author | wenzelm |
Sun, 06 Jan 2019 15:04:34 +0100 | |
changeset 69605 | a96320074298 |
parent 69597 | ff784d5a5bfb |
child 72991 | d0a0b74f0ad7 |
permissions | -rw-r--r-- |
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(* Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1996 University of Cambridge |
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Datatypes of agents and messages; |
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Inductive relations "parts", "analz" and "synth" |
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*)(*<*) |
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section\<open>Theory of Agents and Messages for Security Protocols\<close> |
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theory Message imports Main begin |
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ML_file \<open>../../antiquote_setup.ML\<close> |
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(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*) |
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lemma [simp] : "A \<union> (B \<union> A) = B \<union> A" |
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by blast |
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(*>*) |
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section\<open>Agents and Messages\<close> |
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text \<open> |
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All protocol specifications refer to a syntactic theory of messages. |
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Datatype |
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\<open>agent\<close> introduces the constant \<open>Server\<close> (a trusted central |
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machine, needed for some protocols), an infinite population of |
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friendly agents, and the~\<open>Spy\<close>: |
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\<close> |
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datatype agent = Server | Friend nat | Spy |
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text \<open> |
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Keys are just natural numbers. Function \<open>invKey\<close> maps a public key to |
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the matching private key, and vice versa: |
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\<close> |
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type_synonym key = nat |
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consts invKey :: "key \<Rightarrow> key" |
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(*<*) |
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consts all_symmetric :: bool \<comment> \<open>true if all keys are symmetric\<close> |
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specification (invKey) |
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invKey [simp]: "invKey (invKey K) = K" |
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invKey_symmetric: "all_symmetric \<longrightarrow> invKey = id" |
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by (rule exI [of _ id], auto) |
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text\<open>The inverse of a symmetric key is itself; that of a public key |
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is the private key and vice versa\<close> |
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definition symKeys :: "key set" where |
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"symKeys == {K. invKey K = K}" |
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(*>*) |
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text \<open> |
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Datatype |
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\<open>msg\<close> introduces the message forms, which include agent names, nonces, |
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keys, compound messages, and encryptions. |
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\<close> |
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datatype |
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msg = Agent agent |
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| Nonce nat |
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| Key key |
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| MPair msg msg |
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| Crypt key msg |
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text \<open> |
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\noindent |
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The notation $\comp{X\sb 1,\ldots X\sb{n-1},X\sb n}$ |
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abbreviates |
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$\isa{MPair}\,X\sb 1\,\ldots\allowbreak(\isa{MPair}\,X\sb{n-1}\,X\sb n)$. |
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Since datatype constructors are injective, we have the theorem |
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@{thm [display,indent=0] msg.inject(5) [THEN iffD1, of K X K' X']} |
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A ciphertext can be decrypted using only one key and |
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can yield only one plaintext. In the real world, decryption with the |
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wrong key succeeds but yields garbage. Our model of encryption is |
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realistic if encryption adds some redundancy to the plaintext, such as a |
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checksum, so that garbage can be detected. |
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\<close> |
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(*<*) |
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text\<open>Concrete syntax: messages appear as \<open>\<lbrace>A,B,NA\<rbrace>\<close>, etc...\<close> |
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syntax |
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"_MTuple" :: "['a, args] \<Rightarrow> 'a * 'b" ("(2\<lbrace>_,/ _\<rbrace>)") |
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translations |
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"\<lbrace>x, y, z\<rbrace>" == "\<lbrace>x, \<lbrace>y, z\<rbrace>\<rbrace>" |
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"\<lbrace>x, y\<rbrace>" == "CONST MPair x y" |
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definition keysFor :: "msg set \<Rightarrow> key set" where |
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\<comment> \<open>Keys useful to decrypt elements of a message set\<close> |
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"keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}" |
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subsubsection\<open>Inductive Definition of All Parts" of a Message\<close> |
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inductive_set |
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parts :: "msg set \<Rightarrow> msg set" |
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for H :: "msg set" |
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where |
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Inj [intro]: "X \<in> H \<Longrightarrow> X \<in> parts H" |
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| Fst: "\<lbrace>X,Y\<rbrace> \<in> parts H \<Longrightarrow> X \<in> parts H" |
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| Snd: "\<lbrace>X,Y\<rbrace> \<in> parts H \<Longrightarrow> Y \<in> parts H" |
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| Body: "Crypt K X \<in> parts H \<Longrightarrow> X \<in> parts H" |
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text\<open>Monotonicity\<close> |
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lemma parts_mono: "G \<subseteq> H \<Longrightarrow> parts(G) \<subseteq> parts(H)" |
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apply auto |
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apply (erule parts.induct) |
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apply (blast dest: parts.Fst parts.Snd parts.Body)+ |
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done |
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text\<open>Equations hold because constructors are injective.\<close> |
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lemma Friend_image_eq [simp]: "(Friend x \<in> Friend`A) = (x\<in>A)" |
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by auto |
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lemma Key_image_eq [simp]: "(Key x \<in> Key`A) = (x\<in>A)" |
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by auto |
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lemma Nonce_Key_image_eq [simp]: "(Nonce x \<notin> Key`A)" |
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by auto |
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subsubsection\<open>Inverse of keys\<close> |
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lemma invKey_eq [simp]: "(invKey K = invKey K') = (K=K')" |
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apply safe |
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apply (drule_tac f = invKey in arg_cong, simp) |
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done |
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subsection\<open>keysFor operator\<close> |
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lemma keysFor_empty [simp]: "keysFor {} = {}" |
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by (unfold keysFor_def, blast) |
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lemma keysFor_Un [simp]: "keysFor (H \<union> H') = keysFor H \<union> keysFor H'" |
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by (unfold keysFor_def, blast) |
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lemma keysFor_UN [simp]: "keysFor (\<Union>i\<in>A. H i) = (\<Union>i\<in>A. keysFor (H i))" |
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by (unfold keysFor_def, blast) |
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text\<open>Monotonicity\<close> |
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lemma keysFor_mono: "G \<subseteq> H \<Longrightarrow> keysFor(G) \<subseteq> keysFor(H)" |
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by (unfold keysFor_def, blast) |
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lemma keysFor_insert_Agent [simp]: "keysFor (insert (Agent A) H) = keysFor H" |
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by (unfold keysFor_def, auto) |
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lemma keysFor_insert_Nonce [simp]: "keysFor (insert (Nonce N) H) = keysFor H" |
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by (unfold keysFor_def, auto) |
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lemma keysFor_insert_Key [simp]: "keysFor (insert (Key K) H) = keysFor H" |
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by (unfold keysFor_def, auto) |
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lemma keysFor_insert_MPair [simp]: "keysFor (insert \<lbrace>X,Y\<rbrace> H) = keysFor H" |
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by (unfold keysFor_def, auto) |
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lemma keysFor_insert_Crypt [simp]: |
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"keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)" |
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by (unfold keysFor_def, auto) |
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lemma keysFor_image_Key [simp]: "keysFor (Key`E) = {}" |
