# HG changeset patch
# User paulson
# Date 983535511 -3600
# Node ID 1ea763a5d1867f6a5b53fd1d8b0752b3137da898
# Parent  5d539f1682c3ab2ae93845ce883c8c3d50586d45
conversion of Message.thy to Isar format

diff -r 5d539f1682c3 -r 1ea763a5d186 src/HOL/Auth/Event.thy
--- a/src/HOL/Auth/Event.thy	Fri Mar 02 13:14:37 2001 +0100
+++ b/src/HOL/Auth/Event.thy	Fri Mar 02 13:18:31 2001 +0100
@@ -14,12 +14,6 @@
 theory Event = Message
 files ("Event_lemmas.ML"):
 
-(*from Message.ML*)
-method_setup spy_analz = {*
-    Method.no_args (Method.METHOD (fn facts => spy_analz_tac 1)) *}
-    "for proving the Fake case when analz is involved"
-
-
 consts  (*Initial states of agents -- parameter of the construction*)
   initState :: "agent => msg set"
 
diff -r 5d539f1682c3 -r 1ea763a5d186 src/HOL/Auth/Event_lemmas.ML
--- a/src/HOL/Auth/Event_lemmas.ML	Fri Mar 02 13:14:37 2001 +0100
+++ b/src/HOL/Auth/Event_lemmas.ML	Fri Mar 02 13:18:31 2001 +0100
@@ -1,4 +1,4 @@
-(*  Title:      HOL/Auth/Event
+(*  Title:      HOL/Auth/Event_lemmas
     ID:         $Id$
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1996  University of Cambridge
@@ -20,8 +20,7 @@
       = parts {X} Un parts (knows Spy evs) -- since general case loops*)
 
 bind_thm ("parts_insert_knows_Spy",
-	  parts_insert |> 
-	  read_instantiate_sg (sign_of thy) [("H", "knows Spy evs")]);
+	  inst "H" "knows Spy evs" parts_insert);
 
