--- a/src/HOL/Auth/Yahalom.thy Thu Dec 10 21:31:24 2015 +0100
+++ b/src/HOL/Auth/Yahalom.thy Thu Dec 10 21:39:33 2015 +0100
@@ -3,16 +3,16 @@
Copyright 1996 University of Cambridge
*)
-section{*The Yahalom Protocol*}
+section\<open>The Yahalom Protocol\<close>
theory Yahalom imports Public begin
-text{*From page 257 of
+text\<open>From page 257 of
Burrows, Abadi and Needham (1989). A Logic of Authentication.
Proc. Royal Soc. 426
This theory has the prototypical example of a secrecy relation, KeyCryptNonce.
-*}
+\<close>
inductive_set yahalom :: "event list set"
where
@@ -53,10 +53,10 @@
# evs3 \<in> yahalom"
| YM4:
- --{*Alice receives the Server's (?) message, checks her Nonce, and
+ \<comment>\<open>Alice receives the Server's (?) message, checks her Nonce, and
uses the new session key to send Bob his Nonce. The premise
- @{term "A \<noteq> Server"} is needed for @{text Says_Server_not_range}.
- Alice can check that K is symmetric by its length.*}
+ @{term "A \<noteq> Server"} is needed for \<open>Says_Server_not_range\<close>.
+ Alice can check that K is symmetric by its length.\<close>
"[| evs4 \<in> yahalom; A \<noteq> Server; K \<in> symKeys;
Gets A {|Crypt(shrK A) {|Agent B, Key K, Nonce NA, Nonce NB|}, X|}
\<in> set evs4;
@@ -85,7 +85,7 @@
declare Fake_parts_insert_in_Un [dest]
declare analz_into_parts [dest]
-text{*A "possibility property": there are traces that reach the end*}
+text\<open>A "possibility property": there are traces that reach the end\<close>
lemma "[| A \<noteq> Server; K \<in> symKeys; Key K \<notin> used [] |]
==> \<exists>X NB. \<exists>evs \<in> yahalom.
Says A B {|X, Crypt K (Nonce NB)|} \<in> set evs"
@@ -99,13 +99,13 @@
done
-subsection{*Regularity Lemmas for Yahalom*}
+subsection\<open>Regularity Lemmas for Yahalom\<close>
lemma Gets_imp_Says:
"[| Gets B X \<in> set evs; evs \<in> yahalom |] ==> \<exists>A. Says A B X \<in> set evs"
by (erule rev_mp, erule yahalom.induct, auto)
-text{*Must be proved separately for each protocol*}
+text\<open>Must be proved separately for each protocol\<close>
lemma Gets_imp_knows_Spy:
"[| Gets B X \<in> set evs; evs \<in> yahalom |] ==> X \<in> knows Spy evs"
by (blast dest!: Gets_imp_Says Says_imp_knows_Spy)
@@ -114,7 +114,7 @@
declare Gets_imp_analz_Spy [dest]
-text{*Lets us treat YM4 using a similar argument as for the Fake case.*}
+text\<open>Lets us treat YM4 using a similar argument as for the Fake case.\<close>
lemma YM4_analz_knows_Spy:
"[| Gets A {|Crypt (shrK A) Y, X|} \<in> set evs; evs \<in> yahalom |]
==> X \<in> analz (knows Spy evs)"
@@ -123,16 +123,16 @@
lemmas YM4_parts_knows_Spy =
YM4_analz_knows_Spy [THEN analz_into_parts]
-text{*For Oops*}
+text\<open>For Oops\<close>
lemma YM4_Key_parts_knows_Spy:
"Says Server A {|Crypt (shrK A) {|B,K,NA,NB|}, X|} \<in> set evs
==> K \<in> parts (knows Spy evs)"
by (metis parts.Body parts.Fst parts.Snd Says_imp_knows_Spy parts.Inj)
-text{*Theorems of the form @{term "X \<notin> parts (knows Spy evs)"} imply
-that NOBODY sends messages containing X! *}
+text\<open>Theorems of the form @{term "X \<notin> parts (knows Spy evs)"} imply
+that NOBODY sends messages containing X!\<close>
-text{*Spy never sees a good agent's shared key!*}
+text\<open>Spy never sees a good agent's shared key!\<close>
lemma Spy_see_shrK [simp]:
"evs \<in> yahalom ==> (Key (shrK A) \<in> parts (knows Spy evs)) = (A \<in> bad)"
by (erule yahalom.induct, force,
@@ -146,29 +146,29 @@
"[|Key (shrK A) \<in> parts (knows Spy evs); evs \<in> yahalom|] ==> A \<in> bad"
by (blast dest: Spy_see_shrK)
-text{*Nobody can have used non-existent keys!