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by (unfold keysFor_def, auto) |
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lemma Crypt_imp_invKey_keysFor: "Crypt K X \<in> H \<Longrightarrow> invKey K \<in> keysFor H" |
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by (unfold keysFor_def, blast) |
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subsection\<open>Inductive relation "parts"\<close> |
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lemma MPair_parts: |
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"[| \<lbrace>X,Y\<rbrace> \<in> parts H; |
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[| X \<in> parts H; Y \<in> parts H |] ==> P |] ==> P" |
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by (blast dest: parts.Fst parts.Snd) |
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declare MPair_parts [elim!] parts.Body [dest!] |
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text\<open>NB These two rules are UNSAFE in the formal sense, as they discard the |
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compound message. They work well on THIS FILE. |
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\<open>MPair_parts\<close> is left as SAFE because it speeds up proofs. |
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The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.\<close> |
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|
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lemma parts_increasing: "H \<subseteq> parts(H)" |
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186 |
by blast |
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|
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lemmas parts_insertI = subset_insertI [THEN parts_mono, THEN subsetD] |
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189 |
|
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lemma parts_empty [simp]: "parts{} = {}" |
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191 |
apply safe |
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apply (erule parts.induct, blast+) |
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193 |
done |
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|
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lemma parts_emptyE [elim!]: "X\<in> parts{} \<Longrightarrow> P" |
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by simp |
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|
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text\<open>WARNING: loops if H = {Y}, therefore must not be repeated!\<close> |
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lemma parts_singleton: "X\<in> parts H \<Longrightarrow> \<exists>Y\<in>H. X\<in> parts {Y}" |
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200 |
by (erule parts.induct, fast+) |
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|
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|
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subsubsection\<open>Unions\<close> |
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|
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lemma parts_Un_subset1: "parts(G) \<union> parts(H) \<subseteq> parts(G \<union> H)" |
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by (intro Un_least parts_mono Un_upper1 Un_upper2) |
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|
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lemma parts_Un_subset2: "parts(G \<union> H) \<subseteq> parts(G) \<union> parts(H)" |
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apply (rule subsetI) |
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apply (erule parts.induct, blast+) |
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211 |
done |
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212 |
|
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lemma parts_Un [simp]: "parts(G \<union> H) = parts(G) \<union> parts(H)" |
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by (intro equalityI parts_Un_subset1 parts_Un_subset2) |
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|
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lemma parts_insert: "parts (insert X H) = parts {X} \<union> parts H" |
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217 |
apply (subst insert_is_Un [of _ H]) |
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218 |
apply (simp only: parts_Un) |
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done |
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|
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text\<open>TWO inserts to avoid looping. This rewrite is better than nothing. |
222 |
Not suitable for Addsimps: its behaviour can be strange.\<close> |
|
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lemma parts_insert2: |
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"parts (insert X (insert Y H)) = parts {X} \<union> parts {Y} \<union> parts H" |
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apply (simp add: Un_assoc) |
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apply (simp add: parts_insert [symmetric]) |
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227 |
done |
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|
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lemma parts_UN_subset1: "(\<Union>x\<in>A. parts(H x)) \<subseteq> parts(\<Union>x\<in>A. H x)" |
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by (intro UN_least parts_mono UN_upper) |
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|
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lemma parts_UN_subset2: "parts(\<Union>x\<in>A. H x) \<subseteq> (\<Union>x\<in>A. parts(H x))" |
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apply (rule subsetI) |
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apply (erule parts.induct, blast+) |
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235 |
done |
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|
236 |
|
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237 |
lemma parts_UN [simp]: "parts(\<Union>x\<in>A. H x) = (\<Union>x\<in>A. parts(H x))" |
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238 |
by (intro equalityI parts_UN_subset1 parts_UN_subset2) |
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239 |
|
67406 | 240 |
text\<open>Added to simplify arguments to parts, analz and synth. |
241 |
NOTE: the UN versions are no longer used!\<close> |
|
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242 |
|
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243 |
|
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text\<open>This allows \<open>blast\<close> to simplify occurrences of |
69597 | 245 |
\<^term>\<open>parts(G\<union>H)\<close> in the assumption.\<close> |
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lemmas in_parts_UnE = parts_Un [THEN equalityD1, THEN subsetD, THEN UnE] |
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declare in_parts_UnE [elim!] |
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248 |
|
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249 |
|
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250 |
lemma parts_insert_subset: "insert X (parts H) \<subseteq> parts(insert X H)" |
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251 |
by (blast intro: parts_mono [THEN [2] rev_subsetD]) |
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252 |
|
67406 | 253 |
subsubsection\<open>Idempotence and transitivity\<close> |
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254 |
|
67613 | 255 |
lemma parts_partsD [dest!]: "X \<in> parts (parts H) \<Longrightarrow> X\<in> parts H" |
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256 |
by (erule parts.induct, blast+) |
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257 |
|
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258 |
lemma parts_idem [simp]: "parts (parts H) = parts H" |
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259 |
by blast |
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260 |
|
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261 |
lemma parts_subset_iff [simp]: "(parts G \<subseteq> parts H) = (G \<subseteq> parts H)" |
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262 |
apply (rule iffI) |
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263 |
apply (iprover intro: subset_trans parts_increasing) |
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264 |
apply (frule parts_mono, simp) |
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265 |
done |
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|
266 |
|
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267 |
lemma parts_trans: "[| X\<in> parts G; G \<subseteq> parts H |] ==> X\<in> parts H" |
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268 |
by (drule parts_mono, blast) |
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269 |
|
67406 | 270 |
text\<open>Cut\<close> |
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271 |
lemma parts_cut: |
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272 |
"[| Y\<in> parts (insert X G); X\<in> parts H |] ==> Y\<in> parts (G \<union> H)" |
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273 |
by (blast intro: parts_trans) |
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|
274 |
|
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275 |
|
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276 |
lemma parts_cut_eq [simp]: "X\<in> parts H ==> parts (insert X H) = parts H" |
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277 |
by (force dest!: parts_cut intro: parts_insertI) |
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|
278 |
|
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279 |
|
67406 | 280 |
subsubsection\<open>Rewrite rules for pulling out atomic messages\<close> |
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281 |
|
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282 |
lemmas parts_insert_eq_I = equalityI [OF subsetI parts_insert_subset] |
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|
283 |
|
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|
284 |
|
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|
285 |
lemma parts_insert_Agent [simp]: |
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|
286 |
"parts (insert (Agent agt) H) = insert (Agent agt) (parts H)" |
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|
287 |
apply (rule parts_insert_eq_I) |
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288 |
apply (erule parts.induct, auto) |
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|
289 |
done |
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|
290 |
|
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|
291 |
lemma parts_insert_Nonce [simp]: |
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|
292 |
"parts (insert (Nonce N) H) = insert (Nonce N) (parts H)" |
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|
293 |
apply (rule parts_insert_eq_I) |
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294 |
apply (erule parts.induct, auto) |
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|
295 |
done |
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|
296 |
|
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|
297 |
lemma parts_insert_Key [simp]: |
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|
298 |
"parts (insert (Key K) H) = insert (Key K) (parts H)" |
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|
299 |
apply (rule parts_insert_eq_I) |
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300 |
apply (erule parts.induct, auto) |
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|
301 |
done |
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|
302 |
|
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LaTeX code is now generated directly from theory files.