 
 val expand_event_case = thm "event.split";
diff -r 5d539f1682c3 -r 1ea763a5d186 src/HOL/Auth/Message.ML
--- a/src/HOL/Auth/Message.ML	Fri Mar 02 13:14:37 2001 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,912 +0,0 @@
-(*  Title:      HOL/Auth/Message
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1996  University of Cambridge
-
-Datatypes of agents and messages;
-Inductive relations "parts", "analz" and "synth"
-*)
-
-
-(*Eliminates a commonly-occurring expression*)
-goal HOL.thy "~ (ALL x. x~=y)";
-by (Blast_tac 1);
-Addsimps [result()];
-
-AddIffs msg.inject;
-
-(*Equations hold because constructors are injective; cannot prove for all f*)
-Goal "(Friend x : Friend`A) = (x:A)";
-by Auto_tac;
-qed "Friend_image_eq";
-
-Goal "(Key x : Key`A) = (x:A)";
-by Auto_tac;
-qed "Key_image_eq";
-
-Goal "(Nonce x ~: Key`A)";
-by Auto_tac;
-qed "Nonce_Key_image_eq";
-Addsimps [Friend_image_eq, Key_image_eq, Nonce_Key_image_eq];
-
-
-(** Inverse of keys **)
-
-Goal "(invKey K = invKey K') = (K=K')";
-by Safe_tac;
-by (rtac box_equals 1);
-by (REPEAT (rtac invKey 2));
-by (Asm_simp_tac 1);
-qed "invKey_eq";
-
-Addsimps [invKey, invKey_eq];
-
-
-(**** keysFor operator ****)
-
-Goalw [keysFor_def] "keysFor {} = {}";
-by (Blast_tac 1);
-qed "keysFor_empty";
-
-Goalw [keysFor_def] "keysFor (H Un H') = keysFor H Un keysFor H'";
-by (Blast_tac 1);
-qed "keysFor_Un";
-
-Goalw [keysFor_def] "keysFor (UN i:A. H i) = (UN i:A. keysFor (H i))";
-by (Blast_tac 1);
-qed "keysFor_UN";
-
-(*Monotonicity*)
-Goalw [keysFor_def] "G<=H ==> keysFor(G) <= keysFor(H)";
-by (Blast_tac 1);
-qed "keysFor_mono";
-
-Goalw [keysFor_def] "keysFor (insert (Agent A) H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_Agent";
-
-Goalw [keysFor_def] "keysFor (insert (Nonce N) H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_Nonce";
-
-Goalw [keysFor_def] "keysFor (insert (Number N) H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_Number";
-
-Goalw [keysFor_def] "keysFor (insert (Key K) H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_Key";
-
-Goalw [keysFor_def] "keysFor (insert (Hash X) H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_Hash";
-
-Goalw [keysFor_def] "keysFor (insert {|X,Y|} H) = keysFor H";
-by Auto_tac;
-qed "keysFor_insert_MPair";
-
-Goalw [keysFor_def]
-    "keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)";
-by Auto_tac;
-qed "keysFor_insert_Crypt";
-
-Addsimps [keysFor_empty, keysFor_Un, keysFor_UN, 
-          keysFor_insert_Agent, keysFor_insert_Nonce, 
-	  keysFor_insert_Number, keysFor_insert_Key, 
-          keysFor_insert_Hash, keysFor_insert_MPair, keysFor_insert_Crypt];
-AddSEs [keysFor_Un RS equalityD1 RS subsetD RS UnE,
-	keysFor_UN RS equalityD1 RS subsetD RS UN_E];
-
-Goalw [keysFor_def] "keysFor (Key`E) = {}";
-by Auto_tac;
-qed "keysFor_image_Key";
-Addsimps [keysFor_image_Key];
-
-Goalw [keysFor_def] "Crypt K X : H ==> invKey K : keysFor H";
-by (Blast_tac 1);
-qed "Crypt_imp_invKey_keysFor";
-
-
-(**** Inductive relation "parts" ****)
-
-val major::prems = 
-Goal "[| {|X,Y|} : parts H;       \
-\            [| X : parts H; Y : parts H |] ==> P  \
-\         |] ==> P";
-by (cut_facts_tac [major] 1);
-by (resolve_tac prems 1);
-by (REPEAT (eresolve_tac [asm_rl, parts.Fst, parts.Snd] 1));
-qed "MPair_parts";
-
-AddIs  [parts.Inj];
-
-AddSEs [MPair_parts, make_elim parts.Body];
-(*NB These two rules are UNSAFE in the formal sense, as they discard the
-     compound message.  They work well on THIS FILE.  
-  MPair_parts is left as SAFE because it speeds up proofs.
-  The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.*)
-
-Goal "H <= parts(H)";
-by (Blast_tac 1);
-qed "parts_increasing";
-
-(*Monotonicity*)
-Goalw parts.defs "G<=H ==> parts(G) <= parts(H)";
-by (rtac lfp_mono 1);
-by (REPEAT (ares_tac basic_monos 1));
-qed "parts_mono";
-
-val parts_insertI = impOfSubs (subset_insertI RS parts_mono);
-
-Goal "parts{} = {}";
-by Safe_tac;
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-qed "parts_empty";
-Addsimps [parts_empty];
-
-Goal "X: parts{} ==> P";
-by (Asm_full_simp_tac 1);
-qed "parts_emptyE";
-AddSEs [parts_emptyE];
-
-(*WARNING: loops if H = {Y}, therefore must not be repeated!*)
-Goal "X: parts H ==> EX Y:H. X: parts {Y}";
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-qed "parts_singleton";
-
-
-(** Unions **)
-
-Goal "parts(G) Un parts(H) <= parts(G Un H)";
-by (REPEAT (ares_tac [Un_least, parts_mono, Un_upper1, Un_upper2] 1));
-val parts_Un_subset1 = result();
-
-Goal "parts(G Un H) <= parts(G) Un parts(H)";
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-val parts_Un_subset2 = result();
-
-Goal "parts(G Un H) = parts(G) Un parts(H)";
-by (REPEAT (ares_tac [equalityI, parts_Un_subset1, parts_Un_subset2] 1));
-qed "parts_Un";
-
-Goal "parts (insert X H) = parts {X} Un parts H";
-by (stac (read_instantiate [("A","H")] insert_is_Un) 1);
-by (simp_tac (HOL_ss addsimps [parts_Un]) 1);
-qed "parts_insert";
-
-(*TWO inserts to avoid looping.  This rewrite is better than nothing.
-  Not suitable for Addsimps: its behaviour can be strange.*)
-Goal "parts (insert X (insert Y H)) = parts {X} Un parts {Y} Un parts H";
-by (simp_tac (simpset() addsimps [Un_assoc]) 1);
-by (simp_tac (simpset() addsimps [parts_insert RS sym]) 1);
-qed "parts_insert2";
-
-Goal "(UN x:A. parts(H x)) <= parts(UN x:A. H x)";
-by (REPEAT (ares_tac [UN_least, parts_mono, UN_upper] 1));
-val parts_UN_subset1 = result();
-
-Goal "parts(UN x:A. H x) <= (UN x:A. parts(H x))";
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-val parts_UN_subset2 = result();
-
-Goal "parts(UN x:A. H x) = (UN x:A. parts(H x))";
-by (REPEAT (ares_tac [equalityI, parts_UN_subset1, parts_UN_subset2] 1));
-qed "parts_UN";
-
-(*Added to simplify arguments to parts, analz and synth.
-  NOTE: the UN versions are no longer used!*)
-Addsimps [parts_Un, parts_UN];
-AddSEs [parts_Un RS equalityD1 RS subsetD RS UnE,
-	parts_UN RS equalityD1 RS subsetD RS UN_E];
-
-Goal "insert X (parts H) <= parts(insert X H)";
-by (blast_tac (claset() addIs [impOfSubs parts_mono]) 1);
-qed "parts_insert_subset";
-
-(** Idempotence and transitivity **)
-
-Goal "X: parts (parts H) ==> X: parts H";
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-qed "parts_partsD";
-AddSDs [parts_partsD];
-
-Goal "parts (parts H) = parts H";
-by (Blast_tac 1);
-qed "parts_idem";
-Addsimps [parts_idem];
-
-Goal "[| X: parts G;  G <= parts H |] ==> X: parts H";
-by (dtac parts_mono 1);
-by (Blast_tac 1);
-qed "parts_trans";
-
-(*Cut*)
-Goal "[| Y: parts (insert X G);  X: parts H |] \
-\              ==> Y: parts (G Un H)";
-by (etac parts_trans 1);
-by Auto_tac;
-qed "parts_cut";
-
-Goal "X: parts H ==> parts (insert X H) = parts H";
-by (fast_tac (claset() addSDs [parts_cut]
-                       addIs  [parts_insertI] 
-                       addss (simpset())) 1);
-qed "parts_cut_eq";
-
-Addsimps [parts_cut_eq];
-
-
-(** Rewrite rules for pulling out atomic messages **)
-
-fun parts_tac i =
-  EVERY [rtac ([subsetI, parts_insert_subset] MRS equalityI) i,
-         etac parts.induct i,
-         Auto_tac];
-
-Goal "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)";
-by (parts_tac 1);
-qed "parts_insert_Agent";
-
-Goal "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)";
-by (parts_tac 1);
-qed "parts_insert_Nonce";
-
-Goal "parts (insert (Number N) H) = insert (Number N) (parts H)";
-by (parts_tac 1);
-qed "parts_insert_Number";
-
-Goal "parts (insert (Key K) H) = insert (Key K) (parts H)";
-by (parts_tac 1);
-qed "parts_insert_Key";
-
-Goal "parts (insert (Hash X) H) = insert (Hash X) (parts H)";
-by (parts_tac 1);
-qed "parts_insert_Hash";
-
-Goal "parts (insert (Crypt K X) H) = \
-\         insert (Crypt K X) (parts (insert X H))";
-by (rtac equalityI 1);
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by Auto_tac;
-by (etac parts.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs [parts.Body])));
-qed "parts_insert_Crypt";
-
-Goal "parts (insert {|X,Y|} H) = \
-\         insert {|X,Y|} (parts (insert X (insert Y H)))";
-by (rtac equalityI 1);
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by Auto_tac;
-by (etac parts.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs [parts.Fst, parts.Snd])));
-qed "parts_insert_MPair";
-
-Addsimps [parts_insert_Agent, parts_insert_Nonce, 
-	  parts_insert_Number, parts_insert_Key, 
-          parts_insert_Hash, parts_insert_Crypt, parts_insert_MPair];
-
-
-Goal "parts (Key`N) = Key`N";
-by Auto_tac;
-by (etac parts.induct 1);
-by Auto_tac;
-qed "parts_image_Key";
-Addsimps [parts_image_Key];
-
-
-(*In any message, there is an upper bound N on its greatest nonce.*)
-Goal "EX N. ALL n. N<=n --> Nonce n ~: parts {msg}";
-by (induct_tac "msg" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [exI, parts_insert2])));
-(*MPair case: blast_tac works out the necessary sum itself!*)
-by (blast_tac (claset() addSEs [add_leE]) 2);
-(*Nonce case*)
-by (res_inst_tac [("x","N + Suc nat")] exI 1);
-by (auto_tac (claset() addSEs [add_leE], simpset()));
-qed "msg_Nonce_supply";
-
-
-(**** Inductive relation "analz" ****)
-
-val major::prems = 
-Goal "[| {|X,Y|} : analz H;       \