- Needed to apply @{text analz_insert_Key}*}
+text\<open>Nobody can have used non-existent keys!
+ Needed to apply \<open>analz_insert_Key\<close>\<close>
lemma new_keys_not_used [simp]:
"[|Key K \<notin> used evs; K \<in> symKeys; evs \<in> yahalom|]
==> K \<notin> keysFor (parts (spies evs))"
apply (erule rev_mp)
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy, simp_all)
-txt{*Fake*}
+txt\<open>Fake\<close>
apply (force dest!: keysFor_parts_insert, auto)
done
-text{*Earlier, all protocol proofs declared this theorem.
- But only a few proofs need it, e.g. Yahalom and Kerberos IV.*}
+text\<open>Earlier, all protocol proofs declared this theorem.
+ But only a few proofs need it, e.g. Yahalom and Kerberos IV.\<close>
lemma new_keys_not_analzd:
"[|K \<in> symKeys; evs \<in> yahalom; Key K \<notin> used evs|]
==> K \<notin> keysFor (analz (knows Spy evs))"
by (blast dest: new_keys_not_used intro: keysFor_mono [THEN subsetD])
-text{*Describes the form of K when the Server sends this message. Useful for
- Oops as well as main secrecy property.*}
+text\<open>Describes the form of K when the Server sends this message. Useful for
+ Oops as well as main secrecy property.\<close>
lemma Says_Server_not_range [simp]:
"[| Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|}
\<in> set evs; evs \<in> yahalom |]
@@ -176,7 +176,7 @@
by (erule rev_mp, erule yahalom.induct, simp_all)
-subsection{*Secrecy Theorems*}
+subsection\<open>Secrecy Theorems\<close>
(****
The following is to prove theorems of the form
@@ -187,7 +187,7 @@
A more general formula must be proved inductively.
****)
-text{* Session keys are not used to encrypt other session keys *}
+text\<open>Session keys are not used to encrypt other session keys\<close>
lemma analz_image_freshK [rule_format]:
"evs \<in> yahalom ==>
@@ -207,7 +207,7 @@
by (simp only: analz_image_freshK analz_image_freshK_simps)
-text{*The Key K uniquely identifies the Server's message.*}
+text\<open>The Key K uniquely identifies the Server's message.\<close>
lemma unique_session_keys:
"[| Says Server A
{|Crypt (shrK A) {|Agent B, Key K, na, nb|}, X|} \<in> set evs;
@@ -217,12 +217,12 @@
==> A=A' & B=B' & na=na' & nb=nb'"
apply (erule rev_mp, erule rev_mp)
apply (erule yahalom.induct, simp_all)
-txt{*YM3, by freshness, and YM4*}
+txt\<open>YM3, by freshness, and YM4\<close>
apply blast+
done
-text{*Crucial secrecy property: Spy does not see the keys sent in msg YM3*}
+text\<open>Crucial secrecy property: Spy does not see the keys sent in msg YM3\<close>
lemma secrecy_lemma:
"[| A \<notin> bad; B \<notin> bad; evs \<in> yahalom |]
==> Says Server A
@@ -233,11 +233,11 @@
Key K \<notin> analz (knows Spy evs)"
apply (erule yahalom.induct, force,
drule_tac [6] YM4_analz_knows_Spy)
-apply (simp_all add: pushes analz_insert_eq analz_insert_freshK, spy_analz) --{*Fake*}
-apply (blast dest: unique_session_keys)+ --{*YM3, Oops*}
+apply (simp_all add: pushes analz_insert_eq analz_insert_freshK, spy_analz) \<comment>\<open>Fake\<close>
+apply (blast dest: unique_session_keys)+ \<comment>\<open>YM3, Oops\<close>
done
-text{*Final version*}
+text\<open>Final version\<close>
lemma Spy_not_see_encrypted_key:
"[| Says Server A
{|Crypt (shrK A) {|Agent B, Key K, na, nb|},
@@ -249,9 +249,9 @@
by (blast dest: secrecy_lemma)
-subsubsection{* Security Guarantee for A upon receiving YM3 *}
+subsubsection\<open>Security Guarantee for A upon receiving YM3\<close>
-text{*If the encrypted message appears then it originated with the Server*}