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|
303 |
lemma parts_insert_Crypt [simp]: |
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LaTeX code is now generated directly from theory files.
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|
304 |
"parts (insert (Crypt K X) H) = insert (Crypt K X) (parts (insert X H))" |
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LaTeX code is now generated directly from theory files.
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|
305 |
apply (rule equalityI) |
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LaTeX code is now generated directly from theory files.
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|
306 |
apply (rule subsetI) |
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LaTeX code is now generated directly from theory files.
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|
307 |
apply (erule parts.induct, auto) |
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LaTeX code is now generated directly from theory files.
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|
308 |
apply (blast intro: parts.Body) |
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LaTeX code is now generated directly from theory files.
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|
309 |
done |
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|
310 |
|
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|
311 |
lemma parts_insert_MPair [simp]: |
61992 | 312 |
"parts (insert \<lbrace>X,Y\<rbrace> H) = |
313 |
insert \<lbrace>X,Y\<rbrace> (parts (insert X (insert Y H)))" |
|
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|
314 |
apply (rule equalityI) |
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LaTeX code is now generated directly from theory files.
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changeset
|
315 |
apply (rule subsetI) |
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LaTeX code is now generated directly from theory files.
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|
316 |
apply (erule parts.induct, auto) |
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|
317 |
apply (blast intro: parts.Fst parts.Snd)+ |
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LaTeX code is now generated directly from theory files.
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|
318 |
done |
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LaTeX code is now generated directly from theory files.
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changeset
|
319 |
|
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LaTeX code is now generated directly from theory files.
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|
320 |
lemma parts_image_Key [simp]: "parts (Key`N) = Key`N" |
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berghofe
parents:
23733
diff
changeset
|
321 |
apply auto |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
322 |
apply (erule parts.induct, auto) |
11250 | 323 |
done |
324 |
||
325 |
||
67406 | 326 |
text\<open>In any message, there is an upper bound N on its greatest nonce.\<close> |
67613 | 327 |
lemma msg_Nonce_supply: "\<exists>N. \<forall>n. N\<le>n \<longrightarrow> Nonce n \<notin> parts {msg}" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
328 |
apply (induct_tac "msg") |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
329 |
apply (simp_all (no_asm_simp) add: exI parts_insert2) |
67406 | 330 |
txt\<open>MPair case: blast works out the necessary sum itself!\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
331 |
prefer 2 apply auto apply (blast elim!: add_leE) |
67406 | 332 |
txt\<open>Nonce case\<close> |
58305
57752a91eec4
renamed 'datatype' to 'old_datatype'; 'datatype' is now alias for 'datatype_new'
blanchet
parents:
56059
diff
changeset
|
333 |
apply (rename_tac nat) |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
334 |
apply (rule_tac x = "N + Suc nat" in exI, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
335 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
336 |
(*>*) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
337 |
|
67406 | 338 |
section\<open>Modelling the Adversary\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
339 |
|
67406 | 340 |
text \<open> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
341 |
The spy is part of the system and must be built into the model. He is |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
342 |
a malicious user who does not have to follow the protocol. He |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
343 |
watches the network and uses any keys he knows to decrypt messages. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
344 |
Thus he accumulates additional keys and nonces. These he can use to |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
345 |
compose new messages, which he may send to anybody. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
346 |
|
69505 | 347 |
Two functions enable us to formalize this behaviour: \<open>analz\<close> and |
348 |
\<open>synth\<close>. Each function maps a sets of messages to another set of |
|
349 |
messages. The set \<open>analz H\<close> formalizes what the adversary can learn |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
350 |
from the set of messages~$H$. The closure properties of this set are |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
351 |
defined inductively. |
67406 | 352 |
\<close> |
11250 | 353 |
|
23733 | 354 |
inductive_set |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
355 |
analz :: "msg set \<Rightarrow> msg set" |
23733 | 356 |
for H :: "msg set" |
357 |
where |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
358 |
Inj [intro,simp] : "X \<in> H \<Longrightarrow> X \<in> analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
359 |
| Fst: "\<lbrace>X,Y\<rbrace> \<in> analz H \<Longrightarrow> X \<in> analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
360 |
| Snd: "\<lbrace>X,Y\<rbrace> \<in> analz H \<Longrightarrow> Y \<in> analz H" |
23733 | 361 |
| Decrypt [dest]: |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
362 |
"\<lbrakk>Crypt K X \<in> analz H; Key(invKey K) \<in> analz H\<rbrakk> |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
363 |
\<Longrightarrow> X \<in> analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
364 |
(*<*) |
67406 | 365 |
text\<open>Monotonicity; Lemma 1 of Lowe's paper\<close> |
67613 | 366 |
lemma analz_mono: "G\<subseteq>H \<Longrightarrow> analz(G) \<subseteq> analz(H)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
367 |
apply auto |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
368 |
apply (erule analz.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
369 |
apply (auto dest: analz.Fst analz.Snd) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
370 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
371 |
|
67406 | 372 |
text\<open>Making it safe speeds up proofs\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
373 |
lemma MPair_analz [elim!]: |
61992 | 374 |
"[| \<lbrace>X,Y\<rbrace> \<in> analz H; |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
375 |
[| X \<in> analz H; Y \<in> analz H |] ==> P |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
376 |
|] ==> P" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
377 |
by (blast dest: analz.Fst analz.Snd) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
378 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
379 |
lemma analz_increasing: "H \<subseteq> analz(H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
380 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
381 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
382 |
lemma analz_subset_parts: "analz H \<subseteq> parts H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
383 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
384 |
apply (erule analz.induct, blast+) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
385 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
386 |
|
55142 | 387 |
lemmas analz_into_parts = analz_subset_parts [THEN subsetD] |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
388 |
|
55142 | 389 |
lemmas not_parts_not_analz = analz_subset_parts [THEN contra_subsetD] |
11250 | 390 |
