Moving common declarations and proofs from theories "Shared"
and "Public" to "Event". NB the original "Event" theory was later renamed "Shared".

Addition of the Notes constructor to datatype "event".

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Auth/Event.ML	Fri Jul 11 13:26:15 1997 +0200
@@ -0,0 +1,152 @@
+(*  Title:      HOL/Auth/Event
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1996  University of Cambridge
+
+Theory of events for security protocols
+
+Datatype of events; function "sees"; freshness
+*)
+
+open Event;
+
+(*** Function "sees" ***)
+
+(** Specialized rewrite rules for (sees lost A (Says...#evs)) **)
+
+goal thy "sees lost B (Says A B X # evs) = insert X (sees lost B evs)";
+by (Simp_tac 1);
+qed "sees_own";
+
+goal thy "sees lost B (Notes A X # evs) = \
+\         (if A=B then insert X (sees lost B evs) else sees lost B evs)";
+by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
+qed "sees_Notes";
+
+(** Three special-case rules for rewriting of sees lost A **)
+
+goal thy "!!A. Server ~= B ==> \
+\          sees lost Server (Says A B X # evs) = sees lost Server evs";
+by (Asm_simp_tac 1);
+qed "sees_Server";
+
+goal thy "!!A. Friend i ~= B ==> \
+\          sees lost (Friend i) (Says A B X # evs) = sees lost (Friend i) evs";
+by (Asm_simp_tac 1);
+qed "sees_Friend";
+
+goal thy "sees lost Spy (Says A B X # evs) = insert X (sees lost Spy evs)";
+by (Simp_tac 1);
+qed "sees_Spy";
+
+goal thy "sees lost A (Says A' B X # evs) <= insert X (sees lost A evs)";
+by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
+by (Fast_tac 1);
+qed "sees_Says_subset_insert";
+
+goal thy "sees lost A evs <= sees lost A (Says A' B X # evs)";
+by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
+by (Fast_tac 1);
+qed "sees_subset_sees_Says";
+
+goal thy "sees lost A evs <= sees lost A (Notes A' X # evs)";
+by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
+by (Fast_tac 1);
+qed "sees_subset_sees_Notes";
+
+(*Pushing Unions into parts.  One of the agents A is B, and thus sees Y.*)
+goal thy "(UN A. parts (sees lost A (Says B C Y # evs))) = \
+\         parts {Y} Un (UN A. parts (sees lost A evs))";
+by (Step_tac 1);
+by (etac rev_mp 1);     (*split_tac does not work on assumptions*)
+by (ALLGOALS
+    (fast_tac (!claset addss (!simpset addsimps [parts_Un] 
+				       setloop split_tac [expand_if]))));
+qed "UN_parts_sees_Says";
+
+goal thy "(UN A. parts (sees lost A (Notes B Y # evs))) = \
+\         parts {Y} Un (UN A. parts (sees lost A evs))";
+by (Step_tac 1);
+by (etac rev_mp 1);     (*split_tac does not work on assumptions*)
+by (ALLGOALS
+    (fast_tac (!claset addss (!simpset addsimps [parts_Un] 
+				       setloop split_tac [expand_if]))));
+qed "UN_parts_sees_Notes";
+
+goal thy "Says A B X : set evs --> X : sees lost Spy evs";
+by (list.induct_tac "evs" 1);
+by (Auto_tac ());
+qed_spec_mp "Says_imp_sees_Spy";
+
+(*Use with addSEs to derive contradictions from old Says events containing
+  items known to be fresh*)
+val sees_Spy_partsEs = make_elim (Says_imp_sees_Spy RS parts.Inj):: partsEs;
+
+Addsimps [sees_own, sees_Notes, sees_Server, sees_Friend, sees_Spy];
+
+(**** NOTE REMOVAL--laws above are cleaner--def of sees1 is messy ****)
+Delsimps [sees_Cons];   
+
+
+(*** Fresh nonces ***)
+
+goalw thy [used_def] "!!X. X: parts (sees lost B evs) ==> X: used evs";
+by (etac (impOfSubs parts_mono) 1);
+by (Fast_tac 1);
+qed "usedI";
+AddIs [usedI];
+
+goal thy "used (Says A B X # evs) = parts{X} Un used evs";
+by (simp_tac (!simpset addsimps [used_def, UN_parts_sees_Says]) 1);
+qed "used_Says";
+Addsimps [used_Says];
+
+goal thy "used (Notes A X # evs) = parts{X} Un used evs";
+by (simp_tac (!simpset delsimps [sees_Notes]
+		       addsimps [used_def, UN_parts_sees_Notes]) 1);
+qed "used_Notes";
+Addsimps [used_Notes];
+
+(*These two facts about "used" are unused.*)
+goal thy "used [] <= used l";
+by (list.induct_tac "l" 1);
+by (event.induct_tac "a" 2);
+by (ALLGOALS Asm_simp_tac);
+by (ALLGOALS Blast_tac);
+qed "used_nil_subset";
+
+goal thy "used l <= used (l@l')";
+by (list.induct_tac "l" 1);
+by (simp_tac (!simpset addsimps [used_nil_subset]) 1);
+by (event.induct_tac "a" 1);
+by (ALLGOALS Asm_simp_tac);
+by (ALLGOALS Blast_tac);
+qed "used_subset_append";
+
+
+(** Simplifying   parts (insert X (sees lost A evs))
+      = parts {X} Un parts (sees lost A evs) -- since general case loops*)
+
+val parts_insert_sees = 
+    parts_insert |> read_instantiate_sg (sign_of thy)
+                                        [("H", "sees lost A evs")]
+                 |> standard;
+
+
+
+(*For proving theorems of the form X ~: analz (sees Spy evs) --> P
+  New events added by induction to "evs" are discarded.  Provided 
+  this information isn't needed, the proof will be much shorter, since
+  it will omit complicated reasoning about analz.*)
+val analz_mono_contra_tac = 
+  let val impI' = read_instantiate_sg (sign_of thy)
+                [("P", "?Y ~: analz (sees lost ?A ?evs)")] impI;
+  in
+    rtac impI THEN' 
+    REPEAT1 o 
+      (dresolve_tac 
+       [sees_subset_sees_Says  RS analz_mono RS contra_subsetD,
+	sees_subset_sees_Notes RS analz_mono RS contra_subsetD])
+    THEN'
+    mp_tac
+  end;