-\            [| X : analz H; Y : analz H |] ==> P  \
-\         |] ==> P";
-by (cut_facts_tac [major] 1);
-by (resolve_tac prems 1);
-by (REPEAT (eresolve_tac [asm_rl, analz.Fst, analz.Snd] 1));
-qed "MPair_analz";
-
-AddSEs [MPair_analz];     (*Making it safe speeds up proofs*)
-AddDs  [analz.Decrypt];   (*Unsafe: we don't want to split up certificates!*)
-AddIs  [analz.Inj];
-
-Addsimps [analz.Inj];
-
-Goal "H <= analz(H)";
-by (Blast_tac 1);
-qed "analz_increasing";
-
-Goal "analz H <= parts H";
-by (rtac subsetI 1);
-by (etac analz.induct 1);
-by (ALLGOALS Blast_tac);
-qed "analz_subset_parts";
-
-bind_thm ("not_parts_not_analz", analz_subset_parts RS contra_subsetD);
-
-
-Goal "parts (analz H) = parts H";
-by (rtac equalityI 1);
-by (rtac (analz_subset_parts RS parts_mono RS subset_trans) 1);
-by (Simp_tac 1);
-by (blast_tac (claset() addIs [analz_increasing RS parts_mono RS subsetD]) 1);
-qed "parts_analz";
-Addsimps [parts_analz];
-
-Goal "analz (parts H) = parts H";
-by Auto_tac;
-by (etac analz.induct 1);
-by Auto_tac;
-qed "analz_parts";
-Addsimps [analz_parts];
-
-(*Monotonicity; Lemma 1 of Lowe*)
-Goalw analz.defs "G<=H ==> analz(G) <= analz(H)";
-by (rtac lfp_mono 1);
-by (REPEAT (ares_tac basic_monos 1));
-qed "analz_mono";
-
-bind_thm ("analz_insertI", impOfSubs (subset_insertI RS analz_mono));
-
-(** General equational properties **)
-
-Goal "analz{} = {}";
-by Safe_tac;
-by (etac analz.induct 1);
-by (ALLGOALS Blast_tac);
-qed "analz_empty";
-Addsimps [analz_empty];
-
-(*Converse fails: we can analz more from the union than from the 
-  separate parts, as a key in one might decrypt a message in the other*)
-Goal "analz(G) Un analz(H) <= analz(G Un H)";
-by (REPEAT (ares_tac [Un_least, analz_mono, Un_upper1, Un_upper2] 1));
-qed "analz_Un";
-
-Goal "insert X (analz H) <= analz(insert X H)";
-by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1);
-qed "analz_insert";
-
-(** Rewrite rules for pulling out atomic messages **)
-
-fun analz_tac i =
-  EVERY [rtac ([subsetI, analz_insert] MRS equalityI) i,
-         etac analz.induct i,
-         Auto_tac];
-
-Goal "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Agent";
-
-Goal "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Nonce";
-
-Goal "analz (insert (Number N) H) = insert (Number N) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Number";
-
-Goal "analz (insert (Hash X) H) = insert (Hash X) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Hash";
-
-(*Can only pull out Keys if they are not needed to decrypt the rest*)
-Goalw [keysFor_def]
-    "K ~: keysFor (analz H) ==>  \
-\         analz (insert (Key K) H) = insert (Key K) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Key";
-
-Goal "analz (insert {|X,Y|} H) = \
-\         insert {|X,Y|} (analz (insert X (insert Y H)))";
-by (rtac equalityI 1);
-by (rtac subsetI 1);
-by (etac analz.induct 1);
-by Auto_tac;
-by (etac analz.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs [analz.Fst, analz.Snd])));
-qed "analz_insert_MPair";
-
-(*Can pull out enCrypted message if the Key is not known*)
-Goal "Key (invKey K) ~: analz H ==>  \
-\              analz (insert (Crypt K X) H) = \
-\              insert (Crypt K X) (analz H)";
-by (analz_tac 1);
-qed "analz_insert_Crypt";
-
-Goal "Key (invKey K) : analz H ==>  \
-\              analz (insert (Crypt K X) H) <= \
-\              insert (Crypt K X) (analz (insert X H))";
-by (rtac subsetI 1);
-by (eres_inst_tac [("xa","x")] analz.induct 1);
-by Auto_tac;
-val lemma1 = result();
-
-Goal "Key (invKey K) : analz H ==>  \
-\              insert (Crypt K X) (analz (insert X H)) <= \
-\              analz (insert (Crypt K X) H)";
-by Auto_tac;
-by (eres_inst_tac [("xa","x")] analz.induct 1);
-by Auto_tac;
-by (blast_tac (claset() addIs [analz_insertI, analz.Decrypt]) 1);
-val lemma2 = result();
-
-Goal "Key (invKey K) : analz H ==>  \
-\              analz (insert (Crypt K X) H) = \
-\              insert (Crypt K X) (analz (insert X H))";
-by (REPEAT (ares_tac [equalityI, lemma1, lemma2] 1));
-qed "analz_insert_Decrypt";
-
-(*Case analysis: either the message is secure, or it is not!
-  Effective, but can cause subgoals to blow up!
-  Use with split_if;  apparently split_tac does not cope with patterns
-  such as "analz (insert (Crypt K X) H)" *)
-Goal "analz (insert (Crypt K X) H) =                \
-\         (if (Key (invKey K) : analz H)                \
-\          then insert (Crypt K X) (analz (insert X H)) \
-\          else insert (Crypt K X) (analz H))";
-by (case_tac "Key (invKey K)  : analz H " 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsimps [analz_insert_Crypt, 
-						analz_insert_Decrypt])));
-qed "analz_Crypt_if";
-
-Addsimps [analz_insert_Agent, analz_insert_Nonce, 
-	  analz_insert_Number, analz_insert_Key, 
-          analz_insert_Hash, analz_insert_MPair, analz_Crypt_if];
-
-(*This rule supposes "for the sake of argument" that we have the key.*)
-Goal  "analz (insert (Crypt K X) H) <=  \
-\          insert (Crypt K X) (analz (insert X H))";
-by (rtac subsetI 1);
-by (etac analz.induct 1);
-by Auto_tac;
-qed "analz_insert_Crypt_subset";
-
-
-Goal "analz (Key`N) = Key`N";
-by Auto_tac;
-by (etac analz.induct 1);
-by Auto_tac;
-qed "analz_image_Key";
-
-Addsimps [analz_image_Key];
-
-
-(** Idempotence and transitivity **)
-
-Goal "X: analz (analz H) ==> X: analz H";
-by (etac analz.induct 1);
-by (ALLGOALS Blast_tac);
-qed "analz_analzD";
-AddSDs [analz_analzD];
-
-Goal "analz (analz H) = analz H";
-by (Blast_tac 1);
-qed "analz_idem";
-Addsimps [analz_idem];
-
-Goal "[| X: analz G;  G <= analz H |] ==> X: analz H";
-by (dtac analz_mono 1);
-by (Blast_tac 1);
-qed "analz_trans";
-
-(*Cut; Lemma 2 of Lowe*)
-Goal "[| Y: analz (insert X H);  X: analz H |] ==> Y: analz H";
-by (etac analz_trans 1);
-by (Blast_tac 1);
-qed "analz_cut";
-
-(*Cut can be proved easily by induction on
-   "Y: analz (insert X H) ==> X: analz H --> Y: analz H"
-*)
-
-(*This rewrite rule helps in the simplification of messages that involve
-  the forwarding of unknown components (X).  Without it, removing occurrences
-  of X can be very complicated. *)
-Goal "X: analz H ==> analz (insert X H) = analz H";
-by (blast_tac (claset() addIs [analz_cut, analz_insertI]) 1);
-qed "analz_insert_eq";
-
-
-(** A congruence rule for "analz" **)
-
-Goal "[| analz G <= analz G'; analz H <= analz H' \
-\              |] ==> analz (G Un H) <= analz (G' Un H')";
-by (Clarify_tac 1);
-by (etac analz.induct 1);
-by (ALLGOALS (best_tac (claset() addIs [analz_mono RS subsetD])));
-qed "analz_subset_cong";
-
-Goal "[| analz G = analz G'; analz H = analz H' \
-\              |] ==> analz (G Un H) = analz (G' Un H')";
-by (REPEAT_FIRST (ares_tac [equalityI, analz_subset_cong]
-          ORELSE' etac equalityE));
-qed "analz_cong";
-
-
-Goal "analz H = analz H' ==> analz(insert X H) = analz(insert X H')";
-by (asm_simp_tac (simpset() addsimps [insert_def] delsimps [singleton_conv]
-                            setloop (rtac analz_cong)) 1);
-qed "analz_insert_cong";
-
-(*If there are no pairs or encryptions then analz does nothing*)
-Goal "[| ALL X Y. {|X,Y|} ~: H;  ALL X K. Crypt K X ~: H |] ==> \
-\         analz H = H";
-by Safe_tac;
-by (etac analz.induct 1);
-by (ALLGOALS Blast_tac);
-qed "analz_trivial";
-
-(*These two are obsolete (with a single Spy) but cost little to prove...*)
-Goal "X: analz (UN i:A. analz (H i)) ==> X: analz (UN i:A. H i)";
-by (etac analz.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs [impOfSubs analz_mono])));
-val lemma = result();
-
-Goal "analz (UN i:A. analz (H i)) = analz (UN i:A. H i)";
-by (blast_tac (claset() addIs [lemma, impOfSubs analz_mono]) 1);
-qed "analz_UN_analz";
-Addsimps [analz_UN_analz];
-
-
-(**** Inductive relation "synth" ****)
-
-AddIs  synth.intrs;
-
-(*NO Agent_synth, as any Agent name can be synthesized.  Ditto for Number*)
-val Nonce_synth = synth.mk_cases "Nonce n : synth H";
-val Key_synth   = synth.mk_cases "Key K : synth H";
-val Hash_synth  = synth.mk_cases "Hash X : synth H";
-val MPair_synth = synth.mk_cases "{|X,Y|} : synth H";
-val Crypt_synth = synth.mk_cases "Crypt K X : synth H";
-
-AddSEs [Nonce_synth, Key_synth, Hash_synth, MPair_synth, Crypt_synth];
-
-Goal "H <= synth(H)";
-by (Blast_tac 1);
-qed "synth_increasing";
-
-(*Monotonicity*)
-Goalw synth.defs "G<=H ==> synth(G) <= synth(H)";
-by (rtac lfp_mono 1);
-by (REPEAT (ares_tac basic_monos 1));
-qed "synth_mono";
-
-(** Unions **)
-
-(*Converse fails: we can synth more from the union than from the 
-  separate parts, building a compound message using elements of each.*)
-Goal "synth(G) Un synth(H) <= synth(G Un H)";
-by (REPEAT (ares_tac [Un_least, synth_mono, Un_upper1, Un_upper2] 1));
-qed "synth_Un";
-
-Goal "insert X (synth H) <= synth(insert X H)";
-by (blast_tac (claset() addIs [impOfSubs synth_mono]) 1);
-qed "synth_insert";
-
-(** Idempotence and transitivity **)
-
-Goal "X: synth (synth H) ==> X: synth H";
-by (etac synth.induct 1);
-by (ALLGOALS Blast_tac);
-qed "synth_synthD";
-AddSDs [synth_synthD];
-
-Goal "synth (synth H) = synth H";
-by (Blast_tac 1);
-qed "synth_idem";
-
