--- a/src/HOL/Auth/Message.thy Thu Dec 10 21:31:24 2015 +0100
+++ b/src/HOL/Auth/Message.thy Thu Dec 10 21:39:33 2015 +0100
@@ -6,7 +6,7 @@
Inductive relations "parts", "analz" and "synth"
*)
-section{*Theory of Agents and Messages for Security Protocols*}
+section\<open>Theory of Agents and Messages for Security Protocols\<close>
theory Message
imports Main
@@ -20,8 +20,8 @@
key = nat
consts
- all_symmetric :: bool --{*true if all keys are symmetric*}
- invKey :: "key=>key" --{*inverse of a symmetric key*}
+ all_symmetric :: bool \<comment>\<open>true if all keys are symmetric\<close>
+ invKey :: "key=>key" \<comment>\<open>inverse of a symmetric key\<close>
specification (invKey)
invKey [simp]: "invKey (invKey K) = K"
@@ -29,26 +29,26 @@
by (rule exI [of _ id], auto)
-text{*The inverse of a symmetric key is itself; that of a public key
- is the private key and vice versa*}
+text\<open>The inverse of a symmetric key is itself; that of a public key
+ is the private key and vice versa\<close>
definition symKeys :: "key set" where
"symKeys == {K. invKey K = K}"
-datatype --{*We allow any number of friendly agents*}
+datatype \<comment>\<open>We allow any number of friendly agents\<close>
agent = Server | Friend nat | Spy
datatype
- msg = Agent agent --{*Agent names*}
- | Number nat --{*Ordinary integers, timestamps, ...*}
- | Nonce nat --{*Unguessable nonces*}
- | Key key --{*Crypto keys*}
- | Hash msg --{*Hashing*}
- | MPair msg msg --{*Compound messages*}
- | Crypt key msg --{*Encryption, public- or shared-key*}
+ msg = Agent agent \<comment>\<open>Agent names\<close>
+ | Number nat \<comment>\<open>Ordinary integers, timestamps, ...\<close>
+ | Nonce nat \<comment>\<open>Unguessable nonces\<close>
+ | Key key \<comment>\<open>Crypto keys\<close>
+ | Hash msg \<comment>\<open>Hashing\<close>
+ | MPair msg msg \<comment>\<open>Compound messages\<close>
+ | Crypt key msg \<comment>\<open>Encryption, public- or shared-key\<close>
-text{*Concrete syntax: messages appear as {|A,B,NA|}, etc...*}
+text\<open>Concrete syntax: messages appear as {|A,B,NA|}, etc...\<close>
syntax
"_MTuple" :: "['a, args] => 'a * 'b" ("(2{|_,/ _|})")
@@ -61,15 +61,15 @@
definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
- --{*Message Y paired with a MAC computed with the help of X*}
+ \<comment>\<open>Message Y paired with a MAC computed with the help of X\<close>
"Hash[X] Y == {| Hash{|X,Y|}, Y|}"
definition keysFor :: "msg set => key set" where
- --{*Keys useful to decrypt elements of a message set*}
+ \<comment>\<open>Keys useful to decrypt elements of a message set\<close>
"keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
-subsubsection{*Inductive Definition of All Parts" of a Message*}
+subsubsection\<open>Inductive Definition of All Parts" of a Message\<close>
inductive_set
parts :: "msg set => msg set"
@@ -81,7 +81,7 @@
| Body: "Crypt K X \<in> parts H ==> X \<in> parts H"
-text{*Monotonicity*}
+text\<open>Monotonicity\<close>
lemma parts_mono: "G \<subseteq> H ==> parts(G) \<subseteq> parts(H)"
apply auto
apply (erule parts.induct)
@@ -89,7 +89,7 @@
done
-text{*Equations hold because constructors are injective.*}
+text\<open>Equations hold because constructors are injective.\<close>
lemma Friend_image_eq [simp]: "(Friend x \<in> Friend`A) = (x:A)"
by auto
@@ -100,13 +100,13 @@
by auto
-subsubsection{*Inverse of keys *}
+subsubsection\<open>Inverse of keys\<close>
lemma invKey_eq [simp]: "(invKey K = invKey K') = (K=K')"
by (metis invKey)
-subsection{*keysFor operator*}
+subsection\<open>keysFor operator\<close>
lemma keysFor_empty [simp]: "keysFor {} = {}"
by (unfold keysFor_def, blast)
@@ -117,7 +117,7 @@
lemma keysFor_UN [simp]: "keysFor (\<Union>i\<in>A. H i) = (\<Union>i\<in>A. keysFor (H i))"
by (unfold keysFor_def, blast)
-text{*Monotonicity*}
+text\<open>Monotonicity\<close>
lemma keysFor_mono: "G \<subseteq> H ==> keysFor(G) \<subseteq> keysFor(H)"
by (unfold keysFor_def, blast)
@@ -150,7 +150,7 @@
by (unfold keysFor_def, blast)
-subsection{*Inductive relation "parts"*}
+subsection\<open>Inductive relation "parts"\<close>
lemma MPair_parts:
"[| {|X,Y|} \<in> parts H;
@@ -158,10 +158,10 @@
by (blast dest: parts.Fst parts.Snd)
declare MPair_parts [elim!] parts.Body [dest!]