|
391 |
||
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
392 |
lemma parts_analz [simp]: "parts (analz H) = parts H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
393 |
apply (rule equalityI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
394 |
apply (rule analz_subset_parts [THEN parts_mono, THEN subset_trans], simp) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
395 |
apply (blast intro: analz_increasing [THEN parts_mono, THEN subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
396 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
397 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
398 |
lemma analz_parts [simp]: "analz (parts H) = parts H" |
11250 | 399 |
apply auto |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
400 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
401 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
402 |
|
55142 | 403 |
lemmas analz_insertI = subset_insertI [THEN analz_mono, THEN [2] rev_subsetD] |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
404 |
|
67406 | 405 |
subsubsection\<open>General equational properties\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
406 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
407 |
lemma analz_empty [simp]: "analz{} = {}" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
408 |
apply safe |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
409 |
apply (erule analz.induct, blast+) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
410 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
411 |
|
67406 | 412 |
text\<open>Converse fails: we can analz more from the union than from the |
413 |
separate parts, as a key in one might decrypt a message in the other\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
414 |
lemma analz_Un: "analz(G) \<union> analz(H) \<subseteq> analz(G \<union> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
415 |
by (intro Un_least analz_mono Un_upper1 Un_upper2) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
416 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
417 |
lemma analz_insert: "insert X (analz H) \<subseteq> analz(insert X H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
418 |
by (blast intro: analz_mono [THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
419 |
|
67406 | 420 |
subsubsection\<open>Rewrite rules for pulling out atomic messages\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
421 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
422 |
lemmas analz_insert_eq_I = equalityI [OF subsetI analz_insert] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
423 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
424 |
lemma analz_insert_Agent [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
425 |
"analz (insert (Agent agt) H) = insert (Agent agt) (analz H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
426 |
apply (rule analz_insert_eq_I) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
427 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
428 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
429 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
430 |
lemma analz_insert_Nonce [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
431 |
"analz (insert (Nonce N) H) = insert (Nonce N) (analz H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
432 |
apply (rule analz_insert_eq_I) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
433 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
434 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
435 |
|
67406 | 436 |
text\<open>Can only pull out Keys if they are not needed to decrypt the rest\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
437 |
lemma analz_insert_Key [simp]: |
67613 | 438 |
"K \<notin> keysFor (analz H) \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
439 |
analz (insert (Key K) H) = insert (Key K) (analz H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
440 |
apply (unfold keysFor_def) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
441 |
apply (rule analz_insert_eq_I) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
442 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
443 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
444 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
445 |
lemma analz_insert_MPair [simp]: |
61992 | 446 |
"analz (insert \<lbrace>X,Y\<rbrace> H) = |
447 |
insert \<lbrace>X,Y\<rbrace> (analz (insert X (insert Y H)))" |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
448 |
apply (rule equalityI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
449 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
450 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
451 |
apply (erule analz.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
452 |
apply (blast intro: analz.Fst analz.Snd)+ |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
453 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
454 |
|
67406 | 455 |
text\<open>Can pull out enCrypted message if the Key is not known\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
456 |
lemma analz_insert_Crypt: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
457 |
"Key (invKey K) \<notin> analz H |
67613 | 458 |
\<Longrightarrow> analz (insert (Crypt K X) H) = insert (Crypt K X) (analz H)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
459 |
apply (rule analz_insert_eq_I) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
460 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
461 |
|
11250 | 462 |
done |
463 |
||
67613 | 464 |
lemma lemma1: "Key (invKey K) \<in> analz H \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
465 |
analz (insert (Crypt K X) H) \<subseteq> |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
466 |
insert (Crypt K X) (analz (insert X H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
467 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
468 |
apply (erule_tac x = x in analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
469 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
470 |
|
67613 | 471 |
lemma lemma2: "Key (invKey K) \<in> analz H \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
472 |
insert (Crypt K X) (analz (insert X H)) \<subseteq> |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
473 |
analz (insert (Crypt K X) H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
474 |
apply auto |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
475 |
apply (erule_tac x = x in analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
476 |
apply (blast intro: analz_insertI analz.Decrypt) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
477 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
478 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
479 |
lemma analz_insert_Decrypt: |
67613 | 480 |
"Key (invKey K) \<in> analz H \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
481 |
analz (insert (Crypt K X) H) = |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
482 |
insert (Crypt K X) (analz (insert X H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
483 |
by (intro equalityI lemma1 lemma2) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
484 |
|
67406 | 485 |
text\<open>Case analysis: either the message is secure, or it is not! Effective, |
69505 | 486 |
but can cause subgoals to blow up! Use with \<open>if_split\<close>; apparently |
69597 | 487 |
\<open>split_tac\<close> does not cope with patterns such as \<^term>\<open>analz (insert |
488 |
(Crypt K X) H)\<close>\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
489 |
lemma analz_Crypt_if [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
490 |
"analz (insert (Crypt K X) H) = |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
491 |
(if (Key (invKey K) \<in> analz H) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
492 |
then insert (Crypt K X) (analz (insert X H)) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
493 |
else insert (Crypt K X) (analz H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
494 |
by (simp add: analz_insert_Crypt analz_insert_Decrypt) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
495 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
496 |
|
67406 | 497 |