-Goal "[| X: synth G;  G <= synth H |] ==> X: synth H";
-by (dtac synth_mono 1);
-by (Blast_tac 1);
-qed "synth_trans";
-
-(*Cut; Lemma 2 of Lowe*)
-Goal "[| Y: synth (insert X H);  X: synth H |] ==> Y: synth H";
-by (etac synth_trans 1);
-by (Blast_tac 1);
-qed "synth_cut";
-
-Goal "Agent A : synth H";
-by (Blast_tac 1);
-qed "Agent_synth";
-
-Goal "Number n : synth H";
-by (Blast_tac 1);
-qed "Number_synth";
-
-Goal "(Nonce N : synth H) = (Nonce N : H)";
-by (Blast_tac 1);
-qed "Nonce_synth_eq";
-
-Goal "(Key K : synth H) = (Key K : H)";
-by (Blast_tac 1);
-qed "Key_synth_eq";
-
-Goal "Key K ~: H ==> (Crypt K X : synth H) = (Crypt K X : H)";
-by (Blast_tac 1);
-qed "Crypt_synth_eq";
-
-Addsimps [Agent_synth, Number_synth, 
-	  Nonce_synth_eq, Key_synth_eq, Crypt_synth_eq];
-
-
-Goalw [keysFor_def]
-    "keysFor (synth H) = keysFor H Un invKey`{K. Key K : H}";
-by (Blast_tac 1);
-qed "keysFor_synth";
-Addsimps [keysFor_synth];
-
-
-(*** Combinations of parts, analz and synth ***)
-
-Goal "parts (synth H) = parts H Un synth H";
-by (rtac equalityI 1);
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by (ALLGOALS
-    (blast_tac (claset() addIs ((synth_increasing RS parts_mono RS subsetD)
-				::parts.intrs))));
-qed "parts_synth";
-Addsimps [parts_synth];
-
-Goal "analz (analz G Un H) = analz (G Un H)";
-by (REPEAT_FIRST (resolve_tac [equalityI, analz_subset_cong]));
-by (ALLGOALS Simp_tac);
-qed "analz_analz_Un";
-
-Goal "analz (synth G Un H) = analz (G Un H) Un synth G";
-by (rtac equalityI 1);
-by (rtac subsetI 1);
-by (etac analz.induct 1);
-by (blast_tac (claset() addIs [impOfSubs analz_mono]) 5);
-by (ALLGOALS (blast_tac (claset() addIs analz.intrs)));
-qed "analz_synth_Un";
-
-Goal "analz (synth H) = analz H Un synth H";
-by (cut_inst_tac [("H","{}")] analz_synth_Un 1);
-by (Full_simp_tac 1);
-qed "analz_synth";
-Addsimps [analz_analz_Un, analz_synth_Un, analz_synth];
-
-
-(** For reasoning about the Fake rule in traces **)
-
-Goal "X: G ==> parts(insert X H) <= parts G Un parts H";
-by (rtac ([parts_mono, parts_Un_subset2] MRS subset_trans) 1);
-by (Blast_tac 1);
-qed "parts_insert_subset_Un";
-
-(*More specifically for Fake.  Very occasionally we could do with a version
-  of the form  parts{X} <= synth (analz H) Un parts H *)
-Goal "X: synth (analz H) ==> \
-\     parts (insert X H) <= synth (analz H) Un parts H";
-by (dtac parts_insert_subset_Un 1);
-by (Full_simp_tac 1);
-by (Blast_tac 1);
-qed "Fake_parts_insert";
-
-(*H is sometimes (Key ` KK Un spies evs), so can't put G=H*)
-Goal "X: synth (analz G) ==> \
-\     analz (insert X H) <= synth (analz G) Un analz (G Un H)";
-by (rtac subsetI 1);
-by (subgoal_tac "x : analz (synth (analz G) Un H)" 1);
-by (blast_tac (claset() addIs [impOfSubs analz_mono,
-			       impOfSubs (analz_mono RS synth_mono)]) 2);
-by (Full_simp_tac 1);
-by (Blast_tac 1);
-qed "Fake_analz_insert";
-
-Goal "(X: analz H & X: parts H) = (X: analz H)";
-by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
-val analz_conj_parts = result();
-
-Goal "(X: analz H | X: parts H) = (X: parts H)";
-by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
-val analz_disj_parts = result();
-
-AddIffs [analz_conj_parts, analz_disj_parts];
-
-(*Without this equation, other rules for synth and analz would yield
-  redundant cases*)
-Goal "({|X,Y|} : synth (analz H)) = \
-\     (X : synth (analz H) & Y : synth (analz H))";
-by (Blast_tac 1);
-qed "MPair_synth_analz";
-
-AddIffs [MPair_synth_analz];
-
-Goal "[| Key K : analz H;  Key (invKey K) : analz H |] \
-\      ==> (Crypt K X : synth (analz H)) = (X : synth (analz H))";
-by (Blast_tac 1);
-qed "Crypt_synth_analz";
-
-
-Goal "X ~: synth (analz H) \
-\     ==> (Hash{|X,Y|} : synth (analz H)) = (Hash{|X,Y|} : analz H)";
-by (Blast_tac 1);
-qed "Hash_synth_analz";
-Addsimps [Hash_synth_analz];
-
-
-(**** HPair: a combination of Hash and MPair ****)
-
-(*** Freeness ***)
-
-Goalw [HPair_def] "Agent A ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Agent_neq_HPair";
-
-Goalw [HPair_def] "Nonce N ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Nonce_neq_HPair";
-
-Goalw [HPair_def] "Number N ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Number_neq_HPair";
-
-Goalw [HPair_def] "Key K ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Key_neq_HPair";
-
-Goalw [HPair_def] "Hash Z ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Hash_neq_HPair";
-
-Goalw [HPair_def] "Crypt K X' ~= Hash[X] Y";
-by (Simp_tac 1);
-qed "Crypt_neq_HPair";
-
-val HPair_neqs = [Agent_neq_HPair, Nonce_neq_HPair, Number_neq_HPair, 
-                  Key_neq_HPair, Hash_neq_HPair, Crypt_neq_HPair];
-
-AddIffs HPair_neqs;
-AddIffs (HPair_neqs RL [not_sym]);
-
-Goalw [HPair_def] "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)";
-by (Simp_tac 1);
-qed "HPair_eq";
-
-Goalw [HPair_def] "({|X',Y'|} = Hash[X] Y) = (X' = Hash{|X,Y|} & Y'=Y)";
-by (Simp_tac 1);
-qed "MPair_eq_HPair";
-
-Goalw [HPair_def] "(Hash[X] Y = {|X',Y'|}) = (X' = Hash{|X,Y|} & Y'=Y)";
-by Auto_tac;
-qed "HPair_eq_MPair";
-
-AddIffs [HPair_eq, MPair_eq_HPair, HPair_eq_MPair];
-
-
-(*** Specialized laws, proved in terms of those for Hash and MPair ***)
-
-Goalw [HPair_def] "keysFor (insert (Hash[X] Y) H) = keysFor H";
-by (Simp_tac 1);
-qed "keysFor_insert_HPair";
-
-Goalw [HPair_def]
-    "parts (insert (Hash[X] Y) H) = \
-\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (parts (insert Y H)))";
-by (Simp_tac 1);
-qed "parts_insert_HPair";
-
-Goalw [HPair_def]
-    "analz (insert (Hash[X] Y) H) = \
-\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (analz (insert Y H)))";
-by (Simp_tac 1);
-qed "analz_insert_HPair";
-
-Goalw [HPair_def] "X ~: synth (analz H) \
-\   ==> (Hash[X] Y : synth (analz H)) = \
-\       (Hash {|X, Y|} : analz H & Y : synth (analz H))";
-by (Simp_tac 1);
-by (Blast_tac 1);
-qed "HPair_synth_analz";
-
-Addsimps [keysFor_insert_HPair, parts_insert_HPair, analz_insert_HPair, 
-          HPair_synth_analz, HPair_synth_analz];
-
-
-(*We do NOT want Crypt... messages broken up in protocols!!*)
-Delrules [make_elim parts.Body];
-
-
-(** Rewrites to push in Key and Crypt messages, so that other messages can
-    be pulled out using the analz_insert rules **)
-
-fun insComm thy x y = read_instantiate_sg (sign_of thy) [("x",x), ("y",y)] 
-                          insert_commute;
-
-val pushKeys = map (insComm thy "Key ?K") 
-                   ["Agent ?C", "Nonce ?N", "Number ?N", 
-		    "Hash ?X", "MPair ?X ?Y", "Crypt ?X ?K'"];
-
-val pushCrypts = map (insComm thy "Crypt ?X ?K") 
-                     ["Agent ?C", "Nonce ?N", "Number ?N", 
-		      "Hash ?X'", "MPair ?X' ?Y"];
-
-(*Cannot be added with Addsimps -- we don't always want to re-order messages*)
-bind_thms ("pushes", pushKeys@pushCrypts);
-
-
-(*** Tactics useful for many protocol proofs ***)
-
-(*Prove base case (subgoal i) and simplify others.  A typical base case
-  concerns  Crypt K X ~: Key`shrK`bad  and cannot be proved by rewriting
-  alone.*)
-fun prove_simple_subgoals_tac i = 
-    force_tac (claset(), simpset() addsimps [image_eq_UN]) i THEN
-    ALLGOALS Asm_simp_tac;
-
-fun Fake_parts_insert_tac i = 
-    blast_tac (claset() addIs [parts_insertI]
-			addDs [impOfSubs analz_subset_parts,
-			       impOfSubs Fake_parts_insert]) i;
-
-(*Apply rules to break down assumptions of the form
-  Y : parts(insert X H)  and  Y : analz(insert X H)
-*)
-val Fake_insert_tac = 
-    dresolve_tac [impOfSubs Fake_analz_insert,
-                  impOfSubs Fake_parts_insert] THEN'
-    eresolve_tac [asm_rl, synth.Inj];
-
-fun Fake_insert_simp_tac i = 
-    REPEAT (Fake_insert_tac i) THEN Asm_full_simp_tac i;
-
-
-(*Analysis of Fake cases.  Also works for messages that forward unknown parts,
-  but this application is no longer necessary if analz_insert_eq is used.
-  Abstraction over i is ESSENTIAL: it delays the dereferencing of claset
-  DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
-
-val atomic_spy_analz_tac = SELECT_GOAL
-    (Fake_insert_simp_tac 1
-     THEN
-     IF_UNSOLVED (Blast.depth_tac
-		  (claset() addIs [analz_insertI,
-				   impOfSubs analz_subset_parts]) 4 1));
-
-fun spy_analz_tac i =
-  DETERM
-   (SELECT_GOAL
-     (EVERY 
-      [  (*push in occurrences of X...*)
-       (REPEAT o CHANGED)
-           (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1),
-       (*...allowing further simplifications*)
-       Simp_tac 1,
-       REPEAT (FIRSTGOAL (resolve_tac [allI,impI,notI,conjI,iffI])),
-       DEPTH_SOLVE (atomic_spy_analz_tac 1)]) i);
-
-
-(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*)
-goal Set.thy "A Un (B Un A) = B Un A";
-by (Blast_tac 1);
-val Un_absorb3 = result();
-Addsimps [Un_absorb3];
-
-(*By default only o_apply is built-in.  But in the presence of eta-expansion
-  this means that some terms displayed as (f o g) will be rewritten, and others
-  will not!*)
-Addsimps [o_def];
diff -r 5d539f1682c3 -r 1ea763a5d186 src/HOL/Auth/Message.thy
--- a/src/HOL/Auth/Message.thy	Fri Mar 02 13:14:37 2001 +0100
+++ b/src/HOL/Auth/Message.thy	Fri Mar 02 13:18:31 2001 +0100
@@ -7,22 +7,31 @@
 Inductive relations "parts", "analz" and "synth"
 *)
 
