src/HOL/Auth/Message.thy
author paulson <lp15@cam.ac.uk>
Wed, 26 Apr 2017 15:53:35 +0100
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(*  Title:      HOL/Auth/Message.thy
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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
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imports Main
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begin
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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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type_synonym
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  key = nat
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consts
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  all_symmetric :: bool        \<comment>\<open>true if all keys are symmetric\<close>
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  invKey        :: "key=>key"  \<comment>\<open>inverse of a symmetric key\<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 --> 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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datatype  \<comment>\<open>We allow any number of friendly agents\<close>
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  agent = Server | Friend nat | Spy
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datatype
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     msg = Agent  agent     \<comment>\<open>Agent names\<close>
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         | Number nat       \<comment>\<open>Ordinary integers, timestamps, ...\<close>
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         | Nonce  nat       \<comment>\<open>Unguessable nonces\<close>
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         | Key    key       \<comment>\<open>Crypto keys\<close>
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         | Hash   msg       \<comment>\<open>Hashing\<close>
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         | MPair  msg msg   \<comment>\<open>Compound messages\<close>
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         | Crypt  key msg   \<comment>\<open>Encryption, public- or shared-key\<close>
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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>" \<rightleftharpoons> "\<lbrace>x, \<lbrace>y, z\<rbrace>\<rbrace>"
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  "\<lbrace>x, y\<rbrace>" \<rightleftharpoons> "CONST MPair x y"
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definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
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    \<comment>\<open>Message Y paired with a MAC computed with the help of X\<close>
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    "Hash[X] Y == \<lbrace>Hash\<lbrace>X,Y\<rbrace>, Y\<rbrace>"
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definition keysFor :: "msg set => 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 => msg set"
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  for H :: "msg set"
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  where
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    Inj [intro]: "X \<in> H ==> X \<in> parts H"
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  | Fst:         "\<lbrace>X,Y\<rbrace> \<in> parts H ==> X \<in> parts H"
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  | Snd:         "\<lbrace>X,Y\<rbrace> \<in> parts H ==> Y \<in> parts H"
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  | Body:        "Crypt K X \<in> parts H ==> X \<in> parts H"
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text\<open>Monotonicity\<close>
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lemma parts_mono: "G \<subseteq> H ==> 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: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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by (metis invKey)
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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 ==> 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_Number [simp]: "keysFor (insert (Number 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_Hash [simp]: "keysFor (insert (Hash X) 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 ==> 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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lemma parts_increasing: "H \<subseteq> parts(H)"
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by blast
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lemmas parts_insertI = subset_insertI [THEN parts_mono, THEN subsetD]
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lemma parts_empty [simp]: "parts{} = {}"
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apply safe
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apply (erule parts.induct, blast+)
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done
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lemma parts_emptyE [elim!]: "X\<in> parts{} ==> P"
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by simp
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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 ==> \<exists>Y\<in>H. X\<in> parts {Y}"
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by (erule parts.induct, fast+)
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subsubsection\<open>Unions\<close>
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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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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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done
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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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lemma parts_insert: "parts (insert X H) = parts {X} \<union> parts H"
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by (metis insert_is_Un parts_Un)
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text\<open>TWO inserts to avoid looping.  This rewrite is better than nothing.
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  But 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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by (metis Un_commute Un_empty_right Un_insert_right insert_is_Un parts_Un)
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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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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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done
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62343
24106dc44def prefer abbreviations for compound operators INFIMUM and SUPREMUM
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lemma parts_UN [simp]:
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  "parts (\<Union>x\<in>A. H x) = (\<Union>x\<in>A. parts (H x))"
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  by (intro equalityI parts_UN_subset1 parts_UN_subset2)
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24106dc44def prefer abbreviations for compound operators INFIMUM and SUPREMUM
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lemma parts_image [simp]:
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  "parts (f ` A) = (\<Union>x\<in>A. parts {f x})"
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  apply auto
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  apply (metis (mono_tags, hide_lams) image_iff parts_singleton)
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  apply (metis empty_subsetI image_eqI insert_absorb insert_subset parts_mono)
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  done
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text\<open>Added to simplify arguments to parts, analz and synth.