-text{*NB These two rules are UNSAFE in the formal sense, as they discard the
+text\<open>NB These two rules are UNSAFE in the formal sense, as they discard the
compound message. They work well on THIS FILE.
- @{text MPair_parts} is left as SAFE because it speeds up proofs.
- The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.*}
+ \<open>MPair_parts\<close> is left as SAFE because it speeds up proofs.
+ The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.\<close>
lemma parts_increasing: "H \<subseteq> parts(H)"
by blast
@@ -176,12 +176,12 @@
lemma parts_emptyE [elim!]: "X\<in> parts{} ==> P"
by simp
-text{*WARNING: loops if H = {Y}, therefore must not be repeated!*}
+text\<open>WARNING: loops if H = {Y}, therefore must not be repeated!\<close>
lemma parts_singleton: "X\<in> parts H ==> \<exists>Y\<in>H. X\<in> parts {Y}"
by (erule parts.induct, fast+)
-subsubsection{*Unions *}
+subsubsection\<open>Unions\<close>
lemma parts_Un_subset1: "parts(G) \<union> parts(H) \<subseteq> parts(G \<union> H)"
by (intro Un_least parts_mono Un_upper1 Un_upper2)
@@ -197,8 +197,8 @@
lemma parts_insert: "parts (insert X H) = parts {X} \<union> parts H"
by (metis insert_is_Un parts_Un)
-text{*TWO inserts to avoid looping. This rewrite is better than nothing.
- But its behaviour can be strange.*}
+text\<open>TWO inserts to avoid looping. This rewrite is better than nothing.
+ But its behaviour can be strange.\<close>
lemma parts_insert2:
"parts (insert X (insert Y H)) = parts {X} \<union> parts {Y} \<union> parts H"
by (metis Un_commute Un_empty_right Un_insert_right insert_is_Un parts_Un)
@@ -214,12 +214,12 @@
lemma parts_UN [simp]: "parts(\<Union>x\<in>A. H x) = (\<Union>x\<in>A. parts(H x))"
by (intro equalityI parts_UN_subset1 parts_UN_subset2)
-text{*Added to simplify arguments to parts, analz and synth.
- NOTE: the UN versions are no longer used!*}
+text\<open>Added to simplify arguments to parts, analz and synth.
+ NOTE: the UN versions are no longer used!\<close>
-text{*This allows @{text blast} to simplify occurrences of
- @{term "parts(G\<union>H)"} in the assumption.*}
+text\<open>This allows \<open>blast\<close> to simplify occurrences of
+ @{term "parts(G\<union>H)"} in the assumption.\<close>
lemmas in_parts_UnE = parts_Un [THEN equalityD1, THEN subsetD, THEN UnE]
declare in_parts_UnE [elim!]