-Message = Main +
+theory Message = Main
+files ("Message_lemmas.ML"):
+
+(*Eliminates a commonly-occurring expression*)
+lemma [simp] : "~ (ALL x. x~=y)"
+by blast
+
+(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*)
+lemma [simp] : "A Un (B Un A) = B Un A"
+by blast
 
 types 
   key = nat
 
 consts
-  invKey :: key=>key
+  invKey :: "key=>key"
 
-rules
-  invKey "invKey (invKey K) = K"
+axioms
+  invKey [simp] : "invKey (invKey K) = K"
 
   (*The inverse of a symmetric key is itself;
     that of a public key is the private key and vice versa*)
 
 constdefs
-  isSymKey :: key=>bool
+  isSymKey :: "key=>bool"
   "isSymKey K == (invKey K = K)"
 
 datatype  (*We allow any number of friendly agents*)
@@ -43,7 +52,7 @@
   "@MTuple"      :: "['a, args] => 'a * 'b"       ("(2{|_,/ _|})")
 
 syntax (xsymbols)
-  "@MTuple"      :: "['a, args] => 'a * 'b"       ("(2\\<lbrace>_,/ _\\<rbrace>)")
+  "@MTuple"      :: "['a, args] => 'a * 'b"       ("(2\<lbrace>_,/ _\<rbrace>)")
 
 translations
   "{|x, y, z|}"   == "{|x, {|y, z|}|}"
@@ -52,50 +61,86 @@
 
 constdefs
   (*Message Y, paired with a MAC computed with the help of X*)
-  HPair :: "[msg,msg]=>msg"                       ("(4Hash[_] /_)" [0, 1000])
+  HPair :: "[msg,msg] => msg"                       ("(4Hash[_] /_)" [0, 1000])
     "Hash[X] Y == {| Hash{|X,Y|}, Y|}"
 
   (*Keys useful to decrypt elements of a message set*)
-  keysFor :: msg set => key set
+  keysFor :: "msg set => key set"
   "keysFor H == invKey ` {K. EX X. Crypt K X : H}"
 
 (** Inductive definition of all "parts" of a message.  **)
 