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  NOTE: the UN versions are no longer used!\<close>
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text\<open>This allows \<open>blast\<close> to simplify occurrences of 
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  @{term "parts(G\<union>H)"} 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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lemma parts_insert_subset: "insert X (parts H) \<subseteq> parts(insert X H)"
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by (blast intro: parts_mono [THEN [2] rev_subsetD])
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subsubsection\<open>Idempotence and transitivity\<close>
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lemma parts_partsD [dest!]: "X\<in> parts (parts H) ==> X\<in> parts H"
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by (erule parts.induct, blast+)
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lemma parts_idem [simp]: "parts (parts H) = parts H"
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by blast
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lemma parts_subset_iff [simp]: "(parts G \<subseteq> parts H) = (G \<subseteq> parts H)"
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by (metis parts_idem parts_increasing parts_mono subset_trans)
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lemma parts_trans: "[| X\<in> parts G;  G \<subseteq> parts H |] ==> X\<in> parts H"
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by (metis parts_subset_iff set_mp)
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text\<open>Cut\<close>
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lemma parts_cut:
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     "[| Y\<in> parts (insert X G);  X\<in> parts H |] ==> Y\<in> parts (G \<union> H)" 
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by (blast intro: parts_trans) 
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lemma parts_cut_eq [simp]: "X\<in> parts H ==> parts (insert X H) = parts H"
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by (metis insert_absorb parts_idem parts_insert)
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subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
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lemmas parts_insert_eq_I = equalityI [OF subsetI parts_insert_subset]
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lemma parts_insert_Agent [simp]:
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     "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)"
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apply (rule parts_insert_eq_I) 
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apply (erule parts.induct, auto) 
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done
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lemma parts_insert_Nonce [simp]:
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     "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)"
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apply (rule parts_insert_eq_I) 
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apply (erule parts.induct, auto) 
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done
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lemma parts_insert_Number [simp]:
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     "parts (insert (Number N) H) = insert (Number N) (parts H)"
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apply (rule parts_insert_eq_I) 
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apply (erule parts.induct, auto) 
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done
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lemma parts_insert_Key [simp]:
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     "parts (insert (Key K) H) = insert (Key K) (parts H)"
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apply (rule parts_insert_eq_I) 
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apply (erule parts.induct, auto) 
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done
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lemma parts_insert_Hash [simp]:
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     "parts (insert (Hash X) H) = insert (Hash X) (parts H)"
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apply (rule parts_insert_eq_I) 
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apply (erule parts.induct, auto) 
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done
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lemma parts_insert_Crypt [simp]:
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     "parts (insert (Crypt K X) H) = insert (Crypt K X) (parts (insert X H))"
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apply (rule equalityI)
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apply (rule subsetI)
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apply (erule parts.induct, auto)
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apply (blast intro: parts.Body)
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6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   298
done
6e62e5357a10 converting more HOL-Auth to new-style theories
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parents: 13922
diff changeset
   299
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   300
lemma parts_insert_MPair [simp]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   301
     "parts (insert \<lbrace>X,Y\<rbrace> H) =  
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   302
          insert \<lbrace>X,Y\<rbrace> (parts (insert X (insert Y H)))"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   303
apply (rule equalityI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   304
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   305
apply (erule parts.induct, auto)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   306
apply (blast intro: parts.Fst parts.Snd)+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   307
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   308
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   309
lemma parts_image_Key [simp]: "parts (Key`N) = Key`N"
62343
24106dc44def prefer abbreviations for compound operators INFIMUM and SUPREMUM
haftmann
parents: 61956
diff changeset
   310
by auto
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   311
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   312
text\<open>In any message, there is an upper bound N on its greatest nonce.\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   313
lemma msg_Nonce_supply: "\<exists>N. \<forall>n. N\<le>n --> Nonce n \<notin> parts {msg}"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   314
proof (induct msg)
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   315
  case (Nonce n)
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   316
    show ?case
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   317
      by simp (metis Suc_n_not_le_n)
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   318
next
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   319
  case (MPair X Y)
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   320
    then show ?case \<comment>\<open>metis works out the necessary sum itself!\<close>
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   321
      by (simp add: parts_insert2) (metis le_trans nat_le_linear)
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   322
qed auto
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   323
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   324
subsection\<open>Inductive relation "analz"\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   325
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   326
text\<open>Inductive definition of "analz" -- what can be broken down from a set of
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   327
    messages, including keys.  A form of downward closure.  Pairs can
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   328
    be taken apart; messages decrypted with known keys.\<close>
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   329
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   330
inductive_set
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   331
  analz :: "msg set => msg set"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   332
  for H :: "msg set"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   333
  where
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   334
    Inj [intro,simp]: "X \<in> H ==> X \<in> analz H"
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   335
  | Fst:     "\<lbrace>X,Y\<rbrace> \<in> analz H ==> X \<in> analz H"
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   336
  | Snd:     "\<lbrace>X,Y\<rbrace> \<in> analz H ==> Y \<in> analz H"
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   337
  | Decrypt [dest]: 
11192
5fd02b905a9a a few basic X-symbols
paulson
parents: 11189
diff changeset
   338
             "[|Crypt K X \<in> analz H; Key(invKey K): analz H|] ==> X \<in> analz H"
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   339
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   340
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   341
text\<open>Monotonicity; Lemma 1 of Lowe's paper\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   342
lemma analz_mono: "G\<subseteq>H ==> analz(G) \<subseteq> analz(H)"
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   343
apply auto
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   344
apply (erule analz.induct) 
16818
paulson
parents: 16796
diff changeset
   345
apply (auto dest: analz.Fst analz.Snd) 
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   346
done
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   347
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   348
text\<open>Making it safe speeds up proofs\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   349
lemma MPair_analz [elim!]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   350
     "[| \<lbrace>X,Y\<rbrace> \<in> analz H;        
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   351
             [| X \<in> analz H; Y \<in> analz H |] ==> P   
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   352
          |] ==> P"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   353
by (blast dest: analz.Fst analz.Snd)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   354
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   355
lemma analz_increasing: "H \<subseteq> analz(H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   356
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   357
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   358
lemma analz_subset_parts: "analz H \<subseteq> parts H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   359
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   360
apply (erule analz.induct, blast+)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   361
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   362
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   363
lemmas analz_into_parts = analz_subset_parts [THEN subsetD]
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   364
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   365
lemmas not_parts_not_analz = analz_subset_parts [THEN contra_subsetD]
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   366
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   367
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   368
lemma parts_analz [simp]: "parts (analz H) = parts H"
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   369
by (metis analz_increasing analz_subset_parts equalityI parts_mono parts_subset_iff)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   370
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   371
lemma analz_parts [simp]: "analz (parts H) = parts H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   372
apply auto
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   373
apply (erule analz.induct, auto)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   374
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   375
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   376
lemmas analz_insertI = subset_insertI [THEN analz_mono, THEN [2] rev_subsetD]
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   377
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   378
subsubsection\<open>General equational properties\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   379
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   380