+text\<open>If the encrypted message appears then it originated with the Server\<close>
lemma A_trusts_YM3:
"[| Crypt (shrK A) {|Agent B, Key K, na, nb|} \<in> parts (knows Spy evs);
A \<notin> bad; evs \<in> yahalom |]
@@ -262,12 +262,12 @@
apply (erule rev_mp)
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy, simp_all)
-txt{*Fake, YM3*}
+txt\<open>Fake, YM3\<close>
apply blast+
done
-text{*The obvious combination of @{text A_trusts_YM3} with
- @{text Spy_not_see_encrypted_key}*}
+text\<open>The obvious combination of \<open>A_trusts_YM3\<close> with
+ \<open>Spy_not_see_encrypted_key\<close>\<close>
lemma A_gets_good_key:
"[| Crypt (shrK A) {|Agent B, Key K, na, nb|} \<in> parts (knows Spy evs);
Notes Spy {|na, nb, Key K|} \<notin> set evs;
@@ -276,10 +276,10 @@
by (metis A_trusts_YM3 secrecy_lemma)
-subsubsection{* Security Guarantees for B upon receiving YM4 *}
+subsubsection\<open>Security Guarantees for B upon receiving YM4\<close>
-text{*B knows, by the first part of A's message, that the Server distributed
- the key for A and B. But this part says nothing about nonces.*}
+text\<open>B knows, by the first part of A's message, that the Server distributed
+ the key for A and B. But this part says nothing about nonces.\<close>
lemma B_trusts_YM4_shrK:
"[| Crypt (shrK B) {|Agent A, Key K|} \<in> parts (knows Spy evs);
B \<notin> bad; evs \<in> yahalom |]
@@ -291,15 +291,15 @@
apply (erule rev_mp)
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy, simp_all)
-txt{*Fake, YM3*}
+txt\<open>Fake, YM3\<close>
apply blast+
done
-text{*B knows, by the second part of A's message, that the Server
+text\<open>B knows, by the second part of A's message, that the Server
distributed the key quoting nonce NB. This part says nothing about
agent names. Secrecy of NB is crucial. Note that @{term "Nonce NB
\<notin> analz(knows Spy evs)"} must be the FIRST antecedent of the
- induction formula.*}
+ induction formula.\<close>
lemma B_trusts_YM4_newK [rule_format]:
"[|Crypt K (Nonce NB) \<in> parts (knows Spy evs);
@@ -312,20 +312,20 @@
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy)
apply (analz_mono_contra, simp_all)
-txt{*Fake, YM3*}
+txt\<open>Fake, YM3\<close>
apply blast
apply blast
-txt{*YM4. A is uncompromised because NB is secure
- A's certificate guarantees the existence of the Server message*}
+txt\<open>YM4. A is uncompromised because NB is secure
+ A's certificate guarantees the existence of the Server message\<close>
apply (blast dest!: Gets_imp_Says Crypt_Spy_analz_bad
dest: Says_imp_spies
parts.Inj [THEN parts.Fst, THEN A_trusts_YM3])
done
-subsubsection{* Towards proving secrecy of Nonce NB *}
+subsubsection\<open>Towards proving secrecy of Nonce NB\<close>
-text{*Lemmas about the predicate KeyWithNonce*}
+text\<open>Lemmas about the predicate KeyWithNonce\<close>
lemma KeyWithNonceI:
"Says Server A
@@ -349,14 +349,14 @@
"KeyWithNonce K NB (Gets A X # evs) = KeyWithNonce K NB evs"
by (simp add: KeyWithNonce_def)
-text{*A fresh key cannot be associated with any nonce
- (with respect to a given trace). *}
+text\<open>A fresh key cannot be associated with any nonce
+ (with respect to a given trace).\<close>
lemma fresh_not_KeyWithNonce:
"Key K \<notin> used evs ==> ~ KeyWithNonce K NB evs"
by (unfold KeyWithNonce_def, blast)
-text{*The Server message associates K with NB' and therefore not with any
- other nonce NB.*}
+text\<open>The Server message associates K with NB' and therefore not with any