-consts  parts   :: msg set => msg set
+consts  parts   :: "msg set => msg set"
 inductive "parts H"
-  intrs 
-    Inj     "X: H  ==>  X: parts H"
-    Fst     "{|X,Y|}   : parts H ==> X : parts H"
-    Snd     "{|X,Y|}   : parts H ==> Y : parts H"
-    Body    "Crypt K X : parts H ==> X : parts H"
+  intros 
+    Inj [intro]          : "X: H  ==> X : parts H"
+    Fst:     "{|X,Y|}   : parts H ==> X : parts H"
+    Snd:     "{|X,Y|}   : parts H ==> Y : parts H"
+    Body:    "Crypt K X : parts H ==> X : parts H"
+
+
+(*Monotonicity*)
+lemma parts_mono: "G<=H ==> parts(G) <= parts(H)"
+apply auto
+apply (erule parts.induct) 
+apply (auto dest: Fst Snd Body) 
+done
 
 
 (** Inductive definition of "analz" -- what can be broken down from a set of
     messages, including keys.  A form of downward closure.  Pairs can
     be taken apart; messages decrypted with known keys.  **)
 
-consts  analz   :: msg set => msg set
+consts  analz   :: "msg set => msg set"
 inductive "analz H"
-  intrs 
-    Inj     "X: H ==> X: analz H"
-    Fst     "{|X,Y|} : analz H ==> X : analz H"
-    Snd     "{|X,Y|} : analz H ==> Y : analz H"
-    Decrypt "[| Crypt K X : analz H; Key(invKey K): analz H |] ==> X : analz H"
+  intros 
+    Inj [intro,simp] :    "X: H ==> X: analz H"
+    Fst:     "{|X,Y|} : analz H ==> X : analz H"
+    Snd:     "{|X,Y|} : analz H ==> Y : analz H"
+    Decrypt [dest]: 
+             "[|Crypt K X : analz H; Key(invKey K): analz H|] ==> X : analz H"
 
 
+(*Monotonicity; Lemma 1 of Lowe's paper*)
+lemma analz_mono: "G<=H ==> analz(G) <= analz(H)"
+apply auto
+apply (erule analz.induct) 
+apply (auto dest: Fst Snd) 
+done
+
 (** Inductive definition of "synth" -- what can be built up from a set of
     messages.  A form of upward closure.  Pairs can be built, messages
     encrypted with known keys.  Agent names are public domain.
     Numbers can be guessed, but Nonces cannot be.  **)
 
-consts  synth   :: msg set => msg set
+consts  synth   :: "msg set => msg set"
 inductive "synth H"
-  intrs 
-    Inj     "X: H ==> X: synth H"
-    Agent   "Agent agt : synth H"
-    Number  "Number n  : synth H"
-    Hash    "X: synth H ==> Hash X : synth H"
-    MPair   "[| X: synth H;  Y: synth H |] ==> {|X,Y|} : synth H"
-    Crypt   "[| X: synth H;  Key(K) : H |] ==> Crypt K X : synth H"
+  intros 
+    Inj    [intro]:   "X: H ==> X: synth H"
+    Agent  [intro]:   "Agent agt : synth H"
+    Number [intro]:   "Number n  : synth H"
+    Hash   [intro]:   "X: synth H ==> Hash X : synth H"
+    MPair  [intro]:   "[|X: synth H;  Y: synth H|] ==> {|X,Y|} : synth H"
+    Crypt  [intro]:   "[|X: synth H;  Key(K) : H|] ==> Crypt K X : synth H"
+
+(*Monotonicity*)
+lemma synth_mono: "G<=H ==> synth(G) <= synth(H)"
+apply auto
+apply (erule synth.induct) 
+apply (auto dest: Fst Snd Body) 
+done
+
+(*NO Agent_synth, as any Agent name can be synthesized.  Ditto for Number*)
+inductive_cases Nonce_synth [elim!]: "Nonce n : synth H"
+inductive_cases Key_synth   [elim!]: "Key K : synth H"
+inductive_cases Hash_synth  [elim!]: "Hash X : synth H"
+inductive_cases MPair_synth [elim!]: "{|X,Y|} : synth H"
+inductive_cases Crypt_synth [elim!]: "Crypt K X : synth H"
+
+use "Message_lemmas.ML"
+
+method_setup spy_analz = {*
+    Method.no_args (Method.METHOD (fn facts => spy_analz_tac 1)) *}
+    "for proving the Fake case when analz is involved"
 