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Auth/Event.thy	Fri Jul 11 13:26:15 1997 +0200
@@ -0,0 +1,42 @@
+(*  Title:      HOL/Auth/Event
+    ID:         $Id$
+    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1996  University of Cambridge
+
+Theory of events for security protocols
+
+Datatype of events; function "sees"; freshness
+*)
+
+Event = Message + List + 
+
+consts  (*Initial states of agents -- parameter of the construction*)
+  initState :: [agent set, agent] => msg set
+
+datatype  (*Messages--could add another constructor for agent knowledge*)
+  event = Says  agent agent msg
+        | Notes agent       msg
+
+consts  
+  sees1 :: [agent, event] => msg set
+
+primrec sees1 event
+           (*Spy reads all traffic whether addressed to him or not*)
+  sees1_Says  "sees1 A (Says A' B X)  = (if A:{B,Spy} then {X} else {})"
+  sees1_Notes "sees1 A (Notes A' X)   = (if A = A'    then {X} else {})"
+
+consts  
+  sees :: [agent set, agent, event list] => msg set
+
+primrec sees list
+  sees_Nil  "sees lost A []       = initState lost A"
+  sees_Cons "sees lost A (ev#evs) = sees1 A ev Un sees lost A evs"
+
+
+constdefs
+  (*Set of items that might be visible to somebody: complement of the set
+        of fresh items*)
+  used :: event list => msg set
+    "used evs == parts (UN lost B. sees lost B evs)"
+
+end