@@ -227,7 +227,7 @@
lemma parts_insert_subset: "insert X (parts H) \<subseteq> parts(insert X H)"
by (blast intro: parts_mono [THEN [2] rev_subsetD])
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma parts_partsD [dest!]: "X\<in> parts (parts H) ==> X\<in> parts H"
by (erule parts.induct, blast+)
@@ -241,7 +241,7 @@
lemma parts_trans: "[| X\<in> parts G; G \<subseteq> parts H |] ==> X\<in> parts H"
by (metis parts_subset_iff set_mp)
-text{*Cut*}
+text\<open>Cut\<close>
lemma parts_cut:
"[| Y\<in> parts (insert X G); X\<in> parts H |] ==> Y\<in> parts (G \<union> H)"
by (blast intro: parts_trans)
@@ -250,7 +250,7 @@
by (metis insert_absorb parts_idem parts_insert)
-subsubsection{*Rewrite rules for pulling out atomic messages *}
+subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
lemmas parts_insert_eq_I = equalityI [OF subsetI parts_insert_subset]
@@ -308,7 +308,7 @@
done
-text{*In any message, there is an upper bound N on its greatest nonce.*}
+text\<open>In any message, there is an upper bound N on its greatest nonce.\<close>
lemma msg_Nonce_supply: "\<exists>N. \<forall>n. N\<le>n --> Nonce n \<notin> parts {msg}"
proof (induct msg)
case (Nonce n)
@@ -316,15 +316,15 @@
by simp (metis Suc_n_not_le_n)
next
case (MPair X Y)
- then show ?case --{*metis works out the necessary sum itself!*}
+ then show ?case \<comment>\<open>metis works out the necessary sum itself!\<close>
by (simp add: parts_insert2) (metis le_trans nat_le_linear)
qed auto
-subsection{*Inductive relation "analz"*}
+subsection\<open>Inductive relation "analz"\<close>
-text{*Inductive definition of "analz" -- what can be broken down from a set of
+text\<open>Inductive definition of "analz" -- what can be broken down from a set of
messages, including keys. A form of downward closure. Pairs can
- be taken apart; messages decrypted with known keys. *}
+ be taken apart; messages decrypted with known keys.\<close>
inductive_set
analz :: "msg set => msg set"
@@ -337,14 +337,14 @@
"[|Crypt K X \<in> analz H; Key(invKey K): analz H|] ==> X \<in> analz H"
-text{*Monotonicity; Lemma 1 of Lowe's paper*}
+text\<open>Monotonicity; Lemma 1 of Lowe's paper\<close>
lemma analz_mono: "G\<subseteq>H ==> analz(G) \<subseteq> analz(H)"
apply auto
apply (erule analz.induct)
apply (auto dest: analz.Fst analz.Snd)
done
-text{*Making it safe speeds up proofs*}
+text\<open>Making it safe speeds up proofs\<close>
lemma MPair_analz [elim!]:
"[| {|X,Y|} \<in> analz H;
[| X \<in> analz H; Y \<in> analz H |] ==> P
@@ -374,22 +374,22 @@
lemmas analz_insertI = subset_insertI [THEN analz_mono, THEN [2] rev_subsetD]
-subsubsection{*General equational properties *}
+subsubsection\<open>General equational properties\<close>
lemma analz_empty [simp]: "analz{} = {}"
apply safe
apply (erule analz.induct, blast+)
done
-text{*Converse fails: we can analz more from the union than from the
- separate parts, as a key in one might decrypt a message in the other*}
+text\<open>Converse fails: we can analz more from the union than from the
+ separate parts, as a key in one might decrypt a message in the other\<close>
lemma analz_Un: "analz(G) \<union> analz(H) \<subseteq> analz(G \<union> H)"
by (intro Un_least analz_mono Un_upper1 Un_upper2)
lemma analz_insert: "insert X (analz H) \<subseteq> analz(insert X H)"
by (blast intro: analz_mono [THEN [2] rev_subsetD])
-subsubsection{*Rewrite rules for pulling out atomic messages *}
+subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
lemmas analz_insert_eq_I = equalityI [OF subsetI analz_insert]
@@ -417,7 +417,7 @@
apply (erule analz.induct, auto)
done
-text{*Can only pull out Keys if they are not needed to decrypt the rest*}
+text\<open>Can only pull out Keys if they are not needed to decrypt the rest\<close>
lemma analz_insert_Key [simp]:
"K \<notin> keysFor (analz H) ==>
analz (insert (Key K) H) = insert (Key K) (analz H)"
@@ -436,7 +436,7 @@
apply (blast intro: analz.Fst analz.Snd)+
done
-text{*Can pull out enCrypted message if the Key is not known*}
+text\<open>Can pull out enCrypted message if the Key is not known\<close>
lemma analz_insert_Crypt:
"Key (invKey K) \<notin> analz H