text\<open>This rule supposes "for the sake of argument" that we have the key.\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
498 |
lemma analz_insert_Crypt_subset: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
499 |
"analz (insert (Crypt K X) H) \<subseteq> |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
500 |
insert (Crypt K X) (analz (insert X H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
501 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
502 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
503 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
504 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
505 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
506 |
lemma analz_image_Key [simp]: "analz (Key`N) = Key`N" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
507 |
apply auto |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
508 |
apply (erule analz.induct, auto) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
509 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
510 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
511 |
|
67406 | 512 |
subsubsection\<open>Idempotence and transitivity\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
513 |
|
67613 | 514 |
lemma analz_analzD [dest!]: "X\<in> analz (analz H) \<Longrightarrow> X\<in> analz H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
515 |
by (erule analz.induct, blast+) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
516 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
517 |
lemma analz_idem [simp]: "analz (analz H) = analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
518 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
519 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
520 |
lemma analz_subset_iff [simp]: "(analz G \<subseteq> analz H) = (G \<subseteq> analz H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
521 |
apply (rule iffI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
522 |
apply (iprover intro: subset_trans analz_increasing) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
523 |
apply (frule analz_mono, simp) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
524 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
525 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
526 |
lemma analz_trans: "[| X\<in> analz G; G \<subseteq> analz H |] ==> X\<in> analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
527 |
by (drule analz_mono, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
528 |
|
67406 | 529 |
text\<open>Cut; Lemma 2 of Lowe\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
530 |
lemma analz_cut: "[| Y\<in> analz (insert X H); X\<in> analz H |] ==> Y\<in> analz H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
531 |
by (erule analz_trans, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
532 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
533 |
(*Cut can be proved easily by induction on |
67613 | 534 |
"Y \<in> analz (insert X H) \<Longrightarrow> X \<in> analz H \<longrightarrow> Y \<in> analz H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
535 |
*) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
536 |
|
67406 | 537 |
text\<open>This rewrite rule helps in the simplification of messages that involve |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
538 |
the forwarding of unknown components (X). Without it, removing occurrences |
67406 | 539 |
of X can be very complicated.\<close> |
67613 | 540 |
lemma analz_insert_eq: "X\<in> analz H \<Longrightarrow> analz (insert X H) = analz H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
541 |
by (blast intro: analz_cut analz_insertI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
542 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
543 |
|
67406 | 544 |
text\<open>A congruence rule for "analz"\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
545 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
546 |
lemma analz_subset_cong: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
547 |
"[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
548 |
==> analz (G \<union> H) \<subseteq> analz (G' \<union> H')" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
549 |
apply simp |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
550 |
apply (iprover intro: conjI subset_trans analz_mono Un_upper1 Un_upper2) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
551 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
552 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
553 |
lemma analz_cong: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
554 |
"[| analz G = analz G'; analz H = analz H' |] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
555 |
==> analz (G \<union> H) = analz (G' \<union> H')" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
556 |
by (intro equalityI analz_subset_cong, simp_all) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
557 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
558 |
lemma analz_insert_cong: |
67613 | 559 |
"analz H = analz H' \<Longrightarrow> analz(insert X H) = analz(insert X H')" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
560 |
by (force simp only: insert_def intro!: analz_cong) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
561 |
|
67406 | 562 |
text\<open>If there are no pairs or encryptions then analz does nothing\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
563 |
lemma analz_trivial: |
61992 | 564 |
"[| \<forall>X Y. \<lbrace>X,Y\<rbrace> \<notin> H; \<forall>X K. Crypt K X \<notin> H |] ==> analz H = H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
565 |
apply safe |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
566 |
apply (erule analz.induct, blast+) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
567 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
568 |
|
67406 | 569 |
text\<open>These two are obsolete (with a single Spy) but cost little to prove...\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
570 |
lemma analz_UN_analz_lemma: |
67613 | 571 |
"X\<in> analz (\<Union>i\<in>A. analz (H i)) \<Longrightarrow> X\<in> analz (\<Union>i\<in>A. H i)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
572 |
apply (erule analz.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
573 |
apply (blast intro: analz_mono [THEN [2] rev_subsetD])+ |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
574 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
575 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
576 |
lemma analz_UN_analz [simp]: "analz (\<Union>i\<in>A. analz (H i)) = analz (\<Union>i\<in>A. H i)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
577 |
by (blast intro: analz_UN_analz_lemma analz_mono [THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
578 |
(*>*) |
67406 | 579 |
text \<open> |
69505 | 580 |
Note the \<open>Decrypt\<close> rule: the spy can decrypt a |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
581 |
message encrypted with key~$K$ if he has the matching key,~$K^{-1}$. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
582 |
Properties proved by rule induction include the following: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
583 |
@{named_thms [display,indent=0] analz_mono [no_vars] (analz_mono) analz_idem [no_vars] (analz_idem)} |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
584 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
585 |
The set of fake messages that an intruder could invent |
69505 | 586 |
starting from~\<open>H\<close> is \<open>synth(analz H)\<close>, where \<open>synth H\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
587 |
formalizes what the adversary can build from the set of messages~$H$. |
67406 | 588 |
\<close> |
11250 | 589 |
|
23733 | 590 |
inductive_set |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
591 |
synth :: "msg set \<Rightarrow> msg set" |
23733 | 592 |
for H :: "msg set" |
593 |
where |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
594 |
Inj [intro]: "X \<in> H \<Longrightarrow> X \<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
595 |
| Agent [intro]: "Agent agt \<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
596 |
| MPair [intro]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
597 |