--- a/src/HOL/Auth/Public.ML	Wed Jul 09 17:00:34 1997 +0200
+++ b/src/HOL/Auth/Public.ML	Fri Jul 11 13:26:15 1997 +0200
@@ -11,41 +11,6 @@
 
 open Public;
 
-(*Holds because Friend is injective: thus cannot prove for all f*)
-goal thy "(Friend x : Friend``A) = (x:A)";
-by (Auto_tac());
-qed "Friend_image_eq";
-Addsimps [Friend_image_eq];
-
-Addsimps [Un_insert_left, Un_insert_right];
-
-(*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];
-
-goalw thy [keysFor_def] "keysFor (parts (initState lost C)) = {}";
-by (agent.induct_tac "C" 1);
-by (auto_tac (!claset addIs [range_eqI], !simpset));
-qed "keysFor_parts_initState";
-Addsimps [keysFor_parts_initState];
-
-goalw thy [keysFor_def] "keysFor (Key``E) = {}";
-by (Auto_tac ());
-qed "keysFor_image_Key";
-Addsimps [keysFor_image_Key];
-
-
-(*** Function "sees" ***)
-
-goal thy
-    "!!evs. lost' <= lost ==> sees lost' A evs <= sees lost A evs";
-by (list.induct_tac "evs" 1);
-by (agent.induct_tac "A" 1);
-by (event.induct_tac "a" 2);
-by (Auto_tac ());
-qed "sees_mono";
-
 (*** Basic properties of pubK & priK ***)
 
 AddIffs [inj_pubK RS inj_eq];
@@ -69,81 +34,44 @@
 
 AddIffs [not_isSymKey_pubK, not_isSymKey_priK];
 
+(** Rewrites should not refer to  initState(Friend i) 
+    -- not in normal form! **)
+
+goalw thy [keysFor_def] "keysFor (parts (initState lost C)) = {}";
+by (agent.induct_tac "C" 1);
+by (auto_tac (!claset addIs [range_eqI], !simpset));
+qed "keysFor_parts_initState";
+Addsimps [keysFor_parts_initState];
+
+
+(*** Function "sees" ***)
 
 (*Agents see their own private keys!*)
 goal thy "A ~= Spy --> Key (priK A) : sees lost A evs";
 by (list.induct_tac "evs" 1);
 by (agent.induct_tac "A" 1);
-by (Auto_tac ());
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons])));
 qed_spec_mp "sees_own_priK";
 
 (*All public keys are visible to all*)
 goal thy "Key (pubK A) : sees lost B evs";
 by (list.induct_tac "evs" 1);
 by (agent.induct_tac "B" 1);
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons])));
 by (Auto_tac ());
 qed_spec_mp "sees_pubK";
 
 (*Spy sees private keys of lost agents!*)
 goal thy "!!A. A: lost ==> Key (priK A) : sees lost Spy evs";
 by (list.induct_tac "evs" 1);
-by (Auto_tac());
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons])));
+by (Blast_tac 1);
 qed "Spy_sees_lost";
 
 AddIffs [sees_pubK, sees_pubK RS analz.Inj];
 AddSIs  [sees_own_priK, Spy_sees_lost];
 