==> analz (insert (Crypt K X) H) = insert (Crypt K X) (analz H)"
@@ -466,10 +466,10 @@
insert (Crypt K X) (analz (insert X H))"
by (intro equalityI lemma1 lemma2)
-text{*Case analysis: either the message is secure, or it is not! Effective,
-but can cause subgoals to blow up! Use with @{text "split_if"}; apparently
-@{text "split_tac"} does not cope with patterns such as @{term"analz (insert
-(Crypt K X) H)"} *}
+text\<open>Case analysis: either the message is secure, or it is not! Effective,
+but can cause subgoals to blow up! Use with \<open>split_if\<close>; apparently
+\<open>split_tac\<close> does not cope with patterns such as @{term"analz (insert
+(Crypt K X) H)"}\<close>
lemma analz_Crypt_if [simp]:
"analz (insert (Crypt K X) H) =
(if (Key (invKey K) \<in> analz H)
@@ -478,7 +478,7 @@
by (simp add: analz_insert_Crypt analz_insert_Decrypt)
-text{*This rule supposes "for the sake of argument" that we have the key.*}
+text\<open>This rule supposes "for the sake of argument" that we have the key.\<close>
lemma analz_insert_Crypt_subset:
"analz (insert (Crypt K X) H) \<subseteq>
insert (Crypt K X) (analz (insert X H))"
@@ -493,7 +493,7 @@
done
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma analz_analzD [dest!]: "X\<in> analz (analz H) ==> X\<in> analz H"
by (erule analz.induct, blast+)
@@ -507,7 +507,7 @@
lemma analz_trans: "[| X\<in> analz G; G \<subseteq> analz H |] ==> X\<in> analz H"
by (drule analz_mono, blast)
-text{*Cut; Lemma 2 of Lowe*}
+text\<open>Cut; Lemma 2 of Lowe\<close>
lemma analz_cut: "[| Y\<in> analz (insert X H); X\<in> analz H |] ==> Y\<in> analz H"
by (erule analz_trans, blast)
@@ -515,14 +515,14 @@
"Y: analz (insert X H) ==> X: analz H --> Y: analz H"
*)
-text{*This rewrite rule helps in the simplification of messages that involve
+text\<open>This rewrite rule helps in the simplification of messages that involve
the forwarding of unknown components (X). Without it, removing occurrences
- of X can be very complicated. *}
+ of X can be very complicated.\<close>
lemma analz_insert_eq: "X\<in> analz H ==> analz (insert X H) = analz H"
by (metis analz_cut analz_insert_eq_I insert_absorb)
-text{*A congruence rule for "analz" *}
+text\<open>A congruence rule for "analz"\<close>
lemma analz_subset_cong:
"[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |]
@@ -538,14 +538,14 @@
"analz H = analz H' ==> analz(insert X H) = analz(insert X H')"
by (force simp only: insert_def intro!: analz_cong)
-text{*If there are no pairs or encryptions then analz does nothing*}
+text\<open>If there are no pairs or encryptions then analz does nothing\<close>
lemma analz_trivial:
"[| \<forall>X Y. {|X,Y|} \<notin> H; \<forall>X K. Crypt K X \<notin> H |] ==> analz H = H"
apply safe
apply (erule analz.induct, blast+)
done
-text{*These two are obsolete (with a single Spy) but cost little to prove...*}
+text\<open>These two are obsolete (with a single Spy) but cost little to prove...\<close>
lemma analz_UN_analz_lemma:
"X\<in> analz (\<Union>i\<in>A. analz (H i)) ==> X\<in> analz (\<Union>i\<in>A. H i)"
apply (erule analz.induct)
@@ -556,12 +556,12 @@
by (blast intro: analz_UN_analz_lemma analz_mono [THEN [2] rev_subsetD])
-subsection{*Inductive relation "synth"*}
+subsection\<open>Inductive relation "synth"\<close>
-text{*Inductive definition of "synth" -- what can be built up from a set of
+text\<open>Inductive definition of "synth" -- what can be built up from a set of
messages. A form of upward closure. Pairs can be built, messages
encrypted with known keys. Agent names are public domain.
- Numbers can be guessed, but Nonces cannot be. *}
+ Numbers can be guessed, but Nonces cannot be.\<close>
inductive_set
synth :: "msg set => msg set"
@@ -574,12 +574,12 @@
| MPair [intro]: "[|X \<in> synth H; Y \<in> synth H|] ==> {|X,Y|} \<in> synth H"
| Crypt [intro]: "[|X \<in> synth H; Key(K) \<in> H|] ==> Crypt K X \<in> synth H"
-text{*Monotonicity*}
+text\<open>Monotonicity\<close>
lemma synth_mono: "G\<subseteq>H ==> synth(G) \<subseteq> synth(H)"
by (auto, erule synth.induct, auto)
-text{*NO @{text Agent_synth}, as any Agent name can be synthesized.