"\<lbrakk>X \<in> synth H; Y \<in> synth H\<rbrakk> \<Longrightarrow> \<lbrace>X,Y\<rbrace> \<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
598 |
| Crypt [intro]: |
23929 | 599 |
"\<lbrakk>X \<in> synth H; Key K \<in> H\<rbrakk> \<Longrightarrow> Crypt K X \<in> synth H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
600 |
(*<*) |
67613 | 601 |
lemma synth_mono: "G\<subseteq>H \<Longrightarrow> synth(G) \<subseteq> synth(H)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
602 |
by (auto, erule synth.induct, auto) |
11250 | 603 |
|
604 |
inductive_cases Key_synth [elim!]: "Key K \<in> synth H" |
|
61992 | 605 |
inductive_cases MPair_synth [elim!]: "\<lbrace>X,Y\<rbrace> \<in> synth H" |
11250 | 606 |
inductive_cases Crypt_synth [elim!]: "Crypt K X \<in> synth H" |
607 |
||
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
608 |
lemma analz_synth_Un [simp]: "analz (synth G \<union> H) = analz (G \<union> H) \<union> synth G" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
609 |
apply (rule equalityI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
610 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
611 |
apply (erule analz.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
612 |
prefer 5 apply (blast intro: analz_mono [THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
613 |
apply (blast intro: analz.Fst analz.Snd analz.Decrypt)+ |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
614 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
615 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
616 |
lemma analz_synth [simp]: "analz (synth H) = analz H \<union> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
617 |
apply (cut_tac H = "{}" in analz_synth_Un) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
618 |
apply (simp (no_asm_use)) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
619 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
620 |
(*>*) |
67406 | 621 |
text \<open> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
622 |
The set includes all agent names. Nonces and keys are assumed to be |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
623 |
unguessable, so none are included beyond those already in~$H$. Two |
69597 | 624 |
elements of \<^term>\<open>synth H\<close> can be combined, and an element can be encrypted |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
625 |
using a key present in~$H$. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
626 |
|
69505 | 627 |
Like \<open>analz\<close>, this set operator is monotone and idempotent. It also |
628 |
satisfies an interesting equation involving \<open>analz\<close>: |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
629 |
@{named_thms [display,indent=0] analz_synth [no_vars] (analz_synth)} |
69505 | 630 |
Rule inversion plays a major role in reasoning about \<open>synth\<close>, through |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
631 |
declarations such as this one: |
67406 | 632 |
\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
633 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
634 |
inductive_cases Nonce_synth [elim!]: "Nonce n \<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
635 |
|
67406 | 636 |
text \<open> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
637 |
\noindent |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
638 |
The resulting elimination rule replaces every assumption of the form |
69597 | 639 |
\<^term>\<open>Nonce n \<in> synth H\<close> by \<^term>\<open>Nonce n \<in> H\<close>, |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
640 |
expressing that a nonce cannot be guessed. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
641 |
|
69505 | 642 |
A third operator, \<open>parts\<close>, is useful for stating correctness |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
643 |
properties. The set |
69597 | 644 |
\<^term>\<open>parts H\<close> consists of the components of elements of~$H$. This set |
69505 | 645 |
includes~\<open>H\<close> and is closed under the projections from a compound |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
646 |
message to its immediate parts. |
69505 | 647 |
Its definition resembles that of \<open>analz\<close> except in the rule |
648 |
corresponding to the constructor \<open>Crypt\<close>: |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
649 |
@{thm [display,indent=5] parts.Body [no_vars]} |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
650 |
The body of an encrypted message is always regarded as part of it. We can |
69505 | 651 |
use \<open>parts\<close> to express general well-formedness properties of a protocol, |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
652 |
for example, that an uncompromised agent's private key will never be |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
653 |
included as a component of any message. |
67406 | 654 |
\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
655 |
(*<*) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
656 |
lemma synth_increasing: "H \<subseteq> synth(H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
657 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
658 |
|
67406 | 659 |
subsubsection\<open>Unions\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
660 |
|
67406 | 661 |
text\<open>Converse fails: we can synth more from the union than from the |
662 |
separate parts, building a compound message using elements of each.\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
663 |
lemma synth_Un: "synth(G) \<union> synth(H) \<subseteq> synth(G \<union> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
664 |
by (intro Un_least synth_mono Un_upper1 Un_upper2) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
665 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
666 |
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
667 |
by (blast intro: synth_mono [THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
668 |
|
67406 | 669 |
subsubsection\<open>Idempotence and transitivity\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
670 |
|
67613 | 671 |
lemma synth_synthD [dest!]: "X\<in> synth (synth H) \<Longrightarrow> X\<in> synth H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
672 |
by (erule synth.induct, blast+) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
673 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
674 |
lemma synth_idem: "synth (synth H) = synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
675 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
676 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
677 |
lemma synth_subset_iff [simp]: "(synth G \<subseteq> synth H) = (G \<subseteq> synth H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
678 |
apply (rule iffI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
679 |
apply (iprover intro: subset_trans synth_increasing) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
680 |
apply (frule synth_mono, simp add: synth_idem) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
681 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
682 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
683 |
lemma synth_trans: "[| X\<in> synth G; G \<subseteq> synth H |] ==> X\<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
684 |
by (drule synth_mono, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
685 |
|
67406 | 686 |
text\<open>Cut; Lemma 2 of Lowe\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
687 |
lemma synth_cut: "[| Y\<in> synth (insert X H); X\<in> synth H |] ==> Y\<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
688 |
by (erule synth_trans, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
689 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
690 |
lemma Agent_synth [simp]: "Agent A \<in> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
691 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
692 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
693 |
lemma Nonce_synth_eq [simp]: "(Nonce N \<in> synth H) = (Nonce N \<in> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
694 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
695 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
696 |
lemma Key_synth_eq [simp]: "(Key K \<in> synth H) = (Key K \<in> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