 end
diff -r 5d539f1682c3 -r 1ea763a5d186 src/HOL/Auth/Message_lemmas.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Auth/Message_lemmas.ML	Fri Mar 02 13:18:31 2001 +0100
@@ -0,0 +1,900 @@
+(*  Title:      HOL/Auth/Message
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1996  University of Cambridge
+
+Datatypes of agents and messages;
+Inductive relations "parts", "analz" and "synth"
+*)
+
+(*ML bindings for definitions and axioms*)
+val invKey = thm "invKey";
+val keysFor_def = thm "keysFor_def";
+val parts_mono = thm "parts_mono";
+val analz_mono = thm "analz_mono";
+val synth_mono = thm "synth_mono";
+val HPair_def = thm "HPair_def";
+val isSymKey_def = thm "isSymKey_def";
+
+structure parts =
+  struct
+  val induct = thm "parts.induct";
+  val Inj    = thm "parts.Inj";
+  val Fst    = thm "parts.Fst";
+  val Snd    = thm "parts.Snd";
+  val Body   = thm "parts.Body";
+  end;
+
+structure analz =
+  struct
+  val induct = thm "analz.induct";
+  val Inj    = thm "analz.Inj";
+  val Fst    = thm "analz.Fst";
+  val Snd    = thm "analz.Snd";
+  val Decrypt = thm "analz.Decrypt";
+  end;
+
+structure synth =
+  struct
+  val induct = thm "synth.induct";
+  val Inj    = thm "synth.Inj";
+  val Agent  = thm "synth.Agent";
+  val Number = thm "synth.Number";
+  val Hash   = thm "synth.Hash";
+  val Crypt  = thm "synth.Crypt";
+  end;
+
+
+(*Equations hold because constructors are injective; cannot prove for all f*)
+Goal "(Friend x : Friend`A) = (x:A)";
+by Auto_tac;
+qed "Friend_image_eq";
+
+Goal "(Key x : Key`A) = (x:A)";
+by Auto_tac;
+qed "Key_image_eq";
+
+Goal "(Nonce x ~: Key`A)";
+by Auto_tac;
+qed "Nonce_Key_image_eq";
+Addsimps [Friend_image_eq, Key_image_eq, Nonce_Key_image_eq];
+
+
+(** Inverse of keys **)
+
+Goal "(invKey K = invKey K') = (K=K')";
+by Safe_tac;
+by (rtac box_equals 1);
+by (REPEAT (rtac invKey 2));
+by (Asm_simp_tac 1);
+qed "invKey_eq";
+
+Addsimps [invKey_eq];
+
+
+(**** keysFor operator ****)
+
+Goalw [keysFor_def] "keysFor {} = {}";
+by (Blast_tac 1);
+qed "keysFor_empty";
+
+Goalw [keysFor_def] "keysFor (H Un H') = keysFor H Un keysFor H'";
+by (Blast_tac 1);
+qed "keysFor_Un";
+
+Goalw [keysFor_def] "keysFor (UN i:A. H i) = (UN i:A. keysFor (H i))";
+by (Blast_tac 1);
+qed "keysFor_UN";
+
+(*Monotonicity*)
+Goalw [keysFor_def] "G<=H ==> keysFor(G) <= keysFor(H)";
+by (Blast_tac 1);
+qed "keysFor_mono";
+
+Goalw [keysFor_def] "keysFor (insert (Agent A) H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_Agent";
+
+Goalw [keysFor_def] "keysFor (insert (Nonce N) H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_Nonce";
+
+Goalw [keysFor_def] "keysFor (insert (Number N) H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_Number";
+
+Goalw [keysFor_def] "keysFor (insert (Key K) H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_Key";
+
+Goalw [keysFor_def] "keysFor (insert (Hash X) H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_Hash";
+
+Goalw [keysFor_def] "keysFor (insert {|X,Y|} H) = keysFor H";
+by Auto_tac;
+qed "keysFor_insert_MPair";
+
+Goalw [keysFor_def]
+    "keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)";
+by Auto_tac;
+qed "keysFor_insert_Crypt";
+
+Addsimps [keysFor_empty, keysFor_Un, keysFor_UN, 
+          keysFor_insert_Agent, keysFor_insert_Nonce, 
+	  keysFor_insert_Number, keysFor_insert_Key, 
+          keysFor_insert_Hash, keysFor_insert_MPair, keysFor_insert_Crypt];
+AddSEs [keysFor_Un RS equalityD1 RS subsetD RS UnE,
+	keysFor_UN RS equalityD1 RS subsetD RS UN_E];
+
+Goalw [keysFor_def] "keysFor (Key`E) = {}";
+by Auto_tac;
+qed "keysFor_image_Key";
+Addsimps [keysFor_image_Key];
+
+Goalw [keysFor_def] "Crypt K X : H ==> invKey K : keysFor H";
+by (Blast_tac 1);
+qed "Crypt_imp_invKey_keysFor";
+
+
+(**** Inductive relation "parts" ****)
+
+val major::prems = 
+Goal "[| {|X,Y|} : parts H;       \
+\         [| X : parts H; Y : parts H |] ==> P  \
+\     |] ==> P";
+by (cut_facts_tac [major] 1);
+by (resolve_tac prems 1);
+by (REPEAT (eresolve_tac [asm_rl, parts.Fst, parts.Snd] 1));
+qed "MPair_parts";
+
+AddSEs [MPair_parts, make_elim parts.Body];
+(*NB These two rules are UNSAFE in the formal sense, as they discard the
+     compound message.  They work well on THIS FILE.  
+  MPair_parts is left as SAFE because it speeds up proofs.
+  The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.*)
+
+Goal "H <= parts(H)";
+by (Blast_tac 1);
+qed "parts_increasing";
+
+val parts_insertI = impOfSubs (subset_insertI RS parts_mono);
+
+Goal "parts{} = {}";
+by Safe_tac;
+by (etac parts.induct 1);
+by (ALLGOALS Blast_tac);
+qed "parts_empty";
+Addsimps [parts_empty];
+
+Goal "X: parts{} ==> P";
+by (Asm_full_simp_tac 1);
+qed "parts_emptyE";
+AddSEs [parts_emptyE];
+
+(*WARNING: loops if H = {Y}, therefore must not be repeated!*)
+Goal "X: parts H ==> EX Y:H. X: parts {Y}";
+by (etac parts.induct 1);
+by (ALLGOALS Blast_tac);
+qed "parts_singleton";
+
+
+(** Unions **)
+
+Goal "parts(G) Un parts(H) <= parts(G Un H)";
+by (REPEAT (ares_tac [Un_least, parts_mono, Un_upper1, Un_upper2] 1));
+val parts_Un_subset1 = result();
+
+Goal "parts(G Un H) <= parts(G) Un parts(H)";
+by (rtac subsetI 1);
+by (etac parts.induct 1);
+by (ALLGOALS Blast_tac);
+val parts_Un_subset2 = result();
+
+Goal "parts(G Un H) = parts(G) Un parts(H)";
+by (REPEAT (ares_tac [equalityI, parts_Un_subset1, parts_Un_subset2] 1));
+qed "parts_Un";
+
+Goal "parts (insert X H) = parts {X} Un parts H";
+by (stac (read_instantiate [("A","H")] insert_is_Un) 1);
+by (simp_tac (HOL_ss addsimps [parts_Un]) 1);
+qed "parts_insert";
+
+(*TWO inserts to avoid looping.  This rewrite is better than nothing.
+  Not suitable for Addsimps: its behaviour can be strange.*)
+Goal "parts (insert X (insert Y H)) = parts {X} Un parts {Y} Un parts H";
+by (simp_tac (simpset() addsimps [Un_assoc]) 1);
+by (simp_tac (simpset() addsimps [parts_insert RS sym]) 1);
+qed "parts_insert2";
+
+Goal "(UN x:A. parts(H x)) <= parts(UN x:A. H x)";
+by (REPEAT (ares_tac [UN_least, parts_mono, UN_upper] 1));
+val parts_UN_subset1 = result();
+
+Goal "parts(UN x:A. H x) <= (UN x:A. parts(H x))";
+by (rtac subsetI 1);
+by (etac parts.induct 1);
+by (ALLGOALS Blast_tac);
+val parts_UN_subset2 = result();
+
+Goal "parts(UN x:A. H x) = (UN x:A. parts(H x))";
+by (REPEAT (ares_tac [equalityI, parts_UN_subset1, parts_UN_subset2] 1));
+qed "parts_UN";
+
+(*Added to simplify arguments to parts, analz and synth.
+  NOTE: the UN versions are no longer used!*)
+Addsimps [parts_Un, parts_UN];
+AddSEs [parts_Un RS equalityD1 RS subsetD RS UnE,
+	parts_UN RS equalityD1 RS subsetD RS UN_E];
+
+Goal "insert X (parts H) <= parts(insert X H)";
+by (blast_tac (claset() addIs [impOfSubs parts_mono]) 1);
+qed "parts_insert_subset";
+
+(** Idempotence and transitivity **)
+
+Goal "X: parts (parts H) ==> X: parts H";
+by (etac parts.induct 1);
+by (ALLGOALS Blast_tac);
+qed "parts_partsD";
+AddSDs [parts_partsD];
+
+Goal "parts (parts H) = parts H";
+by (Blast_tac 1);
+qed "parts_idem";
+Addsimps [parts_idem];
+
+Goal "[| X: parts G;  G <= parts H |] ==> X: parts H";
+by (dtac parts_mono 1);
+by (Blast_tac 1);
+qed "parts_trans";
+
+(*Cut*)
+Goal "[| Y: parts (insert X G);  X: parts H |] \
+\              ==> Y: parts (G Un H)";
+by (etac parts_trans 1);
+by Auto_tac;
+qed "parts_cut";
+
+Goal "X: parts H ==> parts (insert X H) = parts H";
+by (fast_tac (claset() addSDs [parts_cut]
+                       addIs  [parts_insertI] 
+                       addss (simpset())) 1);
+qed "parts_cut_eq";
+
+Addsimps [parts_cut_eq];
+
+
+(** Rewrite rules for pulling out atomic messages **)
+
+fun parts_tac i =
+  EVERY [rtac ([subsetI, parts_insert_subset] MRS equalityI) i,
+         etac parts.induct i,
+         Auto_tac];
+
+Goal "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)";
+by (parts_tac 1);
+qed "parts_insert_Agent";
+
+Goal "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)";
+by (parts_tac 1);
+qed "parts_insert_Nonce";
+
+Goal "parts (insert (Number N) H) = insert (Number N) (parts H)";
+by (parts_tac 1);
+qed "parts_insert_Number";
+
+Goal "parts (insert (Key K) H) = insert (Key K) (parts H)";
+by (parts_tac 1);
+qed "parts_insert_Key";
+
+Goal "parts (insert (Hash X) H) = insert (Hash X) (parts H)";
+by (parts_tac 1);
+qed "parts_insert_Hash";
+
+Goal "parts (insert (Crypt K X) H) = \
+\         insert (Crypt K X) (parts (insert X H))";
+by (rtac equalityI 1);
+by (rtac subsetI 1);
+by (etac parts.induct 1);
+by Auto_tac;
+by (etac parts.induct 1);
+by (ALLGOALS (blast_tac (claset() addIs [parts.Body])));
+qed "parts_insert_Crypt";
+
+Goal "parts (insert {|X,Y|} H) = \
+\         insert {|X,Y|} (parts (insert X (insert Y H)))";
+by (rtac equalityI 1);
+by (rtac subsetI 1);
+by (etac parts.induct 1);
+by Auto_tac;
+by (etac parts.induct 1);
+by (ALLGOALS (blast_tac (claset() addIs [parts.Fst, parts.Snd])));
+qed "parts_insert_MPair";
+
+Addsimps [parts_insert_Agent, parts_insert_Nonce, 
+	  parts_insert_Number, parts_insert_Key, 
+          parts_insert_Hash, parts_insert_Crypt, parts_insert_MPair];
+
+
+Goal "parts (Key`N) = Key`N";
+by Auto_tac;
+by (etac parts.induct 1);
+by Auto_tac;
+qed "parts_image_Key";
+Addsimps [parts_image_Key];
+
+
+(*In any message, there is an upper bound N on its greatest nonce.*)
+Goal "EX N. ALL n. N<=n --> Nonce n ~: parts {msg}";
+by (induct_tac "msg" 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [exI, parts_insert2])));
+(*MPair case: blast_tac works out the necessary sum itself!*)
+by (blast_tac (claset() addSEs [add_leE]) 2);
+(*Nonce case*)
+by (res_inst_tac [("x","N + Suc nat")] exI 1);
+by (auto_tac (claset() addSEs [add_leE], simpset()));
+qed "msg_Nonce_supply";
+
+
+(**** Inductive relation "analz" ****)
+
+val major::prems = 
+Goal "[| {|X,Y|} : analz H;       \
+\            [| X : analz H; Y : analz H |] ==> P  \
+\         |] ==> P";
+by (cut_facts_tac [major] 1);
+by (resolve_tac prems 1);
+by (REPEAT (eresolve_tac [asm_rl, analz.Fst, analz.Snd] 1));
+qed "MPair_analz";
+
+AddSEs [MPair_analz];     (*Making it safe speeds up proofs*)
+
+Goal "H <= analz(H)";
+by (Blast_tac 1);
+qed "analz_increasing";
+
+Goal "analz H <= parts H";
+by (rtac subsetI 1);
+by (etac analz.induct 1);
+by (ALLGOALS Blast_tac);
+qed "analz_subset_parts";
+
+bind_thm ("not_parts_not_analz", analz_subset_parts RS contra_subsetD);
+
+
+Goal "parts (analz H) = parts H";
+by (rtac equalityI 1);
+by (rtac (analz_subset_parts RS parts_mono RS subset_trans) 1);
+by (Simp_tac 1);
+by (blast_tac (claset() addIs [analz_increasing RS parts_mono RS subsetD]) 1);
+qed "parts_analz";
+Addsimps [parts_analz];
+
+Goal "analz (parts H) = parts H";
+by Auto_tac;
+by (etac analz.induct 1);
+by Auto_tac;
+qed "analz_parts";
+Addsimps [analz_parts];
+
+bind_thm ("analz_insertI", impOfSubs (subset_insertI RS analz_mono));
+
+(** General equational properties **)
+
+Goal "analz{} = {}";
+by Safe_tac;
+by (etac analz.induct 1);
+by (ALLGOALS Blast_tac);
+qed "analz_empty";
+Addsimps [analz_empty];
+
+(*Converse fails: we can analz more from the union than from the 
+  separate parts, as a key in one might decrypt a message in the other*)
+Goal "analz(G) Un analz(H) <= analz(G Un H)";
+by (REPEAT (ares_tac [Un_least, analz_mono, Un_upper1, Un_upper2] 1));
+qed "analz_Un";
+
+Goal "insert X (analz H) <= analz(insert X H)";
+by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1);
+qed "analz_insert";
+
+(** Rewrite rules for pulling out atomic messages **)
+
+fun analz_tac i =
+  EVERY [rtac ([subsetI, analz_insert] MRS equalityI) i,
+         etac analz.induct i,
+         Auto_tac];
+
+Goal "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Agent";
+
+Goal "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Nonce";
+
+Goal "analz (insert (Number N) H) = insert (Number N) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Number";
+
+Goal "analz (insert (Hash X) H) = insert (Hash X) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Hash";
+
+(*Can only pull out Keys if they are not needed to decrypt the rest*)
+Goalw [keysFor_def]
+    "K ~: keysFor (analz H) ==>  \
+\         analz (insert (Key K) H) = insert (Key K) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Key";
+
+Goal "analz (insert {|X,Y|} H) = \
+\         insert {|X,Y|} (analz (insert X (insert Y H)))";
+by (rtac equalityI 1);
+by (rtac subsetI 1);
+by (etac analz.induct 1);
+by Auto_tac;
+by (etac analz.induct 1);
+by (ALLGOALS (blast_tac (claset() addIs [analz.Fst, analz.Snd])));
+qed "analz_insert_MPair";
+
+(*Can pull out enCrypted message if the Key is not known*)
+Goal "Key (invKey K) ~: analz H ==>  \
+\              analz (insert (Crypt K X) H) = \
+\              insert (Crypt K X) (analz H)";
+by (analz_tac 1);
+qed "analz_insert_Crypt";
+
+Goal "Key (invKey K) : analz H ==>  \
+\              analz (insert (Crypt K X) H) <= \
+\              insert (Crypt K X) (analz (insert X H))";
+by (rtac subsetI 1);
+by (eres_inst_tac [("xa","x")] analz.induct 1);
+by Auto_tac;
+val lemma1 = result();
+
+Goal "Key (invKey K) : analz H ==>  \
+\              insert (Crypt K X) (analz (insert X H)) <= \
+\              analz (insert (Crypt K X) H)";
+by Auto_tac;
+by (eres_inst_tac [("xa","x")] analz.induct 1);
+by Auto_tac;
+by (blast_tac (claset() addIs [analz_insertI, analz.Decrypt]) 1);
+val lemma2 = result();
+
+Goal "Key (invKey K) : analz H ==>  \