- The same holds for @{term Number}*}
+text\<open>NO \<open>Agent_synth\<close>, as any Agent name can be synthesized.
+ The same holds for @{term Number}\<close>
inductive_simps synth_simps [iff]:
"Nonce n \<in> synth H"
@@ -591,17 +591,17 @@
lemma synth_increasing: "H \<subseteq> synth(H)"
by blast
-subsubsection{*Unions *}
+subsubsection\<open>Unions\<close>
-text{*Converse fails: we can synth more from the union than from the
- separate parts, building a compound message using elements of each.*}
+text\<open>Converse fails: we can synth more from the union than from the
+ separate parts, building a compound message using elements of each.\<close>
lemma synth_Un: "synth(G) \<union> synth(H) \<subseteq> synth(G \<union> H)"
by (intro Un_least synth_mono Un_upper1 Un_upper2)
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)"
by (blast intro: synth_mono [THEN [2] rev_subsetD])
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma synth_synthD [dest!]: "X\<in> synth (synth H) ==> X\<in> synth H"
by (erule synth.induct, auto)
@@ -615,7 +615,7 @@
lemma synth_trans: "[| X\<in> synth G; G \<subseteq> synth H |] ==> X\<in> synth H"
by (drule synth_mono, blast)
-text{*Cut; Lemma 2 of Lowe*}
+text\<open>Cut; Lemma 2 of Lowe\<close>
lemma synth_cut: "[| Y\<in> synth (insert X H); X\<in> synth H |] ==> Y\<in> synth H"
by (erule synth_trans, blast)
@@ -629,7 +629,7 @@
by (unfold keysFor_def, blast)
-subsubsection{*Combinations of parts, analz and synth *}
+subsubsection\<open>Combinations of parts, analz and synth\<close>
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H"
apply (rule equalityI)
@@ -656,12 +656,12 @@
by (metis Un_empty_right analz_synth_Un)
-subsubsection{*For reasoning about the Fake rule in traces *}
+subsubsection\<open>For reasoning about the Fake rule in traces\<close>
lemma parts_insert_subset_Un: "X\<in> G ==> parts(insert X H) \<subseteq> parts G \<union> parts H"
by (metis UnCI Un_upper2 insert_subset parts_Un parts_mono)
-text{*More specifically for Fake. See also @{text Fake_parts_sing} below *}
+text\<open>More specifically for Fake. See also \<open>Fake_parts_sing\<close> below\<close>
lemma Fake_parts_insert:
"X \<in> synth (analz H) ==>
parts (insert X H) \<subseteq> synth (analz H) \<union> parts H"
@@ -673,8 +673,8 @@
==> Z \<in> synth (analz H) \<union> parts H"
by (metis Fake_parts_insert set_mp)
-text{*@{term H} is sometimes @{term"Key ` KK \<union> spies evs"}, so can't put
- @{term "G=H"}.*}
+text\<open>@{term H} is sometimes @{term"Key ` KK \<union> spies evs"}, so can't put
+ @{term "G=H"}.\<close>
lemma Fake_analz_insert:
"X\<in> synth (analz G) ==>
analz (insert X H) \<subseteq> synth (analz G) \<union> analz (G \<union> H)"
@@ -691,8 +691,8 @@
"(X \<in> analz H | X \<in> parts H) = (X \<in> parts H)"
by (blast intro: analz_subset_parts [THEN subsetD])
-text{*Without this equation, other rules for synth and analz would yield
- redundant cases*}
+text\<open>Without this equation, other rules for synth and analz would yield
+ redundant cases\<close>
lemma MPair_synth_analz [iff]:
"({|X,Y|} \<in> synth (analz H)) =
(X \<in> synth (analz H) & Y \<in> synth (analz H))"
@@ -710,9 +710,9 @@
by blast
-subsection{*HPair: a combination of Hash and MPair*}
+subsection\<open>HPair: a combination of Hash and MPair\<close>
-subsubsection{*Freeness *}
+subsubsection\<open>Freeness\<close>
lemma Agent_neq_HPair: "Agent A ~= Hash[X] Y"
unfolding HPair_def by simp
@@ -750,7 +750,7 @@
by (auto simp add: HPair_def)
-subsubsection{*Specialized laws, proved in terms of those for Hash and MPair *}