lemma analz_empty [simp]: "analz{} = {}"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   381
apply safe
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   382
apply (erule analz.induct, blast+)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   383
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   384
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   385
text\<open>Converse fails: we can analz more from the union than from the 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   386
  separate parts, as a key in one might decrypt a message in the other\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   387
lemma analz_Un: "analz(G) \<union> analz(H) \<subseteq> analz(G \<union> H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   388
by (intro Un_least analz_mono Un_upper1 Un_upper2)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   389
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   390
lemma analz_insert: "insert X (analz H) \<subseteq> analz(insert X H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   391
by (blast intro: analz_mono [THEN [2] rev_subsetD])
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   392
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   393
subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   394
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   395
lemmas analz_insert_eq_I = equalityI [OF subsetI analz_insert]
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   396
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   397
lemma analz_insert_Agent [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   398
     "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   399
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   400
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   401
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   402
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   403
lemma analz_insert_Nonce [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   404
     "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   405
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   406
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   407
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   408
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   409
lemma analz_insert_Number [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   410
     "analz (insert (Number N) H) = insert (Number N) (analz H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   411
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   412
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   413
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   414
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   415
lemma analz_insert_Hash [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   416
     "analz (insert (Hash X) H) = insert (Hash X) (analz H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   417
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   418
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   419
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   420
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   421
text\<open>Can only pull out Keys if they are not needed to decrypt the rest\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   422
lemma analz_insert_Key [simp]: 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   423
    "K \<notin> keysFor (analz H) ==>   
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   424
          analz (insert (Key K) H) = insert (Key K) (analz H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   425
apply (unfold keysFor_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   426
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   427
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   428
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   429
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   430
lemma analz_insert_MPair [simp]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   431
     "analz (insert \<lbrace>X,Y\<rbrace> H) =  
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   432
          insert \<lbrace>X,Y\<rbrace> (analz (insert X (insert Y H)))"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   433
apply (rule equalityI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   434
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   435
apply (erule analz.induct, auto)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   436
apply (erule analz.induct)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   437
apply (blast intro: analz.Fst analz.Snd)+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   438
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   439
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   440
text\<open>Can pull out enCrypted message if the Key is not known\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   441
lemma analz_insert_Crypt:
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   442
     "Key (invKey K) \<notin> analz H 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   443
      ==> analz (insert (Crypt K X) H) = insert (Crypt K X) (analz H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   444
apply (rule analz_insert_eq_I) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   445
apply (erule analz.induct, auto) 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   446
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   447
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   448
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   449
lemma lemma1: "Key (invKey K) \<in> analz H ==>   
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   450
               analz (insert (Crypt K X) H) \<subseteq>  
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   451
               insert (Crypt K X) (analz (insert X H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   452
apply (rule subsetI)
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   453
apply (erule_tac x = x in analz.induct, auto)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   454
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   455
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   456
lemma lemma2: "Key (invKey K) \<in> analz H ==>   
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   457
               insert (Crypt K X) (analz (insert X H)) \<subseteq>  
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   458
               analz (insert (Crypt K X) H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   459
apply auto
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   460
apply (erule_tac x = x in analz.induct, auto)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   461
apply (blast intro: analz_insertI analz.Decrypt)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   462
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   463
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   464
lemma analz_insert_Decrypt:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   465
     "Key (invKey K) \<in> analz H ==>   
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   466
               analz (insert (Crypt K X) H) =  
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   467
               insert (Crypt K X) (analz (insert X H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   468
by (intro equalityI lemma1 lemma2)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   469
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   470
text\<open>Case analysis: either the message is secure, or it is not! Effective,
62390
842917225d56 more canonical names
nipkow
parents: 62343
diff changeset
   471
but can cause subgoals to blow up! Use with \<open>if_split\<close>; apparently
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   472
\<open>split_tac\<close> does not cope with patterns such as @{term"analz (insert
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   473
(Crypt K X) H)"}\<close> 
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   474
lemma analz_Crypt_if [simp]:
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   475
     "analz (insert (Crypt K X) H) =                 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   476
          (if (Key (invKey K) \<in> analz H)                 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   477
           then insert (Crypt K X) (analz (insert X H))  
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   478
           else insert (Crypt K X) (analz H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   479
by (simp add: analz_insert_Crypt analz_insert_Decrypt)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   480
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   481
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   482
text\<open>This rule supposes "for the sake of argument" that we have the key.\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   483
lemma analz_insert_Crypt_subset:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   484
     "analz (insert (Crypt K X) H) \<subseteq>   
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   485
           insert (Crypt K X) (analz (insert X H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   486
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   487
apply (erule analz.induct, auto)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   488
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   489
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   490
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   491
lemma analz_image_Key [simp]: "analz (Key`N) = Key`N"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   492
apply auto
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   493
apply (erule analz.induct, auto)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   494
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   495
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   496
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   497
subsubsection\<open>Idempotence and transitivity\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   498
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   499
lemma analz_analzD [dest!]: "X\<in> analz (analz H) ==> X\<in> analz H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   500
by (erule analz.induct, blast+)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   501
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   502
lemma analz_idem [simp]: "analz (analz H) = analz H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   503
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   504
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   505
lemma analz_subset_iff [simp]: "(analz G \<subseteq> analz H) = (G \<subseteq> analz H)"
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   506
by (metis analz_idem analz_increasing analz_mono subset_trans)
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   507
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   508
lemma analz_trans: "[| X\<in> analz G;  G \<subseteq> analz H |] ==> X\<in> analz H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   509
by (drule analz_mono, blast)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   510
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   511
text\<open>Cut; Lemma 2 of Lowe\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   512
lemma analz_cut: "[| Y\<in> analz (insert X H);  X\<in> analz H |] ==> Y\<in> analz H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   513
by (erule analz_trans, blast)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   514
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   515
(*Cut can be proved easily by induction on
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   516
   "Y: analz (insert X H) ==> X: analz H --> Y: analz H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   517
*)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   518
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   519
text\<open>This rewrite rule helps in the simplification of messages that involve
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   520
  the forwarding of unknown components (X).  Without it, removing occurrences
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   521
  of X can be very complicated.\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   522
lemma analz_insert_eq: "X\<in> analz H ==> analz (insert X H) = analz H"
41693
47532fe9e075 Introduction of metis calls and other cosmetic modifications.
