, rev_iffD1)];
 
 
 (*Nobody can have used non-existent keys!*)
-Goal "!!evs. evs : ns_shared ==>      \
+Goal "evs : ns_shared ==>      \
 \         Key K ~: used evs --> K ~: keysFor (parts (spies evs))";
 by (parts_induct_tac 1);
 (*Fake*)
 by (blast_tac (claset() addSDs [keysFor_parts_insert]) 1);
 (*NS2, NS4, NS5*)

 
 (** Lemmas concerning the form of items passed in messages **)
 
 (*Describes the form of K, X and K' when the Server sends this message.*)
 Goal 
- "!!evs. [| Says Server A (Crypt K' {|N, Agent B, Key K, X|}) : set evs; \
+ "[| Says Server A (Crypt K' {|N, Agent B, Key K, X|}) : set evs; \
 \           evs : ns_shared |]                           \
 \        ==> K ~: range shrK &                           \
 \            X = (Crypt (shrK B) {|Key K, Agent A|}) &   \
 \            K' = shrK A";
 by (etac rev_mp 1);

 qed "Says_Server_message_form";
 
 
 (*If the encrypted message appears then it originated with the Server*)
 Goal
- "!!evs. [| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \
+ "[| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \
 \           A ~: bad;  evs : ns_shared |]                                 \
 \         ==> Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|})    \
 \               : set evs";
 by (etac rev_mp 1);
 by (parts_induct_tac 1);
 by (Blast_tac 1);
 qed "A_trusts_NS2";
 
 
 Goal
- "!!evs. [| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \
+ "[| Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \
 \           A ~: bad;  evs : ns_shared |]                                 \
 \         ==> K ~: range shrK &  X = (Crypt (shrK B) {|Key K, Agent A|})";
 by (blast_tac (claset() addSDs [A_trusts_NS2, Says_Server_message_form]) 1);
 qed "cert_A_form";
 
 
 (*EITHER describes the form of X when the following message is sent, 
   OR     reduces it to the Fake case.
   Use Says_Server_message_form if applicable.*)
 Goal 
- "!!evs. [| Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})      \
+ "[| Says S A (Crypt (shrK A) {|Nonce NA, Agent B, Key K, X|})      \
 \              : set evs;                                                  \
 \           evs : ns_shared |]                                             \
 \        ==> (K ~: range shrK & X = (Crypt (shrK B) {|Key K, Agent A|}))   \
 \            | X : analz (spies evs)";
 by (case_tac "A : bad" 1);

 
 (*NOT useful in this form, but it says that session keys are not used
   to encrypt messages containing other keys, in the actual protocol.
   We require that agents should behave like this subsequently also.*)
 Goal 
- "!!evs. [| evs : ns_shared;  Kab ~: range shrK |] ==>  \
+ "[| evs : ns_shared;  Kab ~: range shrK |] ==>  \
 \           (Crypt KAB X) : parts (spies evs) &         \
 \           Key K : parts {X} --> Key K : parts (spies evs)";
 by (parts_induct_tac 1);
 (*Fake*)
 by (blast_tac (claset() addSEs partsEs

 
 (** Session keys are not used to encrypt other session keys **)
 
 (*The equality makes the induction hypothesis easier to apply*)
 Goal  
- "!!evs. evs : ns_shared ==>                             \
+ "evs : ns_shared ==>                             \
 \  ALL K KK. KK <= Compl (range shrK) -->                \
 \            (Key K : analz (Key``KK Un (spies evs))) =  \
 \            (K : KK | Key K : analz (spies evs))";
 by (etac ns_shared.induct 1);
 by analz_spies_tac;

 by (spy_analz_tac 1);
 qed_spec_mp "analz_image_freshK";
 
 
 Goal
- "!!evs. [| evs : ns_shared;  KAB ~: range shrK |] ==>  \
+ "[| evs : ns_shared;  KAB ~: range shrK |] ==>  \
 \        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 session key K uniquely identifies the message **)
 
 Goal 
- "!!evs. evs : ns_shared ==>                                               \
+ "evs : ns_shared ==>                                               \
 \      EX A' NA' B' X'. ALL A NA B X.                                      \
 \       Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs \
 \       -->         A=A' & NA=NA' & B=B' & X=X'";
 by (etac ns_shared.induct 1);
 by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));

 by (Blast_tac 1);
 val lemma = result();
 
 (*In messages of this form, the session key uniquely identifies the rest*)
 Goal 
- "!!evs. [| Says Server A                                               \
+ "[| Says Server A                                               \
 \             (Crypt (shrK A) {|NA, Agent B, Key K, X|}) : set evs;     \ 
 \           Says Server A'                                              \
 \             (Crypt (shrK A') {|NA', Agent B', Key K, X'|}) : set evs; \
 \           evs : ns_shared |] ==> A=A' & NA=NA' & B=B' & X = X'";
 by (prove_unique_tac lemma 1);