 
-(** Specialized rewrite rules for (sees lost A (Says...#evs)) **)
-
-goal thy "sees lost B (Says A B X # evs) = insert X (sees lost B evs)";
-by (Simp_tac 1);
-qed "sees_own";
-
-goal thy "!!A. Server ~= B ==> \
-\          sees lost Server (Says A B X # evs) = sees lost Server evs";
-by (Asm_simp_tac 1);
-qed "sees_Server";
-
-goal thy "!!A. Friend i ~= B ==> \
-\          sees lost (Friend i) (Says A B X # evs) = sees lost (Friend i) evs";
-by (Asm_simp_tac 1);
-qed "sees_Friend";
-
-goal thy "sees lost Spy (Says A B X # evs) = insert X (sees lost Spy evs)";
-by (Simp_tac 1);
-qed "sees_Spy";
-
-goal thy "sees lost A (Says A' B X # evs) <= insert X (sees lost A evs)";
-by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
-by (Fast_tac 1);
-qed "sees_Says_subset_insert";
-
-goal thy "sees lost A evs <= sees lost A (Says A' B X # evs)";
-by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
-by (Fast_tac 1);
-qed "sees_subset_sees_Says";
-
-(*Pushing Unions into parts.  One of the agents A is B, and thus sees Y.
-  Once used to prove new_keys_not_seen; now obsolete.*)
-goal thy "(UN A. parts (sees lost A (Says B C Y # evs))) = \
-\         parts {Y} Un (UN A. parts (sees lost A evs))";
-by (Step_tac 1);
-by (etac rev_mp 1);     (*split_tac does not work on assumptions*)
-by (ALLGOALS
-    (fast_tac (!claset addss (!simpset addsimps [parts_Un, sees_Cons] 
-				            setloop split_tac [expand_if]))));
-qed "UN_parts_sees_Says";
-
-goal thy "Says A B X : set evs --> X : sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (Auto_tac ());
-qed_spec_mp "Says_imp_sees_Spy";
-
-(*Use with addSEs to derive contradictions from old Says events containing
-  items known to be fresh*)
-val sees_Spy_partsEs = make_elim (Says_imp_sees_Spy RS parts.Inj):: partsEs;
-
 (*For not_lost_tac*)
 goal thy "!!A. [| Crypt (pubK A) X : analz (sees lost Spy evs);  A: lost |] \
 \              ==> X : analz (sees lost Spy evs)";
@@ -162,9 +90,6 @@
          (has_fewer_prems 1, size_of_thm)
          (Step_tac 1));
 
-Addsimps [sees_own, sees_Server, sees_Friend, sees_Spy];
-Delsimps [sees_Cons];   (**** NOTE REMOVAL -- laws above are cleaner ****)
-
 
 (*** Fresh nonces ***)
 
@@ -172,17 +97,15 @@
 by (agent.induct_tac "B" 1);
 by (Auto_tac ());
 qed "Nonce_notin_initState";
-
 AddIffs [Nonce_notin_initState];
 
-goalw thy [used_def] "!!X. X: parts (sees lost B evs) ==> X: used evs";
-by (etac (impOfSubs parts_mono) 1);
-by (Fast_tac 1);
-qed "usedI";
+goal thy "Nonce N ~: used []";
+by (simp_tac (!simpset addsimps [used_def]) 1);
+qed "Nonce_notin_used_empty";
+Addsimps [Nonce_notin_used_empty];
 
-AddIs [usedI];
 
-(** A supply of fresh nonces for possibility theorems. **)
+(*** Supply fresh nonces for possibility theorems. ***)
 
 goalw thy [used_def] "EX N. ALL n. N<=n --> Nonce n ~: used evs";
 by (list.induct_tac "evs" 1);
@@ -191,16 +114,12 @@
 by (Full_simp_tac 1);
 (*Inductive step*)
 by (event.induct_tac "a" 1);
-by (full_simp_tac (!simpset addsimps [UN_parts_sees_Says]) 1);
-by (msg.induct_tac "msg" 1);
-by (ALLGOALS (asm_simp_tac (!simpset addsimps [exI, parts_insert2])));
-by (Step_tac 1);
-(*MPair case*)
-by (res_inst_tac [("x","Na+Nb")] exI 2);
-by (fast_tac (!claset addSEs [add_leE]) 2);
-(*Nonce case*)
-by (res_inst_tac [("x","N + Suc nat")] exI 1);
-by (fast_tac (!claset addSEs [add_leE] addaltern trans_tac) 1);
+by (ALLGOALS (full_simp_tac 
+	      (!simpset delsimps [sees_Notes]
+		        addsimps [UN_parts_sees_Says,
+				  UN_parts_sees_Notes])));
+by (ALLGOALS (rtac (msg_Nonce_supply RS exE)));
+by (ALLGOALS (blast_tac (!claset addSEs [add_leE])));
 val lemma = result();
 