paulson
parents: 39216
diff changeset
   523
by (metis analz_cut analz_insert_eq_I insert_absorb)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   524
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   525
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   526
text\<open>A congruence rule for "analz"\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   527
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   528
lemma analz_subset_cong:
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   529
     "[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |] 
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   530
      ==> analz (G \<union> H) \<subseteq> analz (G' \<union> H')"
41693
47532fe9e075 Introduction of metis calls and other cosmetic modifications.
paulson
parents: 39216
diff changeset
   531
by (metis Un_mono analz_Un analz_subset_iff subset_trans)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   532
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   533
lemma analz_cong:
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   534
     "[| analz G = analz G'; analz H = analz H' |] 
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   535
      ==> analz (G \<union> H) = analz (G' \<union> H')"
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   536
by (intro equalityI analz_subset_cong, simp_all) 
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   537
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   538
lemma analz_insert_cong:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   539
     "analz H = analz H' ==> analz(insert X H) = analz(insert X H')"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   540
by (force simp only: insert_def intro!: analz_cong)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   541
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   542
text\<open>If there are no pairs or encryptions then analz does nothing\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   543
lemma analz_trivial:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   544
     "[| \<forall>X Y. \<lbrace>X,Y\<rbrace> \<notin> H;  \<forall>X K. Crypt K X \<notin> H |] ==> analz H = H"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   545
apply safe
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   546
apply (erule analz.induct, blast+)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   547
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   548
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   549
text\<open>These two are obsolete (with a single Spy) but cost little to prove...\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   550
lemma analz_UN_analz_lemma:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   551
     "X\<in> analz (\<Union>i\<in>A. analz (H i)) ==> X\<in> analz (\<Union>i\<in>A. H i)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   552
apply (erule analz.induct)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   553
apply (blast intro: analz_mono [THEN [2] rev_subsetD])+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   554
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   555
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   556
lemma analz_UN_analz [simp]: "analz (\<Union>i\<in>A. analz (H i)) = analz (\<Union>i\<in>A. H i)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   557
by (blast intro: analz_UN_analz_lemma analz_mono [THEN [2] rev_subsetD])
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   558
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   559
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   560
subsection\<open>Inductive relation "synth"\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   561
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   562
text\<open>Inductive definition of "synth" -- what can be built up from a set of
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   563
    messages.  A form of upward closure.  Pairs can be built, messages
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 2516
diff changeset
   564
    encrypted with known keys.  Agent names are public domain.
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   565
    Numbers can be guessed, but Nonces cannot be.\<close>
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   566
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   567
inductive_set
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   568
  synth :: "msg set => msg set"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   569
  for H :: "msg set"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   570
  where
11192
5fd02b905a9a a few basic X-symbols
paulson
parents: 11189
diff changeset
   571
    Inj    [intro]:   "X \<in> H ==> X \<in> synth H"
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   572
  | Agent  [intro]:   "Agent agt \<in> synth H"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   573
  | Number [intro]:   "Number n  \<in> synth H"
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   574
  | Hash   [intro]:   "X \<in> synth H ==> Hash X \<in> synth H"
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   575
  | MPair  [intro]:   "[|X \<in> synth H;  Y \<in> synth H|] ==> \<lbrace>X,Y\<rbrace> \<in> synth H"
23746
a455e69c31cc Adapted to new inductive definition package.
berghofe
parents: 22843
diff changeset
   576
  | Crypt  [intro]:   "[|X \<in> synth H;  Key(K) \<in> H|] ==> Crypt K X \<in> synth H"
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   577
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   578
text\<open>Monotonicity\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   579
lemma synth_mono: "G\<subseteq>H ==> synth(G) \<subseteq> synth(H)"
16818
paulson
parents: 16796
diff changeset
   580
  by (auto, erule synth.induct, auto)  
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   581
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   582
text\<open>NO \<open>Agent_synth\<close>, as any Agent name can be synthesized.  
