--- a/src/HOL/Auth/OtwayRees_AN.ML Mon Jul 14 12:44:09 1997 +0200
+++ b/src/HOL/Auth/OtwayRees_AN.ML Mon Jul 14 12:47:21 1997 +0200
@@ -21,7 +21,7 @@
(*A "possibility property": there are traces that reach the end*)
goal thy
"!!A B. [| A ~= B; A ~= Server; B ~= Server |] \
-\ ==> EX K. EX NA. EX evs: otway lost. \
+\ ==> EX K. EX NA. EX evs: otway. \
\ Says B A (Crypt (shrK A) {|Nonce NA, Agent A, Agent B, Key K|}) \
\ : set evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
@@ -33,7 +33,7 @@
(**** Inductive proofs about otway ****)
(*Nobody sends themselves messages*)
-goal thy "!!evs. evs : otway lost ==> ALL A X. Says A A X ~: set evs";
+goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set evs";
by (etac otway.induct 1);
by (Auto_tac());
qed_spec_mp "not_Says_to_self";
@@ -44,12 +44,12 @@
(** For reasoning about the encrypted portion of messages **)
goal thy "!!evs. Says S' B {|X, Crypt(shrK B) X'|} : set evs ==> \
-\ X : analz (sees lost Spy evs)";
+\ X : analz (sees Spy evs)";
by (blast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
qed "OR4_analz_sees_Spy";
goal thy "!!evs. Says Server B {|X, Crypt K' {|NB, a, Agent B, K|}|} \
-\ : set evs ==> K : parts (sees lost Spy evs)";
+\ : set evs ==> K : parts (sees Spy evs)";
by (blast_tac (!claset addSEs sees_Spy_partsEs) 1);
qed "Oops_parts_sees_Spy";
@@ -60,40 +60,34 @@
bind_thm ("OR4_parts_sees_Spy",
OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts));
-(*For proving the easier theorems about X ~: parts (sees lost Spy evs).
- We instantiate the variable to "lost" since leaving it as a Var would
- interfere with simplification.*)
-val parts_induct_tac =
- let val tac = forw_inst_tac [("lost","lost")]
- in etac otway.induct 1 THEN
- tac OR4_parts_sees_Spy 6 THEN
- tac Oops_parts_sees_Spy 7 THEN
- prove_simple_subgoals_tac 1
- end;
+(*For proving the easier theorems about X ~: parts (sees Spy 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
+ prove_simple_subgoals_tac i;
-(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY
+(** Theorems of the form X ~: parts (sees Spy 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 lost \
-\ ==> (Key (shrK A) : parts (sees lost Spy evs)) = (A : lost)";
-by parts_induct_tac;
+ "!!evs. evs : otway ==> (Key (shrK A) : parts (sees Spy evs)) = (A : lost)";
+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 lost \
-\ ==> (Key (shrK A) : analz (sees lost Spy evs)) = (A : lost)";
+ "!!evs. evs : otway ==> (Key (shrK A) : analz (sees Spy evs)) = (A : lost)";
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 lost Spy evs); \
-\ evs : otway lost |] ==> A:lost";
+goal thy "!!A. [| Key (shrK A) : parts (sees Spy evs); \
+\ evs : otway |] ==> A:lost";
by (blast_tac (!claset addDs [Spy_see_shrK]) 1);
qed "Spy_see_shrK_D";
@@ -102,9 +96,9 @@
(*Nobody can have used non-existent keys!*)
-goal thy "!!evs. evs : otway lost ==> \
-\ Key K ~: used evs --> K ~: keysFor (parts (sees lost Spy evs))";
-by parts_induct_tac;
+goal thy "!!evs. evs : otway ==> \
+\ Key K ~: used evs --> K ~: keysFor (parts (sees Spy evs))";
+by (parts_induct_tac 1);
(*Fake*)
by (best_tac
(!claset addIs [impOfSubs analz_subset_parts]
@@ -131,7 +125,7 @@
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}, \
\ Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \
\ : set evs; \
-\ evs : otway lost |] \
+\ evs : otway |] \
\ ==> K ~: range shrK & (EX i. NA = Nonce i) & (EX j. NB = Nonce j)";
by (etac rev_mp 1);
by (etac otway.induct 1);
@@ -140,10 +134,10 @@
qed "Says_Server_message_form";
-(*For proofs involving analz. We again instantiate the variable to "lost".*)
+(*For proofs involving analz.*)
val analz_sees_tac =
- dres_inst_tac [("lost","lost")] OR4_analz_sees_Spy 6 THEN
- forw_inst_tac [("lost","lost")] Says_Server_message_form 7 THEN
+ dtac OR4_analz_sees_Spy 6 THEN
+ forward_tac [Says_Server_message_form] 7 THEN
assume_tac 7 THEN
REPEAT ((eresolve_tac [exE, conjE] ORELSE' hyp_subst_tac) 7);
@@ -151,8 +145,8 @@
(****
The following is to prove theorems of the form
- Key K : analz (insert (Key KAB) (sees lost Spy evs)) ==>
- Key K : analz (sees lost Spy evs)
+ Key K : analz (insert (Key KAB) (sees Spy evs)) ==>
+ Key K : analz (sees Spy evs)
A more general formula must be proved inductively.