 goal thy "Nonce (@ N. Nonce N ~: used evs) ~: used evs";
@@ -211,35 +130,30 @@
 
 (*Tactic for possibility theorems*)
 val possibility_tac =
-    REPEAT 
-    (ALLGOALS (simp_tac (!simpset setSolver safe_solver))
+    REPEAT (*omit used_Says so that Nonces, Keys start from different traces!*)
+    (ALLGOALS (simp_tac (!simpset delsimps [used_Says] setSolver safe_solver))
      THEN
      REPEAT_FIRST (eq_assume_tac ORELSE' 
                    resolve_tac [refl, conjI, Nonce_supply]));
 
-(** Power of the Spy **)
+
+(*** Specialized rewriting for the analz_image_... theorems ***)
 
-(*The Spy can see more than anybody else, except for their initial state*)
-goal thy "sees lost A evs <= initState lost A Un sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (event.induct_tac "a" 2);
-by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] 
-                                addss (!simpset))));
-qed "sees_agent_subset_sees_Spy";
+goal thy "insert (Key K) H = Key `` {K} Un H";
+by (Blast_tac 1);
+qed "insert_Key_singleton";
+
+goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C";
+by (Blast_tac 1);
+qed "insert_Key_image";
 
-(*The Spy can see more than anybody else who's lost their key!*)
-goal thy "A: lost --> A ~= Server --> sees lost A evs <= sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (event.induct_tac "a" 2);
-by (agent.induct_tac "A" 1);
-by (auto_tac (!claset addDs [sees_Says_subset_insert RS subsetD], (!simpset)));
-qed_spec_mp "sees_lost_agent_subset_sees_Spy";
+(*Reverse the normal simplification of "image" to build up (not break down)
+  the set of keys.  Based on analz_image_freshK_ss, but simpler.*)
+val analz_image_keys_ss = 
+     !simpset delsimps [image_insert, image_Un]
+              addsimps [image_insert RS sym, image_Un RS sym,
+			rangeI, 
+			insert_Key_singleton, 
+			insert_Key_image, Un_assoc RS sym]
+              setloop split_tac [expand_if];
 
-
-(** Simplifying   parts (insert X (sees lost A evs))
-      = parts {X} Un parts (sees lost A evs) -- since general case loops*)
-
-val parts_insert_sees = 
-    parts_insert |> read_instantiate_sg (sign_of thy)
-                                        [("H", "sees lost A evs")]
-                 |> standard;

--- a/src/HOL/Auth/Public.thy	Wed Jul 09 17:00:34 1997 +0200
+++ b/src/HOL/Auth/Public.thy	Fri Jul 11 13:26:15 1997 +0200
@@ -3,12 +3,12 @@
     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     Copyright   1996  University of Cambridge
 
-Theory of Public Keys (common to all symmetric-key protocols)
+Theory of Public Keys (common to all public-key protocols)
 
-Server keys; initial states of agents; new nonces and keys; function "sees" 
+Private and public keys; initial states of agents
 *)
 
-Public = Message + List + 
+Public = Event + 
 
 consts
   pubK    :: agent => key
@@ -19,9 +19,6 @@
 translations  (*BEWARE! expressions like  (inj priK)  will NOT work!*)
   "priK x"  == "invKey(pubK x)"
 
-consts  (*Initial states of agents -- parameter of the construction*)
-  initState :: [agent set, agent] => msg set
-
 primrec initState agent
         (*Agents know their private key and all public keys*)
   initState_Server  "initState lost Server     =    
@@ -32,31 +29,6 @@
  		         (Key``invKey``pubK``lost) Un (Key `` range pubK)"
 