+ other nonce NB.\<close>
lemma Says_Server_KeyWithNonce:
"[| Says Server A {|Crypt (shrK A) {|Agent B, Key K, na, Nonce NB'|}, X|}
\<in> set evs;
@@ -365,13 +365,13 @@
by (unfold KeyWithNonce_def, blast dest: unique_session_keys)
-text{*The only nonces that can be found with the help of session keys are
+text\<open>The only nonces that can be found with the help of session keys are
those distributed as nonce NB by the Server. The form of the theorem
- recalls @{text analz_image_freshK}, but it is much more complicated.*}
+ recalls \<open>analz_image_freshK\<close>, but it is much more complicated.\<close>
-text{*As with @{text analz_image_freshK}, we take some pains to express the
- property as a logical equivalence so that the simplifier can apply it.*}
+text\<open>As with \<open>analz_image_freshK\<close>, we take some pains to express the
+ property as a logical equivalence so that the simplifier can apply it.\<close>
lemma Nonce_secrecy_lemma:
"P --> (X \<in> analz (G Un H)) --> (X \<in> analz H) ==>
P --> (X \<in> analz (G Un H)) = (X \<in> analz H)"
@@ -392,29 +392,29 @@
analz_image_freshK fresh_not_KeyWithNonce
imp_disj_not1 (*Moves NBa\<noteq>NB to the front*)
Says_Server_KeyWithNonce)
-txt{*For Oops, simplification proves @{prop "NBa\<noteq>NB"}. By
+txt\<open>For Oops, simplification proves @{prop "NBa\<noteq>NB"}. By
@{term Says_Server_KeyWithNonce}, we get @{prop "~ KeyWithNonce K NB
evs"}; then simplification can apply the induction hypothesis with
- @{term "KK = {K}"}.*}
-txt{*Fake*}
+ @{term "KK = {K}"}.\<close>
+txt\<open>Fake\<close>
apply spy_analz
-txt{*YM2*}
+txt\<open>YM2\<close>
apply blast
-txt{*YM3*}
+txt\<open>YM3\<close>
apply blast
-txt{*YM4*}
+txt\<open>YM4\<close>
apply (erule_tac V = "\<forall>KK. P KK" for P in thin_rl, clarify)
-txt{*If @{prop "A \<in> bad"} then @{term NBa} is known, therefore
+txt\<open>If @{prop "A \<in> bad"} then @{term NBa} is known, therefore
@{prop "NBa \<noteq> NB"}. Previous two steps make the next step
- faster.*}
+ faster.\<close>
apply (metis A_trusts_YM3 Gets_imp_analz_Spy Gets_imp_knows_Spy KeyWithNonce_def
Spy_analz_shrK analz.Fst analz.Snd analz_shrK_Decrypt parts.Fst parts.Inj)
done
-text{*Version required below: if NB can be decrypted using a session key then
+text\<open>Version required below: if NB can be decrypted using a session key then
it was distributed with that key. The more general form above is required
- for the induction to carry through.*}
+ for the induction to carry through.\<close>
lemma single_Nonce_secrecy:
"[| Says Server A
{|Crypt (shrK A) {|Agent B, Key KAB, na, Nonce NB'|}, X|}
@@ -427,7 +427,7 @@
Nonce_secrecy Says_Server_KeyWithNonce)
-subsubsection{* The Nonce NB uniquely identifies B's message. *}
+subsubsection\<open>The Nonce NB uniquely identifies B's message.\<close>
lemma unique_NB:
"[| Crypt (shrK B) {|Agent A, Nonce NA, nb|} \<in> parts (knows Spy evs);
@@ -437,13 +437,13 @@
apply (erule rev_mp, erule rev_mp)
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy, simp_all)
-txt{*Fake, and YM2 by freshness*}
+txt\<open>Fake, and YM2 by freshness\<close>
apply blast+
done
-text{*Variant useful for proving secrecy of NB. Because nb is assumed to be
- secret, we no longer must assume B, B' not bad.*}
+text\<open>Variant useful for proving secrecy of NB. Because nb is assumed to be
+ secret, we no longer must assume B, B' not bad.\<close>
lemma Says_unique_NB:
"[| Says C S {|X, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|}
\<in> set evs;
@@ -455,7 +455,7 @@
dest: Says_imp_spies unique_NB parts.Inj analz.Inj)
-subsubsection{* A nonce value is never used both as NA and as NB *}
+subsubsection\<open>A nonce value is never used both as NA and as NB\<close>
lemma no_nonce_YM1_YM2:
"[|Crypt (shrK B') {|Agent A', Nonce NB, nb'|} \<in> parts(knows Spy evs);
@@ -465,11 +465,11 @@
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy)
apply (analz_mono_contra, simp_all)
-txt{*Fake, YM2*}
+txt\<open>Fake, YM2\<close>
apply blast+
done
-text{*The Server sends YM3 only in response to YM2.*}
+text\<open>The Server sends YM3 only in response to YM2.\<close>
lemma Says_Server_imp_YM2:
"[| Says Server A {|Crypt (shrK A) {|Agent B, k, na, nb|}, X|} \<in> set evs;
evs \<in> yahalom |]
@@ -477,7 +477,7 @@
\<in> set evs"
by (erule rev_mp, erule yahalom.induct, auto)
-text{*A vital theorem for B, that nonce NB remains secure from the Spy.*}
+text\<open>A vital theorem for B, that nonce NB remains secure from the Spy.\<close>
lemma Spy_not_see_NB :
"[| Says B Server
{|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, Nonce NB|}|}
@@ -490,36 +490,36 @@
frule_tac [6] YM4_analz_knows_Spy)
apply (simp_all add: split_ifs pushes new_keys_not_analzd analz_insert_eq
analz_insert_freshK)
-txt{*Fake*}
+txt\<open>Fake\<close>
apply spy_analz
-txt{*YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!*}
+txt\<open>YM1: NB=NA is impossible anyway, but NA is secret because it is fresh!\<close>
apply blast
-txt{*YM2*}
+txt\<open>YM2\<close>
apply blast
-txt{*Prove YM3 by showing that no NB can also be an NA*}
+txt\<open>Prove YM3 by showing that no NB can also be an NA\<close>
apply (blast dest!: no_nonce_YM1_YM2 dest: Gets_imp_Says Says_unique_NB)
-txt{*LEVEL 7: YM4 and Oops remain*}
+txt\<open>LEVEL 7: YM4 and Oops remain\<close>
apply (clarify, simp add: all_conj_distrib)
-txt{*YM4: key K is visible to Spy, contradicting session key secrecy theorem*}
-txt{*Case analysis on Aa:bad; PROOF FAILED problems
- use @{text Says_unique_NB} to identify message components: @{term "Aa=A"}, @{term "Ba=B"}*}
+txt\<open>YM4: key K is visible to Spy, contradicting session key secrecy theorem\<close>
+txt\<open>Case analysis on Aa:bad; PROOF FAILED problems
+ use \<open>Says_unique_NB\<close> to identify message components: @{term "Aa=A"}, @{term "Ba=B"}\<close>
apply (blast dest!: Says_unique_NB analz_shrK_Decrypt
parts.Inj [THEN parts.Fst, THEN A_trusts_YM3]
dest: Gets_imp_Says Says_imp_spies Says_Server_imp_YM2
Spy_not_see_encrypted_key)
-txt{*Oops case: if the nonce is betrayed now, show that the Oops event is
- covered by the quantified Oops assumption.*}
+txt\<open>Oops case: if the nonce is betrayed now, show that the Oops event is
+ covered by the quantified Oops assumption.\<close>
apply (clarify, simp add: all_conj_distrib)
apply (frule Says_Server_imp_YM2, assumption)
apply (metis Gets_imp_Says Says_Server_not_range Says_unique_NB no_nonce_YM1_YM2 parts.Snd single_Nonce_secrecy spies_partsEs(1))
done
-text{*B's session key guarantee from YM4. The two certificates contribute to a
+text\<open>B's session key guarantee from YM4. The two certificates contribute to a
single conclusion about the Server's message. Note that the "Notes Spy"
- assumption must quantify over @{text \<forall>} POSSIBLE keys instead of our particular K.
+ assumption must quantify over \<open>\<forall>\<close> POSSIBLE keys instead of our particular K.