 
 
 (** Crucial secrecy property: Spy does not see the keys sent in msg NS2 **)
 
 Goal 
- "!!evs. [| A ~: bad;  B ~: bad;  evs : ns_shared |]                   \
+ "[| A ~: bad;  B ~: bad;  evs : ns_shared |]                   \
 \        ==> Says Server A                                             \
 \              (Crypt (shrK A) {|NA, Agent B, Key K,                   \
 \                                Crypt (shrK B) {|Key K, Agent A|}|})  \
 \             : set evs -->                                            \
 \        (ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs) -->          \

 val lemma = result() RS mp RS mp RSN(2,rev_notE);
 
 
 (*Final version: Server's message in the most abstract form*)
 Goal 
- "!!evs. [| Says Server A                                        \
+ "[| Says Server A                                        \
 \              (Crypt K' {|NA, Agent B, Key K, X|}) : set evs;   \
 \           ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs;      \
 \           A ~: bad;  B ~: bad;  evs : ns_shared                \
 \        |] ==> Key K ~: analz (spies evs)";
 by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);

 A_trusts_NS2 RS Spy_not_see_encrypted_key;
 
 
 (*If the encrypted message appears then it originated with the Server*)
 Goal
- "!!evs. [| Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs);     \
+ "[| Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs);     \
 \           B ~: bad;  evs : ns_shared |]                              \
 \         ==> EX NA. Says Server A                                     \
 \              (Crypt (shrK A) {|NA, Agent B, Key K,                   \
 \                                Crypt (shrK B) {|Key K, Agent A|}|})  \
 \             : set evs";

 by (ALLGOALS Blast_tac);
 qed "B_trusts_NS3";
 
 
 Goal
- "!!evs. [| Crypt K (Nonce NB) : parts (spies evs);                   \
+ "[| Crypt K (Nonce NB) : parts (spies evs);                   \
 \           Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|})  \
 \              : set evs;                                             \
 \           Key K ~: analz (spies evs);                               \
 \           evs : ns_shared |]                  \
 \        ==> Says B A (Crypt K (Nonce NB)) : set evs";

 qed "A_trusts_NS4_lemma";
 
 
 (*This version no longer assumes that K is secure*)
 Goal
- "!!evs. [| Crypt K (Nonce NB) : parts (spies evs);                   \
+ "[| Crypt K (Nonce NB) : parts (spies evs);                   \
 \           Crypt (shrK A) {|NA, Agent B, Key K, X|} : parts (spies evs); \
 \           ALL NB. Notes Spy {|NA, NB, Key K|} ~: set evs;           \
 \           A ~: bad;  B ~: bad;  evs : ns_shared |]                  \
 \        ==> Says B A (Crypt K (Nonce NB)) : set evs";
 by (blast_tac (claset() addSIs [A_trusts_NS2, A_trusts_NS4_lemma]

 
 (*If the session key has been used in NS4 then somebody has forwarded
   component X in some instance of NS4.  Perhaps an interesting property, 
   but not needed (after all) for the proofs below.*)
 Goal
- "!!evs. [| Crypt K (Nonce NB) : parts (spies evs);     \
+ "[| Crypt K (Nonce NB) : parts (spies evs);     \
 \           Says Server A (Crypt (shrK A) {|NA, Agent B, Key K, X|})  \
 \             : set evs;                                              \
 \           Key K ~: analz (spies evs);                               \
 \           evs : ns_shared |]                              \
 \        ==> EX A'. Says A' B X : set evs";

 by (blast_tac (claset() addDs [unique_session_keys]) 1);
 qed "NS4_implies_NS3";
 
 
 Goal
- "!!evs. [| B ~: bad;  evs : ns_shared |]                              \
+ "[| B ~: bad;  evs : ns_shared |]                              \
 \        ==> Key K ~: analz (spies evs) -->                            \
 \            Says Server A                                             \
 \              (Crypt (shrK A) {|NA, Agent B, Key K,                   \
 \                                Crypt (shrK B) {|Key K, Agent A|}|})  \
 \             : set evs -->                                            \

 qed_spec_mp "B_trusts_NS5_lemma";
 
 
 (*Very strong Oops condition reveals protocol's weakness*)
 Goal
- "!!evs. [| Crypt K {|Nonce NB, Nonce NB|} : parts (spies evs);      \
+ "[| Crypt K {|Nonce NB, Nonce NB|} : parts (spies evs);      \
 \           Says B A (Crypt K (Nonce NB))  : set evs;                \
 \           Crypt (shrK B) {|Key K, Agent A|} : parts (spies evs);   \
 \           ALL NA NB. Notes Spy {|NA, NB, Key K|} ~: set evs;       \
 \           A ~: bad;  B ~: bad;  evs : ns_shared |]                 \
 \        ==> Says A B (Crypt K {|Nonce NB, Nonce NB|}) : set evs";