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   583
  The same holds for @{term Number}\<close>
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   584
39216
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   585
inductive_simps synth_simps [iff]:
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   586
 "Nonce n \<in> synth H"
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   587
 "Key K \<in> synth H"
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   588
 "Hash X \<in> synth H"
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   589
 "\<lbrace>X,Y\<rbrace> \<in> synth H"
39216
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   590
 "Crypt K X \<in> synth H"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   591
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   592
lemma synth_increasing: "H \<subseteq> synth(H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   593
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   594
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   595
subsubsection\<open>Unions\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   596
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   597
text\<open>Converse fails: we can synth more from the union than from the 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   598
  separate parts, building a compound message using elements of each.\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   599
lemma synth_Un: "synth(G) \<union> synth(H) \<subseteq> synth(G \<union> H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   600
by (intro Un_least synth_mono Un_upper1 Un_upper2)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   601
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   602
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   603
by (blast intro: synth_mono [THEN [2] rev_subsetD])
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   604
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   605
subsubsection\<open>Idempotence and transitivity\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   606
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   607
lemma synth_synthD [dest!]: "X\<in> synth (synth H) ==> X\<in> synth H"
39216
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   608
by (erule synth.induct, auto)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   609
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   610
lemma synth_idem: "synth (synth H) = synth H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   611
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   612
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   613
lemma synth_subset_iff [simp]: "(synth G \<subseteq> synth H) = (G \<subseteq> synth H)"
35566
3c01f5ad1d34 Simplified a couple of proofs and corrected a comment
paulson
parents: 35416
diff changeset
   614
by (metis subset_trans synth_idem synth_increasing synth_mono)
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   615
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   616
lemma synth_trans: "[| X\<in> synth G;  G \<subseteq> synth H |] ==> X\<in> synth H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   617
by (drule synth_mono, blast)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   618
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   619
text\<open>Cut; Lemma 2 of Lowe\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   620
lemma synth_cut: "[| Y\<in> synth (insert X H);  X\<in> synth H |] ==> Y\<in> synth H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   621
by (erule synth_trans, blast)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   622
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   623
lemma Crypt_synth_eq [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   624
     "Key K \<notin> H ==> (Crypt K X \<in> synth H) = (Crypt K X \<in> H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   625
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   626
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   627
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   628
lemma keysFor_synth [simp]: 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   629
    "keysFor (synth H) = keysFor H \<union> invKey`{K. Key K \<in> H}"
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   630
by (unfold keysFor_def, blast)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   631
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   632
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   633
subsubsection\<open>Combinations of parts, analz and synth\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   634
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   635
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   636
apply (rule equalityI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   637
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   638
apply (erule parts.induct)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   639
apply (blast intro: synth_increasing [THEN parts_mono, THEN subsetD] 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   640
                    parts.Fst parts.Snd parts.Body)+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   641
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   642
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   643
lemma analz_analz_Un [simp]: "analz (analz G \<union> H) = analz (G \<union> H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   644
apply (intro equalityI analz_subset_cong)+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   645
apply simp_all
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   646
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   647
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   648
lemma analz_synth_Un [simp]: "analz (synth G \<union> H) = analz (G \<union> H) \<union> synth G"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   649
apply (rule equalityI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   650
apply (rule subsetI)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   651
apply (erule analz.induct)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   652
prefer 5 apply (blast intro: analz_mono [THEN [2] rev_subsetD])
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   653
apply (blast intro: analz.Fst analz.Snd analz.Decrypt)+
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   654
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   655
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   656
lemma analz_synth [simp]: "analz (synth H) = analz H \<union> synth H"
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   657
by (metis Un_empty_right analz_synth_Un)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   658
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   659
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   660
subsubsection\<open>For reasoning about the Fake rule in traces\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   661
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   662
lemma parts_insert_subset_Un: "X\<in> G ==> parts(insert X H) \<subseteq> parts G \<union> parts H"
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   663
by (metis UnCI Un_upper2 insert_subset parts_Un parts_mono)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   664
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   665
text\<open>More specifically for Fake. See also \<open>Fake_parts_sing\<close> below\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   666
lemma Fake_parts_insert:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   667
     "X \<in> synth (analz H) ==>  
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   668
      parts (insert X H) \<subseteq> synth (analz H) \<union> parts H"
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   669
by (metis Un_commute analz_increasing insert_subset parts_analz parts_mono 
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   670
          parts_synth synth_mono synth_subset_iff)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   671
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   672
lemma Fake_parts_insert_in_Un:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   673
     "[|Z \<in> parts (insert X H);  X: synth (analz H)|] 
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   674
      ==> Z \<in>  synth (analz H) \<union> parts H"
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   675
by (metis Fake_parts_insert set_mp)
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   676
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   677
text\<open>@{term H} is sometimes @{term"Key ` KK \<union> spies evs"}, so can't put 
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   678
  @{term "G=H"}.\<close>
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   679
lemma Fake_analz_insert:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   680
     "X\<in> synth (analz G) ==>  
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   681
      analz (insert X H) \<subseteq> synth (analz G) \<union> analz (G \<union> H)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   682
apply (rule subsetI)
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   683
apply (subgoal_tac "x \<in> analz (synth (analz G) \<union> H)", force)
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   684
apply (blast intro: analz_mono [THEN [2] rev_subsetD] analz_mono [THEN synth_mono, THEN [2] rev_subsetD])
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   685
done
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   686
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   687
lemma analz_conj_parts [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   688
     "(X \<in> analz H & X \<in> parts H) = (X \<in> analz H)"
14145
2e31b8cc8788 ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents: 14126
diff changeset
   689
by (blast intro: analz_subset_parts [THEN subsetD])
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   690
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   691
lemma analz_disj_parts [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   692
     "(X \<in> analz H | X \<in> parts H) = (X \<in> parts H)"