If this run is broken and the spy substitutes a certificate containing an
- old key, B has no means of telling.*}
+ old key, B has no means of telling.\<close>
lemma B_trusts_YM4:
"[| Gets B {|Crypt (shrK B) {|Agent A, Key K|},
Crypt K (Nonce NB)|} \<in> set evs;
@@ -538,8 +538,8 @@
-text{*The obvious combination of @{text B_trusts_YM4} with
- @{text Spy_not_see_encrypted_key}*}
+text\<open>The obvious combination of \<open>B_trusts_YM4\<close> with
+ \<open>Spy_not_see_encrypted_key\<close>\<close>
lemma B_gets_good_key:
"[| Gets B {|Crypt (shrK B) {|Agent A, Key K|},
Crypt K (Nonce NB)|} \<in> set evs;
@@ -552,9 +552,9 @@
by (metis B_trusts_YM4 Spy_not_see_encrypted_key)
-subsection{*Authenticating B to A*}
+subsection\<open>Authenticating B to A\<close>
-text{*The encryption in message YM2 tells us it cannot be faked.*}
+text\<open>The encryption in message YM2 tells us it cannot be faked.\<close>
lemma B_Said_YM2 [rule_format]:
"[|Crypt (shrK B) {|Agent A, Nonce NA, nb|} \<in> parts (knows Spy evs);
evs \<in> yahalom|]
@@ -563,11 +563,11 @@
\<in> set evs"
apply (erule rev_mp, erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy, simp_all)
-txt{*Fake*}
+txt\<open>Fake\<close>
apply blast
done
-text{*If the server sends YM3 then B sent YM2*}
+text\<open>If the server sends YM3 then B sent YM2\<close>
lemma YM3_auth_B_to_A_lemma:
"[|Says Server A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|}
\<in> set evs; evs \<in> yahalom|]
@@ -575,11 +575,11 @@
Says B Server {|Agent B, Crypt (shrK B) {|Agent A, Nonce NA, nb|}|}
\<in> set evs"
apply (erule rev_mp, erule yahalom.induct, simp_all)
-txt{*YM3, YM4*}
+txt\<open>YM3, YM4\<close>
apply (blast dest!: B_Said_YM2)+
done
-text{*If A receives YM3 then B has used nonce NA (and therefore is alive)*}
+text\<open>If A receives YM3 then B has used nonce NA (and therefore is alive)\<close>
lemma YM3_auth_B_to_A:
"[| Gets A {|Crypt (shrK A) {|Agent B, Key K, Nonce NA, nb|}, X|}
\<in> set evs;
@@ -590,12 +590,12 @@
not_parts_not_analz)
-subsection{*Authenticating A to B using the certificate
- @{term "Crypt K (Nonce NB)"}*}
+subsection\<open>Authenticating A to B using the certificate
+ @{term "Crypt K (Nonce NB)"}\<close>
-text{*Assuming the session key is secure, if both certificates are present then
+text\<open>Assuming the session key is secure, if both certificates are present then
A has said NB. We can't be sure about the rest of A's message, but only
- NB matters for freshness.*}
+ NB matters for freshness.\<close>
lemma A_Said_YM3_lemma [rule_format]:
"evs \<in> yahalom
==> Key K \<notin> analz (knows Spy evs) -->
@@ -606,23 +606,23 @@
apply (erule yahalom.induct, force,
frule_tac [6] YM4_parts_knows_Spy)
apply (analz_mono_contra, simp_all)
-txt{*Fake*}
+txt\<open>Fake\<close>
apply blast
-txt{*YM3: by @{text new_keys_not_used}, the message
- @{term "Crypt K (Nonce NB)"} could not exist*}
+txt\<open>YM3: by \<open>new_keys_not_used\<close>, the message
+ @{term "Crypt K (Nonce NB)"} could not exist\<close>
apply (force dest!: Crypt_imp_keysFor)
-txt{*YM4: was @{term "Crypt K (Nonce NB)"} the very last message?
- If not, use the induction hypothesis*}
+txt\<open>YM4: was @{term "Crypt K (Nonce NB)"} the very last message?
+ If not, use the induction hypothesis\<close>
apply (simp add: ex_disj_distrib)
-txt{*yes: apply unicity of session keys*}
+txt\<open>yes: apply unicity of session keys\<close>
apply (blast dest!: Gets_imp_Says A_trusts_YM3 B_trusts_YM4_shrK
Crypt_Spy_analz_bad
dest: Says_imp_knows_Spy [THEN parts.Inj] unique_session_keys)
done
-text{*If B receives YM4 then A has used nonce NB (and therefore is alive).
+text\<open>If B receives YM4 then A has used nonce NB (and therefore is alive).
Moreover, A associates K with NB (thus is talking about the same run).
- Other premises guarantee secrecy of K.*}
+ Other premises guarantee secrecy of K.\<close>
lemma YM4_imp_A_Said_YM3 [rule_format]:
"[| Gets B {|Crypt (shrK B) {|Agent A, Key K|},
Crypt K (Nonce NB)|} \<in> set evs;