+\              analz (insert (Crypt K X) H) = \
+\              insert (Crypt K X) (analz (insert X H))";
+by (REPEAT (ares_tac [equalityI, lemma1, lemma2] 1));
+qed "analz_insert_Decrypt";
+
+(*Case analysis: either the message is secure, or it is not!
+  Effective, but can cause subgoals to blow up!
+  Use with split_if;  apparently split_tac does not cope with patterns
+  such as "analz (insert (Crypt K X) H)" *)
+Goal "analz (insert (Crypt K X) H) =                \
+\         (if (Key (invKey K) : analz H)                \
+\          then insert (Crypt K X) (analz (insert X H)) \
+\          else insert (Crypt K X) (analz H))";
+by (case_tac "Key (invKey K)  : analz H " 1);
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [analz_insert_Crypt, 
+						analz_insert_Decrypt])));
+qed "analz_Crypt_if";
+
+Addsimps [analz_insert_Agent, analz_insert_Nonce, 
+	  analz_insert_Number, analz_insert_Key, 
+          analz_insert_Hash, analz_insert_MPair, analz_Crypt_if];
+
+(*This rule supposes "for the sake of argument" that we have the key.*)
+Goal  "analz (insert (Crypt K X) H) <=  \
+\          insert (Crypt K X) (analz (insert X H))";
+by (rtac subsetI 1);
+by (etac analz.induct 1);
+by Auto_tac;
+qed "analz_insert_Crypt_subset";
+
+
+Goal "analz (Key`N) = Key`N";
+by Auto_tac;
+by (etac analz.induct 1);
+by Auto_tac;
+qed "analz_image_Key";
+
+Addsimps [analz_image_Key];
+
+
+(** Idempotence and transitivity **)
+
+Goal "X: analz (analz H) ==> X: analz H";
+by (etac analz.induct 1);
+by (ALLGOALS Blast_tac);
+qed "analz_analzD";
+AddSDs [analz_analzD];
+
+Goal "analz (analz H) = analz H";
+by (Blast_tac 1);
+qed "analz_idem";
+Addsimps [analz_idem];
+
+Goal "[| X: analz G;  G <= analz H |] ==> X: analz H";
+by (dtac analz_mono 1);
+by (Blast_tac 1);
+qed "analz_trans";
+
+(*Cut; Lemma 2 of Lowe*)
+Goal "[| Y: analz (insert X H);  X: analz H |] ==> Y: analz H";
+by (etac analz_trans 1);
+by (Blast_tac 1);
+qed "analz_cut";
+
+(*Cut can be proved easily by induction on
+   "Y: analz (insert X H) ==> X: analz H --> Y: analz H"
+*)
+
+(*This rewrite rule helps in the simplification of messages that involve
+  the forwarding of unknown components (X).  Without it, removing occurrences
+  of X can be very complicated. *)
+Goal "X: analz H ==> analz (insert X H) = analz H";
+by (blast_tac (claset() addIs [analz_cut, analz_insertI]) 1);
+qed "analz_insert_eq";
+
+
+(** A congruence rule for "analz" **)
+
+Goal "[| analz G <= analz G'; analz H <= analz H' \
+\              |] ==> analz (G Un H) <= analz (G' Un H')";
+by (Clarify_tac 1);
+by (etac analz.induct 1);
+by (ALLGOALS (best_tac (claset() addIs [analz_mono RS subsetD])));
+qed "analz_subset_cong";
+
+Goal "[| analz G = analz G'; analz H = analz H' \
+\              |] ==> analz (G Un H) = analz (G' Un H')";
+by (REPEAT_FIRST (ares_tac [equalityI, analz_subset_cong]
+          ORELSE' etac equalityE));
+qed "analz_cong";
+
+
+Goal "analz H = analz H' ==> analz(insert X H) = analz(insert X H')";
+by (asm_simp_tac (simpset() addsimps [insert_def] delsimps [singleton_conv]
+                            setloop (rtac analz_cong)) 1);
+qed "analz_insert_cong";
+
+(*If there are no pairs or encryptions then analz does nothing*)
+Goal "[| ALL X Y. {|X,Y|} ~: H;  ALL X K. Crypt K X ~: H |] ==> \
+\         analz H = H";
+by Safe_tac;
+by (etac analz.induct 1);
+by (ALLGOALS Blast_tac);
+qed "analz_trivial";
+
+(*These two are obsolete (with a single Spy) but cost little to prove...*)
+Goal "X: analz (UN i:A. analz (H i)) ==> X: analz (UN i:A. H i)";
+by (etac analz.induct 1);
+by (ALLGOALS (blast_tac (claset() addIs [impOfSubs analz_mono])));
+val lemma = result();
+
+Goal "analz (UN i:A. analz (H i)) = analz (UN i:A. H i)";
+by (blast_tac (claset() addIs [lemma, impOfSubs analz_mono]) 1);
+qed "analz_UN_analz";
+Addsimps [analz_UN_analz];
+
+
+(**** Inductive relation "synth" ****)
+
+Goal "H <= synth(H)";
+by (Blast_tac 1);
+qed "synth_increasing";
+
+(** Unions **)
+
+(*Converse fails: we can synth more from the union than from the 
+  separate parts, building a compound message using elements of each.*)
+Goal "synth(G) Un synth(H) <= synth(G Un H)";
+by (REPEAT (ares_tac [Un_least, synth_mono, Un_upper1, Un_upper2] 1));
+qed "synth_Un";
+
+Goal "insert X (synth H) <= synth(insert X H)";
+by (blast_tac (claset() addIs [impOfSubs synth_mono]) 1);
+qed "synth_insert";
+
+(** Idempotence and transitivity **)
+
+Goal "X: synth (synth H) ==> X: synth H";
+by (etac synth.induct 1);
+by (ALLGOALS Blast_tac);
+qed "synth_synthD";
+AddSDs [synth_synthD];
+
+Goal "synth (synth H) = synth H";
+by (Blast_tac 1);
+qed "synth_idem";
+
+Goal "[| X: synth G;  G <= synth H |] ==> X: synth H";
+by (dtac synth_mono 1);
+by (Blast_tac 1);
+qed "synth_trans";
+
+(*Cut; Lemma 2 of Lowe*)
+Goal "[| Y: synth (insert X H);  X: synth H |] ==> Y: synth H";
+by (etac synth_trans 1);
+by (Blast_tac 1);
+qed "synth_cut";
+
+Goal "Agent A : synth H";
+by (Blast_tac 1);
+qed "Agent_synth";
+
+Goal "Number n : synth H";
+by (Blast_tac 1);
+qed "Number_synth";
+
+Goal "(Nonce N : synth H) = (Nonce N : H)";
+by (Blast_tac 1);
+qed "Nonce_synth_eq";
+
+Goal "(Key K : synth H) = (Key K : H)";
+by (Blast_tac 1);
+qed "Key_synth_eq";
+
+Goal "Key K ~: H ==> (Crypt K X : synth H) = (Crypt K X : H)";
+by (Blast_tac 1);
+qed "Crypt_synth_eq";
+
+Addsimps [Agent_synth, Number_synth, 
+	  Nonce_synth_eq, Key_synth_eq, Crypt_synth_eq];
+
+
+Goalw [keysFor_def]
+    "keysFor (synth H) = keysFor H Un invKey`{K. Key K : H}";
+by (Blast_tac 1);
+qed "keysFor_synth";
+Addsimps [keysFor_synth];
+
+
+(*** Combinations of parts, analz and synth ***)
+
+Goal "parts (synth H) = parts H Un synth H";
+by (rtac equalityI 1);
+by (rtac subsetI 1);
+by (etac parts.induct 1);
+by (ALLGOALS
+    (blast_tac (claset() addIs [synth_increasing RS parts_mono RS subsetD,
+                                parts.Fst, parts.Snd, parts.Body])));
+qed "parts_synth";
+Addsimps [parts_synth];
+
+Goal "analz (analz G Un H) = analz (G Un H)";
+by (REPEAT_FIRST (resolve_tac [equalityI, analz_subset_cong]));
+by (ALLGOALS Simp_tac);
+qed "analz_analz_Un";
+
+Goal "analz (synth G Un H) = analz (G Un H) Un synth G";
+by (rtac equalityI 1);
+by (rtac subsetI 1);
+by (etac analz.induct 1);
+by (blast_tac (claset() addIs [impOfSubs analz_mono]) 5);
+by (ALLGOALS 
+    (blast_tac (claset() addIs [analz.Fst, analz.Snd, analz.Decrypt])));
+qed "analz_synth_Un";
+
+Goal "analz (synth H) = analz H Un synth H";
+by (cut_inst_tac [("H","{}")] analz_synth_Un 1);
+by (Full_simp_tac 1);
+qed "analz_synth";
+Addsimps [analz_analz_Un, analz_synth_Un, analz_synth];
+
+
+(** For reasoning about the Fake rule in traces **)
+
+Goal "X: G ==> parts(insert X H) <= parts G Un parts H";
+by (rtac ([parts_mono, parts_Un_subset2] MRS subset_trans) 1);
+by (Blast_tac 1);
+qed "parts_insert_subset_Un";
+
+(*More specifically for Fake.  Very occasionally we could do with a version
+  of the form  parts{X} <= synth (analz H) Un parts H *)
+Goal "X: synth (analz H) ==> \
+\     parts (insert X H) <= synth (analz H) Un parts H";
+by (dtac parts_insert_subset_Un 1);
+by (Full_simp_tac 1);
+by (Blast_tac 1);
+qed "Fake_parts_insert";
+
+(*H is sometimes (Key ` KK Un spies evs), so can't put G=H*)
+Goal "X: synth (analz G) ==> \
+\     analz (insert X H) <= synth (analz G) Un analz (G Un H)";
+by (rtac subsetI 1);
+by (subgoal_tac "x : analz (synth (analz G) Un H)" 1);
+by (blast_tac (claset() addIs [impOfSubs analz_mono,
+			       impOfSubs (analz_mono RS synth_mono)]) 2);
+by (Full_simp_tac 1);
+by (Blast_tac 1);
+qed "Fake_analz_insert";
+
+Goal "(X: analz H & X: parts H) = (X: analz H)";
+by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
+val analz_conj_parts = result();
+
+Goal "(X: analz H | X: parts H) = (X: parts H)";
+by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
+val analz_disj_parts = result();
+
+AddIffs [analz_conj_parts, analz_disj_parts];
+
+(*Without this equation, other rules for synth and analz would yield
+  redundant cases*)
+Goal "({|X,Y|} : synth (analz H)) = \
+\     (X : synth (analz H) & Y : synth (analz H))";
+by (Blast_tac 1);
+qed "MPair_synth_analz";
+
+AddIffs [MPair_synth_analz];
+
+Goal "[| Key K : analz H;  Key (invKey K) : analz H |] \
+\      ==> (Crypt K X : synth (analz H)) = (X : synth (analz H))";
+by (Blast_tac 1);
+qed "Crypt_synth_analz";
+
+
+Goal "X ~: synth (analz H) \
+\     ==> (Hash{|X,Y|} : synth (analz H)) = (Hash{|X,Y|} : analz H)";
+by (Blast_tac 1);
+qed "Hash_synth_analz";
+Addsimps [Hash_synth_analz];
+
+
+(**** HPair: a combination of Hash and MPair ****)
+
+(*** Freeness ***)
+
+Goalw [HPair_def] "Agent A ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Agent_neq_HPair";
+
+Goalw [HPair_def] "Nonce N ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Nonce_neq_HPair";
+
+Goalw [HPair_def] "Number N ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Number_neq_HPair";
+
+Goalw [HPair_def] "Key K ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Key_neq_HPair";
+
+Goalw [HPair_def] "Hash Z ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Hash_neq_HPair";
+
+Goalw [HPair_def] "Crypt K X' ~= Hash[X] Y";
+by (Simp_tac 1);
+qed "Crypt_neq_HPair";
+
+val HPair_neqs = [Agent_neq_HPair, Nonce_neq_HPair, Number_neq_HPair, 
+                  Key_neq_HPair, Hash_neq_HPair, Crypt_neq_HPair];
+
+AddIffs HPair_neqs;
+AddIffs (HPair_neqs RL [not_sym]);
+
+Goalw [HPair_def] "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)";
+by (Simp_tac 1);
+qed "HPair_eq";
+
+Goalw [HPair_def] "({|X',Y'|} = Hash[X] Y) = (X' = Hash{|X,Y|} & Y'=Y)";
+by (Simp_tac 1);
+qed "MPair_eq_HPair";
+
+Goalw [HPair_def] "(Hash[X] Y = {|X',Y'|}) = (X' = Hash{|X,Y|} & Y'=Y)";
+by Auto_tac;
+qed "HPair_eq_MPair";
+
+AddIffs [HPair_eq, MPair_eq_HPair, HPair_eq_MPair];
+
+
+(*** Specialized laws, proved in terms of those for Hash and MPair ***)
+
+Goalw [HPair_def] "keysFor (insert (Hash[X] Y) H) = keysFor H";
+by (Simp_tac 1);
+qed "keysFor_insert_HPair";
+
+Goalw [HPair_def]
+    "parts (insert (Hash[X] Y) H) = \
+\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (parts (insert Y H)))";
+by (Simp_tac 1);
+qed "parts_insert_HPair";
+
+Goalw [HPair_def]
+    "analz (insert (Hash[X] Y) H) = \
+\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (analz (insert Y H)))";
+by (Simp_tac 1);
+qed "analz_insert_HPair";
+
+Goalw [HPair_def] "X ~: synth (analz H) \
+\   ==> (Hash[X] Y : synth (analz H)) = \
+\       (Hash {|X, Y|} : analz H & Y : synth (analz H))";
+by (Simp_tac 1);
+by (Blast_tac 1);
+qed "HPair_synth_analz";
+
+Addsimps [keysFor_insert_HPair, parts_insert_HPair, analz_insert_HPair, 
+          HPair_synth_analz, HPair_synth_analz];
+
+
+(*We do NOT want Crypt... messages broken up in protocols!!*)
+Delrules [make_elim parts.Body];
+
+
+(** Rewrites to push in Key and Crypt messages, so that other messages can
+    be pulled out using the analz_insert rules **)
+
+fun insComm x y = inst "x" x (inst "y" y insert_commute);
+
+val pushKeys = map (insComm "Key ?K") 
+                   ["Agent ?C", "Nonce ?N", "Number ?N", 
+		    "Hash ?X", "MPair ?X ?Y", "Crypt ?X ?K'"];
+
+val pushCrypts = map (insComm "Crypt ?X ?K") 
+                     ["Agent ?C", "Nonce ?N", "Number ?N", 
+		      "Hash ?X'", "MPair ?X' ?Y"];
+
+(*Cannot be added with Addsimps -- we don't always want to re-order messages*)
+bind_thms ("pushes", pushKeys@pushCrypts);
+
+
+(*** Tactics useful for many protocol proofs ***)
+
+(*Prove base case (subgoal i) and simplify others.  A typical base case
+  concerns  Crypt K X ~: Key`shrK`bad  and cannot be proved by rewriting
+  alone.*)
+fun prove_simple_subgoals_tac i = 
+    force_tac (claset(), simpset() addsimps [image_eq_UN]) i THEN
+    ALLGOALS Asm_simp_tac;
+
+fun Fake_parts_insert_tac i = 
+    blast_tac (claset() addIs [parts_insertI]
+			addDs [impOfSubs analz_subset_parts,
+			       impOfSubs Fake_parts_insert]) i;
+
+(*Apply rules to break down assumptions of the form
+  Y : parts(insert X H)  and  Y : analz(insert X H)
+*)
+val Fake_insert_tac = 
+    dresolve_tac [impOfSubs Fake_analz_insert,
+                  impOfSubs Fake_parts_insert] THEN'
+    eresolve_tac [asm_rl, synth.Inj];
+
+fun Fake_insert_simp_tac i = 
+    REPEAT (Fake_insert_tac i) THEN Asm_full_simp_tac i;
+
+
+(*Analysis of Fake cases.  Also works for messages that forward unknown parts,
+  but this application is no longer necessary if analz_insert_eq is used.
+  Abstraction over i is ESSENTIAL: it delays the dereferencing of claset
+  DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
+
+val atomic_spy_analz_tac = SELECT_GOAL
+    (Fake_insert_simp_tac 1
+     THEN
+     IF_UNSOLVED (Blast.depth_tac
+		  (claset() addIs [analz_insertI,
+				   impOfSubs analz_subset_parts]) 4 1));
+
+fun spy_analz_tac i =
+  DETERM
+   (SELECT_GOAL
+     (EVERY 
+      [  (*push in occurrences of X...*)
+       (REPEAT o CHANGED)
+           (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1),
+       (*...allowing further simplifications*)
+       Simp_tac 1,
+       REPEAT (FIRSTGOAL (resolve_tac [allI,impI,notI,conjI,iffI])),
+       DEPTH_SOLVE (atomic_spy_analz_tac 1)]) i);
+
+(*By default only o_apply is built-in.  But in the presence of eta-expansion
+  this means that some terms displayed as (f o g) will be rewritten, and others
+  will not!*)
+Addsimps [o_def];