 
-datatype  (*Messages, and components of agent stores*)
-  event = Says agent agent msg
-
-consts  
-  sees1 :: [agent, event] => msg set
-
-primrec sees1 event
-           (*Spy reads all traffic whether addressed to him or not*)
-  sees1_Says  "sees1 A (Says A' B X)  = (if A:{B,Spy} then {X} else {})"
-
-consts  
-  sees :: [agent set, agent, event list] => msg set
-
-primrec sees list
-  sees_Nil  "sees lost A []       = initState lost A"
-  sees_Cons "sees lost A (ev#evs) = sees1 A ev Un sees lost A evs"
-
-
-constdefs
-  (*Set of items that might be visible to somebody: complement of the set
-        of fresh items*)
-  used :: event list => msg set
-    "used evs == parts (UN lost B. sees lost B evs)"
-
-
 rules
   (*Public keys are disjoint, and never clash with private keys*)
   inj_pubK        "inj pubK"

--- a/src/HOL/Auth/Shared.ML	Wed Jul 09 17:00:34 1997 +0200
+++ b/src/HOL/Auth/Shared.ML	Fri Jul 11 13:26:15 1997 +0200
@@ -5,25 +5,12 @@
 
 Theory of Shared Keys (common to all symmetric-key protocols)
 
-Server keys; initial states of agents; freshness; function "sees" 
+Shared, long-term keys; initial states of agents
 *)
 
 
 open Shared;
 
-(*Holds because Friend is injective: thus cannot prove for all f*)
-goal thy "(Friend x : Friend``A) = (x:A)";
-by (Auto_tac());
-qed "Friend_image_eq";
-Addsimps [Friend_image_eq];
-
-Addsimps [Un_insert_left, Un_insert_right];
-
-(*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];
-
 (*** Basic properties of shrK ***)
 
 (*Injectiveness: Agents' long-term keys are distinct.*)
@@ -41,87 +28,26 @@
 qed "keysFor_parts_initState";
 Addsimps [keysFor_parts_initState];
 
-goalw thy [keysFor_def] "keysFor (Key``E) = {}";
-by (Auto_tac ());
-qed "keysFor_image_Key";
-Addsimps [keysFor_image_Key];
-
 
 (*** Function "sees" ***)
 
-goal thy
-    "!!evs. lost' <= lost ==> sees lost' A evs <= sees lost A evs";
-by (list.induct_tac "evs" 1);
-by (agent.induct_tac "A" 1);
-by (event.induct_tac "a" 2);
-by (Auto_tac ());
-qed "sees_mono";
-
 (*Agents see their own shared keys!*)
 goal thy "A ~= Spy --> Key (shrK A) : sees lost A evs";
 by (list.induct_tac "evs" 1);
 by (agent.induct_tac "A" 1);
-by (Auto_tac ());
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons])));
+by (Blast_tac 1);
 qed_spec_mp "sees_own_shrK";
 
 (*Spy sees shared keys of lost agents!*)
 goal thy "!!A. A: lost ==> Key (shrK A) : sees lost Spy evs";
 by (list.induct_tac "evs" 1);
-by (Auto_tac());
+by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons])));
+by (Blast_tac 1);
 qed "Spy_sees_lost";
 
 AddSIs [sees_own_shrK, Spy_sees_lost];
 