+subsubsection\<open>Specialized laws, proved in terms of those for Hash and MPair\<close>
lemma keysFor_insert_HPair [simp]: "keysFor (insert (Hash[X] Y) H) = keysFor H"
by (simp add: HPair_def)
@@ -772,12 +772,12 @@
by (auto simp add: HPair_def)
-text{*We do NOT want Crypt... messages broken up in protocols!!*}
+text\<open>We do NOT want Crypt... messages broken up in protocols!!\<close>
declare parts.Body [rule del]
-text{*Rewrites to push in Key and Crypt messages, so that other messages can
- be pulled out using the @{text analz_insert} rules*}
+text\<open>Rewrites to push in Key and Crypt messages, so that other messages can
+ be pulled out using the \<open>analz_insert\<close> rules\<close>
lemmas pushKeys =
insert_commute [of "Key K" "Agent C"]
@@ -797,12 +797,12 @@
insert_commute [of "Crypt X K" "MPair X' Y"]
for X K C N X' Y
-text{*Cannot be added with @{text "[simp]"} -- messages should not always be
- re-ordered. *}
+text\<open>Cannot be added with \<open>[simp]\<close> -- messages should not always be
+ re-ordered.\<close>
lemmas pushes = pushKeys pushCrypts
-subsection{*The set of key-free messages*}
+subsection\<open>The set of key-free messages\<close>
(*Note that even the encryption of a key-free message remains key-free.
This concept is valuable because of the theorem analz_keyfree_into_Un, proved below. *)
@@ -833,9 +833,9 @@
apply (metis Un_absorb2 keyfree_KeyE parts_Un parts_keyfree UnI2)
done
-subsection{*Tactics useful for many protocol proofs*}
+subsection\<open>Tactics useful for many protocol proofs\<close>
ML
-{*
+\<open>
(*Analysis of Fake cases. Also works for messages that forward unknown parts,
but this application is no longer necessary if analz_insert_eq is used.
DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
@@ -872,11 +872,11 @@
simp_tac ctxt 1,
REPEAT (FIRSTGOAL (resolve_tac ctxt [allI,impI,notI,conjI,iffI])),
DEPTH_SOLVE (atomic_spy_analz_tac ctxt 1)]) i);
-*}
+\<close>
-text{*By default only @{text o_apply} is built-in. But in the presence of
+text\<open>By default only \<open>o_apply\<close> is built-in. But in the presence of
eta-expansion this means that some terms displayed as @{term "f o g"} will be
-rewritten, and others will not!*}
+rewritten, and others will not!\<close>
declare o_def [simp]
@@ -894,7 +894,7 @@
by (metis Fake_analz_insert Un_absorb Un_absorb1 Un_commute
subset_insertI synth_analz_mono synth_increasing synth_subset_iff)
-text{*Two generalizations of @{text analz_insert_eq}*}
+text\<open>Two generalizations of \<open>analz_insert_eq\<close>\<close>
lemma gen_analz_insert_eq [rule_format]:
"X \<in> analz H ==> ALL G. H \<subseteq> G --> analz (insert X G) = analz G"
by (blast intro: analz_cut analz_insertI analz_mono [THEN [2] rev_subsetD])
@@ -912,16 +912,16 @@
lemmas Fake_parts_sing_imp_Un = Fake_parts_sing [THEN [2] rev_subsetD]
-method_setup spy_analz = {*
- Scan.succeed (SIMPLE_METHOD' o spy_analz_tac) *}
+method_setup spy_analz = \<open>
+ Scan.succeed (SIMPLE_METHOD' o spy_analz_tac)\<close>
"for proving the Fake case when analz is involved"
-method_setup atomic_spy_analz = {*
- Scan.succeed (SIMPLE_METHOD' o atomic_spy_analz_tac) *}
+method_setup atomic_spy_analz = \<open>
+ Scan.succeed (SIMPLE_METHOD' o atomic_spy_analz_tac)\<close>
"for debugging spy_analz"
-method_setup Fake_insert_simp = {*
- Scan.succeed (SIMPLE_METHOD' o Fake_insert_simp_tac) *}
+method_setup Fake_insert_simp = \<open>
+ Scan.succeed (SIMPLE_METHOD' o Fake_insert_simp_tac)\<close>
"for debugging spy_analz"
end