14145
2e31b8cc8788 ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents: 14126
diff changeset
   693
by (blast intro: analz_subset_parts [THEN subsetD])
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   694
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   695
text\<open>Without this equation, other rules for synth and analz would yield
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   696
  redundant cases\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   697
lemma MPair_synth_analz [iff]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   698
     "(\<lbrace>X,Y\<rbrace> \<in> synth (analz H)) =  
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   699
      (X \<in> synth (analz H) & Y \<in> synth (analz H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   700
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   701
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   702
lemma Crypt_synth_analz:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   703
     "[| Key K \<in> analz H;  Key (invKey K) \<in> analz H |]  
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   704
       ==> (Crypt K X \<in> synth (analz H)) = (X \<in> synth (analz H))"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   705
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   706
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   707
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   708
lemma Hash_synth_analz [simp]:
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   709
     "X \<notin> synth (analz H)  
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   710
      ==> (Hash\<lbrace>X,Y\<rbrace> \<in> synth (analz H)) = (Hash\<lbrace>X,Y\<rbrace> \<in> analz H)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   711
by blast
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   712
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   713
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   714
subsection\<open>HPair: a combination of Hash and MPair\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   715
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   716
subsubsection\<open>Freeness\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   717
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   718
lemma Agent_neq_HPair: "Agent A ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   719
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   720
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   721
lemma Nonce_neq_HPair: "Nonce N ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   722
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   723
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   724
lemma Number_neq_HPair: "Number N ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   725
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   726
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   727
lemma Key_neq_HPair: "Key K ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   728
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   729
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   730
lemma Hash_neq_HPair: "Hash Z ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   731
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   732
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   733
lemma Crypt_neq_HPair: "Crypt K X' ~= Hash[X] Y"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   734
  unfolding HPair_def by simp
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   735
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   736
lemmas HPair_neqs = Agent_neq_HPair Nonce_neq_HPair Number_neq_HPair 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   737
                    Key_neq_HPair Hash_neq_HPair Crypt_neq_HPair
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   738
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   739
declare HPair_neqs [iff]
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   740
declare HPair_neqs [symmetric, iff]
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   741
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   742
lemma HPair_eq [iff]: "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   743
by (simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   744
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   745
lemma MPair_eq_HPair [iff]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   746
     "(\<lbrace>X',Y'\<rbrace> = Hash[X] Y) = (X' = Hash\<lbrace>X,Y\<rbrace> & Y'=Y)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   747
by (simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   748
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   749
lemma HPair_eq_MPair [iff]:
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   750
     "(Hash[X] Y = \<lbrace>X',Y'\<rbrace>) = (X' = Hash\<lbrace>X,Y\<rbrace> & Y'=Y)"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   751
by (auto simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   752
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   753
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   754
subsubsection\<open>Specialized laws, proved in terms of those for Hash and MPair\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   755
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   756
lemma keysFor_insert_HPair [simp]: "keysFor (insert (Hash[X] Y) H) = keysFor H"
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   757
by (simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   758
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   759
lemma parts_insert_HPair [simp]: 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   760
    "parts (insert (Hash[X] Y) H) =  
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   761
     insert (Hash[X] Y) (insert (Hash\<lbrace>X,Y\<rbrace>) (parts (insert Y H)))"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   762
by (simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   763
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   764
lemma analz_insert_HPair [simp]: 
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   765
    "analz (insert (Hash[X] Y) H) =  
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   766
     insert (Hash[X] Y) (insert (Hash\<lbrace>X,Y\<rbrace>) (analz (insert Y H)))"
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   767
by (simp add: HPair_def)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   768
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   769
lemma HPair_synth_analz [simp]:
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   770
     "X \<notin> synth (analz H)  
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   771
    ==> (Hash[X] Y \<in> synth (analz H)) =  
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   772
        (Hash \<lbrace>X, Y\<rbrace> \<in> analz H & Y \<in> synth (analz H))"
39216
62332b382dba tidied using inductive_simps
paulson
parents: 37936
diff changeset
   773
by (auto simp add: HPair_def)
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   774
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   775
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   776
text\<open>We do NOT want Crypt... messages broken up in protocols!!\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   777
declare parts.Body [rule del]
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   778
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   779
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   780
text\<open>Rewrites to push in Key and Crypt messages, so that other messages can
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   781
    be pulled out using the \<open>analz_insert\<close> rules\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   782
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   783
lemmas pushKeys =
27225
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   784
  insert_commute [of "Key K" "Agent C"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   785
  insert_commute [of "Key K" "Nonce N"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   786
  insert_commute [of "Key K" "Number N"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   787
  insert_commute [of "Key K" "Hash X"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   788
  insert_commute [of "Key K" "MPair X Y"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   789
  insert_commute [of "Key K" "Crypt X K'"]
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   790
  for K C N X Y K'
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   791
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   792
lemmas pushCrypts =
27225
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   793
  insert_commute [of "Crypt X K" "Agent C"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   794
  insert_commute [of "Crypt X K" "Agent C"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   795
  insert_commute [of "Crypt X K" "Nonce N"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   796
  insert_commute [of "Crypt X K" "Number N"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   797
  insert_commute [of "Crypt X K" "Hash X'"]
b316dde851f5 eliminated OldGoals.inst;
wenzelm
parents: 27154
diff changeset
   798
  insert_commute [of "Crypt X K" "MPair X' Y"]
45605
a89b4bc311a5 eliminated obsolete "standard";
wenzelm
parents: 44174
diff changeset
   799
  for X K C N X' Y
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   800
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   801
text\<open>Cannot be added with \<open>[simp]\<close> -- messages should not always be
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   802
  re-ordered.\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   803
lemmas pushes = pushKeys pushCrypts
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   804
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   805
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   806
subsection\<open>The set of key-free messages\<close>
43582
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   807
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   808
(*Note that even the encryption of a key-free message remains key-free.