697 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
698 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
699 |
lemma Crypt_synth_eq [simp]: |
67613 | 700 |
"Key K \<notin> H \<Longrightarrow> (Crypt K X \<in> synth H) = (Crypt K X \<in> H)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
701 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
702 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
703 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
704 |
lemma keysFor_synth [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
705 |
"keysFor (synth H) = keysFor H \<union> invKey`{K. Key K \<in> H}" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
706 |
by (unfold keysFor_def, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
707 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
708 |
|
67406 | 709 |
subsubsection\<open>Combinations of parts, analz and synth\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
710 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
711 |
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
712 |
apply (rule equalityI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
713 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
714 |
apply (erule parts.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
715 |
apply (blast intro: synth_increasing [THEN parts_mono, THEN subsetD] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
716 |
parts.Fst parts.Snd parts.Body)+ |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
717 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
718 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
719 |
lemma analz_analz_Un [simp]: "analz (analz G \<union> H) = analz (G \<union> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
720 |
apply (intro equalityI analz_subset_cong)+ |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
721 |
apply simp_all |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
722 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
723 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
724 |
|
67406 | 725 |
subsubsection\<open>For reasoning about the Fake rule in traces\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
726 |
|
67613 | 727 |
lemma parts_insert_subset_Un: "X \<in> G \<Longrightarrow> parts(insert X H) \<subseteq> parts G \<union> parts H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
728 |
by (rule subset_trans [OF parts_mono parts_Un_subset2], blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
729 |
|
67406 | 730 |
text\<open>More specifically for Fake. Very occasionally we could do with a version |
69597 | 731 |
of the form \<^term>\<open>parts{X} \<subseteq> synth (analz H) \<union> parts H\<close>\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
732 |
lemma Fake_parts_insert: |
67613 | 733 |
"X \<in> synth (analz H) \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
734 |
parts (insert X H) \<subseteq> synth (analz H) \<union> parts H" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
735 |
apply (drule parts_insert_subset_Un) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
736 |
apply (simp (no_asm_use)) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
737 |
apply blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
738 |
done |
11250 | 739 |
|
740 |
lemma Fake_parts_insert_in_Un: |
|
67613 | 741 |
"[|Z \<in> parts (insert X H); X \<in> synth (analz H)|] |
58860 | 742 |
==> Z \<in> synth (analz H) \<union> parts H" |
11250 | 743 |
by (blast dest: Fake_parts_insert [THEN subsetD, dest]) |
744 |
||
69597 | 745 |
text\<open>\<^term>\<open>H\<close> is sometimes \<^term>\<open>Key ` KK \<union> spies evs\<close>, so can't put |
746 |
\<^term>\<open>G=H\<close>.\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
747 |
lemma Fake_analz_insert: |
67613 | 748 |
"X \<in> synth (analz G) \<Longrightarrow> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
749 |
analz (insert X H) \<subseteq> synth (analz G) \<union> analz (G \<union> H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
750 |
apply (rule subsetI) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
751 |
apply (subgoal_tac "x \<in> analz (synth (analz G) \<union> H) ") |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
752 |
prefer 2 apply (blast intro: analz_mono [THEN [2] rev_subsetD] analz_mono [THEN synth_mono, THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
753 |
apply (simp (no_asm_use)) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
754 |
apply blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
755 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
756 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
757 |
lemma analz_conj_parts [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
758 |
"(X \<in> analz H & X \<in> parts H) = (X \<in> analz H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
759 |
by (blast intro: analz_subset_parts [THEN subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
760 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
761 |
lemma analz_disj_parts [simp]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
762 |
"(X \<in> analz H | X \<in> parts H) = (X \<in> parts H)" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
763 |
by (blast intro: analz_subset_parts [THEN subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
764 |
|
67406 | 765 |
text\<open>Without this equation, other rules for synth and analz would yield |
766 |
redundant cases\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
767 |
lemma MPair_synth_analz [iff]: |
61992 | 768 |
"(\<lbrace>X,Y\<rbrace> \<in> synth (analz H)) = |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
769 |
(X \<in> synth (analz H) & Y \<in> synth (analz H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
770 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
771 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
772 |
lemma Crypt_synth_analz: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
773 |
"[| Key K \<in> analz H; Key (invKey K) \<in> analz H |] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
774 |
==> (Crypt K X \<in> synth (analz H)) = (X \<in> synth (analz H))" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
775 |
by blast |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
776 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
777 |
|
67406 | 778 |
text\<open>We do NOT want Crypt... messages broken up in protocols!!\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
779 |
declare parts.Body [rule del] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
780 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
781 |
|
67406 | 782 |
text\<open>Rewrites to push in Key and Crypt messages, so that other messages can |
69505 | 783 |
be pulled out using the \<open>analz_insert\<close> rules\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
784 |
|
55142 | 785 |
lemmas pushKeys = |
27225 | 786 |
insert_commute [of "Key K" "Agent C"] |
787 |
insert_commute [of "Key K" "Nonce N"] |
|
788 |
insert_commute [of "Key K" "MPair X Y"] |
|
789 |
insert_commute [of "Key K" "Crypt X K'"] |
|
55142 | 790 |
for K C N X Y K' |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
791 |
|
55142 | 792 |
lemmas pushCrypts = |
27225 | 793 |
insert_commute [of "Crypt X K" "Agent C"] |
794 |
insert_commute [of "Crypt X K" "Agent C"] |
|
795 |
insert_commute [of "Crypt X K" "Nonce N"] |
|
796 |
insert_commute [of "Crypt X K" "MPair X' Y"] |
|
55142 | 797 |
for X K C N X' Y |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
798 |
|
69505 | 799 |
text\<open>Cannot be added with \<open>[simp]\<close> -- messages should not always be |
67406 | 800 |
re-ordered.\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
801 |
lemmas pushes = pushKeys pushCrypts |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
802 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
803 |
|
67406 | 804 |
subsection\<open>Tactics useful for many protocol proofs\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
805 |
ML |
67406 | 806 |
\<open> |
39282 | 807 |
val invKey = @{thm invKey}; |
808 |
val keysFor_def = @{thm keysFor_def}; |
|
809 |
val symKeys_def = @{thm symKeys_def}; |
|
810 |