****)
@@ -162,10 +156,10 @@
(*The equality makes the induction hypothesis easier to apply*)
goal thy
- "!!evs. evs : otway lost ==> \
-\ ALL K KK. KK <= Compl (range shrK) --> \
-\ (Key K : analz (Key``KK Un (sees lost Spy evs))) = \
-\ (K : KK | Key K : analz (sees lost Spy evs))";
+ "!!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;
by (REPEAT_FIRST (resolve_tac [allI, impI]));
@@ -179,9 +173,9 @@
goal thy
- "!!evs. [| evs : otway lost; KAB ~: range shrK |] ==> \
-\ Key K : analz (insert (Key KAB) (sees lost Spy evs)) = \
-\ (K = KAB | Key K : analz (sees lost Spy evs))";
+ "!!evs. [| evs : otway; KAB ~: range shrK |] ==> \
+\ Key K : analz (insert (Key KAB) (sees Spy evs)) = \
+\ (K = KAB | Key K : analz (sees Spy evs))";
by (asm_simp_tac (analz_image_freshK_ss addsimps [analz_image_freshK]) 1);
qed "analz_insert_freshK";
@@ -189,7 +183,7 @@
(*** The Key K uniquely identifies the Server's message. **)
goal thy
- "!!evs. evs : otway lost ==> \
+ "!!evs. evs : otway ==> \
\ EX A' B' NA' NB'. ALL A B NA NB. \
\ Says Server B \
\ {|Crypt (shrK A) {|NA, Agent A, Agent B, K|}, \
@@ -218,7 +212,7 @@
\ {|Crypt (shrK A') {|NA', Agent A', Agent B', K|}, \
\ Crypt (shrK B') {|NB', Agent A', Agent B', K|}|} \
\ : set evs; \
-\ evs : otway lost |] \
+\ evs : otway |] \
\ ==> A=A' & B=B' & NA=NA' & NB=NB'";
by (prove_unique_tac lemma 1);
qed "unique_session_keys";
@@ -229,14 +223,14 @@
(*If the encrypted message appears then it originated with the Server!*)
goal thy
- "!!evs. [| A ~: lost; evs : otway lost |] \
-\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|} \
-\ : parts (sees lost Spy evs) \
+ "!!evs. [| A ~: lost; evs : otway |] \
+\ ==> Crypt (shrK A) {|NA, Agent A, Agent B, Key K|} \
+\ : parts (sees Spy 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;
+by (parts_induct_tac 1);
by (Fake_parts_insert_tac 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib])));
(*OR3*)
@@ -249,7 +243,7 @@
goal thy
"!!evs. [| Says B' A (Crypt (shrK A) {|NA, Agent A, Agent B, Key K|}) \
\ : set evs; \
-\ A ~: lost; evs : otway lost |] \
+\ A ~: lost; 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|}|} \
@@ -264,13 +258,13 @@
the premises, e.g. by having A=Spy **)
goal thy
- "!!evs. [| A ~: lost; B ~: lost; evs : otway lost |] \
+ "!!evs. [| A ~: lost; B ~: lost; 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 lost Spy evs)";
+\ Key K ~: analz (sees Spy evs)";
by (etac otway.induct 1);
by analz_sees_tac;
by (ALLGOALS
@@ -295,8 +289,8 @@
\ 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 lost |] \
-\ ==> Key K ~: analz (sees lost Spy evs)";
+\ A ~: lost; B ~: lost; evs : otway |] \
+\ ==> Key K ~: analz (sees Spy 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";
@@ -306,14 +300,14 @@
(*If the encrypted message appears then it originated with the Server!*)
goal thy
- "!!evs. [| B ~: lost; evs : otway lost |] \
-\ ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|} \
-\ : parts (sees lost Spy evs) \
+ "!!evs. [| B ~: lost; evs : otway |] \
+\ ==> Crypt (shrK B) {|NB, Agent A, Agent B, Key K|} \
+\ : parts (sees Spy 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;
+by (parts_induct_tac 1);
by (Fake_parts_insert_tac 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib])));
(*OR3*)
@@ -324,7 +318,7 @@
(*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 lost; \
+ "!!evs. [| B ~: lost; evs : otway; \
\ Says S' B {|X, Crypt (shrK B) {|NB, Agent A, Agent B, Key K|}|} \
\ : set evs |] \
\ ==> EX NA. Says Server B \