-(** Specialized rewrite rules for (sees lost A (Says...#evs)) **)
-
-goal thy "sees lost B (Says A B X # evs) = insert X (sees lost B evs)";
-by (Simp_tac 1);
-qed "sees_own";
-
-goal thy "!!A. Server ~= B ==> \
-\          sees lost Server (Says A B X # evs) = sees lost Server evs";
-by (Asm_simp_tac 1);
-qed "sees_Server";
-
-goal thy "!!A. Friend i ~= B ==> \
-\          sees lost (Friend i) (Says A B X # evs) = sees lost (Friend i) evs";
-by (Asm_simp_tac 1);
-qed "sees_Friend";
-
-goal thy "sees lost Spy (Says A B X # evs) = insert X (sees lost Spy evs)";
-by (Simp_tac 1);
-qed "sees_Spy";
-
-goal thy "sees lost A (Says A' B X # evs) <= insert X (sees lost A evs)";
-by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
-by (Blast_tac 1);
-qed "sees_Says_subset_insert";
-
-goal thy "sees lost A evs <= sees lost A (Says A' B X # evs)";
-by (simp_tac (!simpset setloop split_tac [expand_if]) 1);
-by (Blast_tac 1);
-qed "sees_subset_sees_Says";
-
-(*Pushing Unions into parts.  One of the agents A is B, and thus sees Y.
-  Once used to prove new_keys_not_seen; now obsolete.*)
-goal thy "(UN A. parts (sees lost A (Says B C Y # evs))) = \
-\         parts {Y} Un (UN A. parts (sees lost A evs))";
-by (Step_tac 1);
-by (etac rev_mp 1);     (*split_tac does not work on assumptions*)
-by (ALLGOALS
-    (fast_tac (!claset addss (!simpset addsimps [parts_Un, sees_Cons] 
-				            setloop split_tac [expand_if]))));
-qed "UN_parts_sees_Says";
-
-goal thy "Says A B X : set evs --> X : sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (Auto_tac ());
-qed_spec_mp "Says_imp_sees_Spy";
-
-(*Use with addSEs to derive contradictions from old Says events containing
-  items known to be fresh*)
-val sees_Spy_partsEs = make_elim (Says_imp_sees_Spy RS parts.Inj):: partsEs;
-
 (*For not_lost_tac*)
 goal thy "!!A. [| Crypt (shrK A) X : analz (sees lost Spy evs);  A: lost |] \
 \              ==> X : analz (sees lost Spy evs)";
@@ -140,25 +66,6 @@
          (has_fewer_prems 1, size_of_thm)
          (Step_tac 1));
 
-Addsimps [sees_own, sees_Server, sees_Friend, sees_Spy];
-Delsimps [sees_Cons];   (**** NOTE REMOVAL -- laws above are cleaner ****)
-
-
-(*** Fresh nonces ***)
-
-goal thy "Nonce N ~: parts (initState lost B)";
-by (agent.induct_tac "B" 1);
-by (Auto_tac ());
-qed "Nonce_notin_initState";
-
-AddIffs [Nonce_notin_initState];
-
-goalw thy [used_def] "!!X. X: parts (sees lost B evs) ==> X: used evs";
-by (etac (impOfSubs parts_mono) 1);
-by (Blast_tac 1);
-qed "usedI";
-
-AddIs [usedI];
 
 (** Fresh keys never clash with long-term shared keys **)
 
@@ -181,29 +88,23 @@
 Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym];
 
 
-goal thy "used (Says A B X # evs) = parts{X} Un used evs";
-by (simp_tac (!simpset addsimps [used_def, UN_parts_sees_Says]) 1);
-qed "used_Says";
-Addsimps [used_Says];
+(*** Fresh nonces ***)
 
-goal thy "used [] <= used l";
-by (list.induct_tac "l" 1);
-by (event.induct_tac "a" 2);
-by (ALLGOALS Asm_simp_tac);
-by (Blast_tac 1);
-qed "used_nil_subset";
+goal thy "Nonce N ~: parts (initState lost B)";
+by (agent.induct_tac "B" 1);
+by (Auto_tac ());
+qed "Nonce_notin_initState";
+AddIffs [Nonce_notin_initState];
 
-goal thy "used l <= used (l@l')";
-by (list.induct_tac "l" 1);
-by (simp_tac (!simpset addsimps [used_nil_subset]) 1);
-by (event.induct_tac "a" 1);
-by (Asm_simp_tac 1);
-by (Blast_tac 1);
-qed "used_subset_append";
+goal thy "Nonce N ~: used []";
+by (simp_tac (!simpset addsimps [used_def]) 1);
+qed "Nonce_notin_used_empty";
+Addsimps [Nonce_notin_used_empty];
 