val parts_mono = @{thm parts_mono}; |
|
811 |
val analz_mono = @{thm analz_mono}; |
|
812 |
val synth_mono = @{thm synth_mono}; |
|
813 |
val analz_increasing = @{thm analz_increasing}; |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
814 |
|
39282 | 815 |
val analz_insertI = @{thm analz_insertI}; |
816 |
val analz_subset_parts = @{thm analz_subset_parts}; |
|
817 |
val Fake_parts_insert = @{thm Fake_parts_insert}; |
|
818 |
val Fake_analz_insert = @{thm Fake_analz_insert}; |
|
819 |
val pushes = @{thms pushes}; |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
820 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
821 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
822 |
(*Analysis of Fake cases. Also works for messages that forward unknown parts, |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
823 |
but this application is no longer necessary if analz_insert_eq is used. |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
824 |
Abstraction over i is ESSENTIAL: it delays the dereferencing of claset |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
825 |
DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
826 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
827 |
(*Apply rules to break down assumptions of the form |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
828 |
Y \<in> parts(insert X H) and Y \<in> analz(insert X H) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
829 |
*) |
32265 | 830 |
fun impOfSubs th = th RSN (2, @{thm rev_subsetD}) |
831 |
||
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
58889
diff
changeset
|
832 |
fun Fake_insert_tac ctxt = |
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
58889
diff
changeset
|
833 |
dresolve_tac ctxt [impOfSubs Fake_analz_insert, |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
834 |
impOfSubs Fake_parts_insert] THEN' |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
58889
diff
changeset
|
835 |
eresolve_tac ctxt [asm_rl, @{thm synth.Inj}]; |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
836 |
|
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49322
diff
changeset
|
837 |
fun Fake_insert_simp_tac ctxt i = |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
58889
diff
changeset
|
838 |
REPEAT (Fake_insert_tac ctxt i) THEN asm_full_simp_tac ctxt i; |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
839 |
|
42475 | 840 |
fun atomic_spy_analz_tac ctxt = |
42793 | 841 |
SELECT_GOAL |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49322
diff
changeset
|
842 |
(Fake_insert_simp_tac ctxt 1 THEN |
42793 | 843 |
IF_UNSOLVED (Blast.depth_tac (ctxt addIs [analz_insertI, impOfSubs analz_subset_parts]) 4 1)); |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
844 |
|
42475 | 845 |
fun spy_analz_tac ctxt i = |
42793 | 846 |
DETERM |
847 |
(SELECT_GOAL |
|
848 |
(EVERY |
|
849 |
[ (*push in occurrences of X...*) |
|
850 |
(REPEAT o CHANGED) |
|
59780 | 851 |
(Rule_Insts.res_inst_tac ctxt [((("x", 1), Position.none), "X")] [] |
852 |
(insert_commute RS ssubst) 1), |
|
42793 | 853 |
(*...allowing further simplifications*) |
51717
9e7d1c139569
simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents:
49322
diff
changeset
|
854 |
simp_tac ctxt 1, |
59498
50b60f501b05
proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents:
58889
diff
changeset
|
855 |
REPEAT (FIRSTGOAL (resolve_tac ctxt [allI,impI,notI,conjI,iffI])), |
42793 | 856 |
DEPTH_SOLVE (atomic_spy_analz_tac ctxt 1)]) i); |
67406 | 857 |
\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
858 |
|
69505 | 859 |
text\<open>By default only \<open>o_apply\<close> is built-in. But in the presence of |
69597 | 860 |
eta-expansion this means that some terms displayed as \<^term>\<open>f o g\<close> will be |
67406 | 861 |
rewritten, and others will not!\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
862 |
declare o_def [simp] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
863 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
864 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
865 |
lemma Crypt_notin_image_Key [simp]: "Crypt K X \<notin> Key ` A" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
866 |
by auto |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
867 |
|
67613 | 868 |
lemma synth_analz_mono: "G\<subseteq>H \<Longrightarrow> synth (analz(G)) \<subseteq> synth (analz(H))" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
869 |
by (iprover intro: synth_mono analz_mono) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
870 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
871 |
lemma Fake_analz_eq [simp]: |
67613 | 872 |
"X \<in> synth(analz H) \<Longrightarrow> synth (analz (insert X H)) = synth (analz H)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
873 |
apply (drule Fake_analz_insert[of _ _ "H"]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
874 |
apply (simp add: synth_increasing[THEN Un_absorb2]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
875 |
apply (drule synth_mono) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
876 |
apply (simp add: synth_idem) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
877 |
apply (rule equalityI) |
58860 | 878 |
apply (simp add: ) |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
879 |
apply (rule synth_analz_mono, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
880 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
881 |
|
69505 | 882 |
text\<open>Two generalizations of \<open>analz_insert_eq\<close>\<close> |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
883 |
lemma gen_analz_insert_eq [rule_format]: |
67613 | 884 |
"X \<in> analz H \<Longrightarrow> \<forall>G. H \<subseteq> G \<longrightarrow> analz (insert X G) = analz G" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
885 |
by (blast intro: analz_cut analz_insertI analz_mono [THEN [2] rev_subsetD]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
886 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
887 |
lemma synth_analz_insert_eq [rule_format]: |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
888 |
"X \<in> synth (analz H) |
67613 | 889 |
\<Longrightarrow> \<forall>G. H \<subseteq> G \<longrightarrow> (Key K \<in> analz (insert X G)) = (Key K \<in> analz G)" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
890 |
apply (erule synth.induct) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
891 |
apply (simp_all add: gen_analz_insert_eq subset_trans [OF _ subset_insertI]) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
892 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
893 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
894 |
lemma Fake_parts_sing: |
67613 | 895 |
"X \<in> synth (analz H) \<Longrightarrow> parts{X} \<subseteq> synth (analz H) \<union> parts H" |
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
896 |
apply (rule subset_trans) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
897 |
apply (erule_tac [2] Fake_parts_insert) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
898 |
apply (rule parts_mono, blast) |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
899 |
done |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
900 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
901 |
lemmas Fake_parts_sing_imp_Un = Fake_parts_sing [THEN [2] rev_subsetD] |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
902 |
|
67406 | 903 |
method_setup spy_analz = \<open> |
904 |
Scan.succeed (SIMPLE_METHOD' o spy_analz_tac)\<close> |
|
11250 | 905 |
"for proving the Fake case when analz is involved" |
906 |
||
67406 | 907 |
method_setup atomic_spy_analz = \<open> |
908 |
Scan.succeed (SIMPLE_METHOD' o atomic_spy_analz_tac)\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
909 |
"for debugging spy_analz" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
910 |
|
67406 | 911 |
method_setup Fake_insert_simp = \<open> |
912 |
Scan.succeed (SIMPLE_METHOD' o Fake_insert_simp_tac)\<close> |
|
23925
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
913 |
"for debugging spy_analz" |
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
914 |
|
ee98c2528a8f
LaTeX code is now generated directly from theory files.
berghofe
parents:
23733
diff
changeset
|
915 |
|
11250 | 916 |
end |
62392 | 917 |
(*>*) |