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   809
  This concept is valuable because of the theorem analz_keyfree_into_Un, proved below. *)
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   810
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   811
inductive_set
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   812
  keyfree :: "msg set"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   813
  where
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   814
    Agent:  "Agent A \<in> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   815
  | Number: "Number N \<in> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   816
  | Nonce:  "Nonce N \<in> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   817
  | Hash:   "Hash X \<in> keyfree"
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   818
  | MPair:  "[|X \<in> keyfree;  Y \<in> keyfree|] ==> \<lbrace>X,Y\<rbrace> \<in> keyfree"
43582
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   819
  | Crypt:  "[|X \<in> keyfree|] ==> Crypt K X \<in> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   820
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   821
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   822
declare keyfree.intros [intro] 
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   823
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   824
inductive_cases keyfree_KeyE: "Key K \<in> keyfree"
61956
38b73f7940af more symbols;
wenzelm
parents: 61830
diff changeset
   825
inductive_cases keyfree_MPairE: "\<lbrace>X,Y\<rbrace> \<in> keyfree"
43582
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   826
inductive_cases keyfree_CryptE: "Crypt K X \<in> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   827
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   828
lemma parts_keyfree: "parts (keyfree) \<subseteq> keyfree"
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   829
  by (clarify, erule parts.induct, auto elim!: keyfree_KeyE keyfree_MPairE keyfree_CryptE)
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   830
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   831
(*The key-free part of a set of messages can be removed from the scope of the analz operator.*)
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   832
lemma analz_keyfree_into_Un: "\<lbrakk>X \<in> analz (G \<union> H); G \<subseteq> keyfree\<rbrakk> \<Longrightarrow> X \<in> parts G \<union> analz H"
57394
7621a3b42ce7 tiny refinements
paulson <lp15@cam.ac.uk>
parents: 51717
diff changeset
   833
apply (erule analz.induct, auto dest: parts.Body)
44174
d1d79f0e1ea6 make more HOL theories work with separate set type
huffman
parents: 43582
diff changeset
   834
apply (metis Un_absorb2 keyfree_KeyE parts_Un parts_keyfree UnI2)
43582
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   835
done
ddca453102ab keyfree: The set of key-free messages (and associated theorems)
paulson
parents: 42793
diff changeset
   836
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   837
subsection\<open>Tactics useful for many protocol proofs\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   838
ML
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   839
\<open>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   840
(*Analysis of Fake cases.  Also works for messages that forward unknown parts,
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   841
  but this application is no longer necessary if analz_insert_eq is used.
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   842
  DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   843
32117
0762b9ad83df Set.thy: prefer = over == where possible; tuned ML setup; dropped (moved) ML legacy
haftmann
parents: 30607
diff changeset
   844
fun impOfSubs th = th RSN (2, @{thm rev_subsetD})
0762b9ad83df Set.thy: prefer = over == where possible; tuned ML setup; dropped (moved) ML legacy
haftmann
parents: 30607
diff changeset
   845
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   846
(*Apply rules to break down assumptions of the form
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   847
  Y \<in> parts(insert X H)  and  Y \<in> analz(insert X H)
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   848
*)
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 58889
diff changeset
   849
fun Fake_insert_tac ctxt = 
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 58889
diff changeset
   850
    dresolve_tac ctxt [impOfSubs @{thm Fake_analz_insert},
24122
fc7f857d33c8 tuned ML bindings (for multithreading);
wenzelm
parents: 23746
diff changeset
   851
                  impOfSubs @{thm Fake_parts_insert}] THEN'
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 58889
diff changeset
   852
    eresolve_tac ctxt [asm_rl, @{thm synth.Inj}];
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   853
51717
9e7d1c139569 simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents: 51702
diff changeset
   854
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
   855
  REPEAT (Fake_insert_tac ctxt i) THEN asm_full_simp_tac ctxt i;
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   856
42474
8b139b8ee366 simplified/modernized method setup;
wenzelm
parents: 41774
diff changeset
   857
fun atomic_spy_analz_tac ctxt =
42793
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   858
  SELECT_GOAL
51717
9e7d1c139569 simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents: 51702
diff changeset
   859
   (Fake_insert_simp_tac ctxt 1 THEN
42793
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   860
    IF_UNSOLVED
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   861
      (Blast.depth_tac
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   862
        (ctxt addIs [@{thm analz_insertI}, impOfSubs @{thm analz_subset_parts}]) 4 1));
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   863
42474
8b139b8ee366 simplified/modernized method setup;
wenzelm
parents: 41774
diff changeset
   864
fun spy_analz_tac ctxt i =
42793
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   865
  DETERM
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   866
   (SELECT_GOAL
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   867
     (EVERY 
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   868
      [  (*push in occurrences of X...*)
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   869
       (REPEAT o CHANGED)
59780
23b67731f4f0 support 'for' fixes in rule_tac etc.;
wenzelm
parents: 59763
diff changeset
   870
         (Rule_Insts.res_inst_tac ctxt [((("x", 1), Position.none), "X")] []
23b67731f4f0 support 'for' fixes in rule_tac etc.;
wenzelm
parents: 59763
diff changeset
   871
           (insert_commute RS ssubst) 1),
42793
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   872
       (*...allowing further simplifications*)
51717
9e7d1c139569 simplifier uses proper Proof.context instead of historic type simpset;
wenzelm
parents: 51702
diff changeset
   873
       simp_tac ctxt 1,
59498
50b60f501b05 proper context for resolve_tac, eresolve_tac, dresolve_tac, forward_tac etc.;
wenzelm
parents: 58889
diff changeset
   874
       REPEAT (FIRSTGOAL (resolve_tac ctxt [allI,impI,notI,conjI,iffI])),
42793
88bee9f6eec7 proper Proof.context for classical tactics;
wenzelm
parents: 42474
diff changeset
   875
       DEPTH_SOLVE (atomic_spy_analz_tac ctxt 1)]) i);
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   876
\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   877
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   878
text\<open>By default only \<open>o_apply\<close> is built-in.  But in the presence of
16818
paulson
parents: 16796
diff changeset
   879
eta-expansion this means that some terms displayed as @{term "f o g"} will be
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   880
rewritten, and others will not!\<close>
13926
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   881
declare o_def [simp]
6e62e5357a10 converting more HOL-Auth to new-style theories
paulson
parents: 13922
diff changeset
   882
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   883
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   884
lemma Crypt_notin_image_Key [simp]: "Crypt K X \<notin> Key ` A"
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   885
by auto
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   886
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   887
lemma Hash_notin_image_Key [simp] :"Hash X \<notin> Key ` A"
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   888
by auto
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   889
14200
d8598e24f8fa Removal of the Key_supply axiom (affects many possbility proofs) and minor
paulson
parents: 14181
diff changeset
   890
lemma synth_analz_mono: "G\<subseteq>H ==> synth (analz(G)) \<subseteq> synth (analz(H))"
17689
a04b5b43625e streamlined theory; conformance to recent publication
paulson
parents: 16818
diff changeset
   891
by (iprover intro: synth_mono analz_mono) 
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   892
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   893
lemma Fake_analz_eq [simp]:
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   894
     "X \<in> synth(analz H) ==> synth (analz (insert X H)) = synth (analz H)"
35566
3c01f5ad1d34 Simplified a couple of proofs and corrected a comment
paulson
parents: 35416
diff changeset
   895
by (metis Fake_analz_insert Un_absorb Un_absorb1 Un_commute 
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   896
          subset_insertI synth_analz_mono synth_increasing synth_subset_iff)
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   897
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   898
text\<open>Two generalizations of \<open>analz_insert_eq\<close>\<close>
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   899
lemma gen_analz_insert_eq [rule_format]:
35566
3c01f5ad1d34 Simplified a couple of proofs and corrected a comment
paulson
parents: 35416
diff changeset
   900
     "X \<in> analz H ==> ALL G. H \<subseteq> G --> analz (insert X G) = analz G"
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   901
by (blast intro: analz_cut analz_insertI analz_mono [THEN [2] rev_subsetD])
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   902
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   903
lemma synth_analz_insert_eq [rule_format]:
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   904
     "X \<in> synth (analz H) 
35566
3c01f5ad1d34 Simplified a couple of proofs and corrected a comment
paulson
parents: 35416
diff changeset
   905
      ==> ALL G. H \<subseteq> G --> (Key K \<in> analz (insert X G)) = (Key K \<in> analz G)"
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   906
apply (erule synth.induct) 
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   907
apply (simp_all add: gen_analz_insert_eq subset_trans [OF _ subset_insertI]) 
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   908
done
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   909
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   910
lemma Fake_parts_sing:
34185
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   911
     "X \<in> synth (analz H) ==> parts{X} \<subseteq> synth (analz H) \<union> parts H"
9316b8f56d83 tidied proofs
paulson
parents: 32960
diff changeset
   912
by (metis Fake_parts_insert empty_subsetI insert_mono parts_mono subset_trans)
13922
75ae4244a596 Changes required by the certified email protocol
paulson
parents: 11270
diff changeset
   913
14145
2e31b8cc8788 ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents: 14126
diff changeset
   914
lemmas Fake_parts_sing_imp_Un = Fake_parts_sing [THEN [2] rev_subsetD]
2e31b8cc8788 ZhouGollmann: new example (fair non-repudiation protocol)
paulson
parents: 14126
diff changeset
   915
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   916
method_setup spy_analz = \<open>
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   917
    Scan.succeed (SIMPLE_METHOD' o spy_analz_tac)\<close>
11189
1ea763a5d186 conversion of Message.thy to Isar format
paulson
parents: 10833
diff changeset
   918
    "for proving the Fake case when analz is involved"
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   919
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   920
method_setup atomic_spy_analz = \<open>
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   921
    Scan.succeed (SIMPLE_METHOD' o atomic_spy_analz_tac)\<close>
11264
a47a9288f3f6 (rough) conversion of Auth/Recur to Isar format
paulson
parents: 11251
diff changeset
   922
    "for debugging spy_analz"
a47a9288f3f6 (rough) conversion of Auth/Recur to Isar format
paulson
parents: 11251
diff changeset
   923
61830
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   924
method_setup Fake_insert_simp = \<open>
4f5ab843cf5b isabelle update_cartouches -c -t;
wenzelm
parents: 59780
diff changeset
   925
    Scan.succeed (SIMPLE_METHOD' o Fake_insert_simp_tac)\<close>
11264
a47a9288f3f6 (rough) conversion of Auth/Recur to Isar format
paulson
parents: 11251
diff changeset
   926
    "for debugging spy_analz"
a47a9288f3f6 (rough) conversion of Auth/Recur to Isar format
paulson
parents: 11251
diff changeset
   927
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   928
end