 
 (*** Supply fresh nonces for possibility theorems. ***)
 
+(*In any trace, there is an upper bound N on the greatest nonce in use.*)
 goalw thy [used_def] "EX N. ALL n. N<=n --> Nonce n ~: used evs";
 by (list.induct_tac "evs" 1);
 by (res_inst_tac [("x","0")] exI 1);
@@ -211,16 +112,12 @@
 by (Full_simp_tac 1);
 (*Inductive step*)
 by (event.induct_tac "a" 1);
-by (full_simp_tac (!simpset addsimps [UN_parts_sees_Says]) 1);
-by (msg.induct_tac "msg" 1);
-by (ALLGOALS (asm_simp_tac (!simpset addsimps [exI, parts_insert2])));
-by (Step_tac 1);
-(*MPair case*)
-by (res_inst_tac [("x","Na+Nb")] exI 2);
-by (blast_tac (!claset addSEs [add_leE]) 2);
-(*Nonce case*)
-by (res_inst_tac [("x","N + Suc nat")] exI 1);
-by (fast_tac (!claset addSEs [add_leE] addaltern trans_tac) 1);
+by (ALLGOALS (full_simp_tac 
+	      (!simpset delsimps [sees_Notes]
+		        addsimps [UN_parts_sees_Says,
+				  UN_parts_sees_Notes])));
+by (ALLGOALS (rtac (msg_Nonce_supply RS exE)));
+by (ALLGOALS (blast_tac (!claset addSEs [add_leE])));
 val lemma = result();
 
 goal thy "EX N. Nonce N ~: used evs";
@@ -302,8 +199,7 @@
 
 val possibility_tac =
     REPEAT (*omit used_Says so that Nonces, Keys start from different traces!*)
-    (ALLGOALS (simp_tac 
-               (!simpset delsimps [used_Says] setSolver safe_solver))
+    (ALLGOALS (simp_tac (!simpset delsimps [used_Says] setSolver safe_solver))
      THEN
      REPEAT_FIRST (eq_assume_tac ORELSE' 
                    resolve_tac [refl, conjI, Nonce_supply, Key_supply]));
@@ -317,35 +213,6 @@
      REPEAT_FIRST (resolve_tac [refl, conjI]));
 
 
-(** Power of the Spy **)
-
-(*The Spy can see more than anybody else, except for their initial state*)
-goal thy "sees lost A evs <= initState lost A Un sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (event.induct_tac "a" 2);
-by (ALLGOALS Asm_simp_tac);
-by (ALLGOALS (blast_tac (!claset addDs [sees_Says_subset_insert RS subsetD])));
-qed "sees_agent_subset_sees_Spy";
-
-(*The Spy can see more than anybody else who's lost their key!*)
-goal thy "A: lost --> A ~= Server --> sees lost A evs <= sees lost Spy evs";
-by (list.induct_tac "evs" 1);
-by (event.induct_tac "a" 2);
-by (agent.induct_tac "A" 1);
-by (ALLGOALS Asm_simp_tac);
-by (ALLGOALS (blast_tac (!claset addDs [sees_Says_subset_insert RS subsetD])));
-qed_spec_mp "sees_lost_agent_subset_sees_Spy";
-
-
-(** Simplifying   parts (insert X (sees lost A evs))
-      = parts {X} Un parts (sees lost A evs) -- since general case loops*)
-
-val parts_insert_sees = 
-    parts_insert |> read_instantiate_sg (sign_of thy)
-                                        [("H", "sees lost A evs")]
-                 |> standard;
-
-
 (*** Specialized rewriting for analz_insert_freshK ***)
 
 goal thy "!!A. A <= Compl (range shrK) ==> shrK x ~: A";

--- a/src/HOL/Auth/Shared.thy	Wed Jul 09 17:00:34 1997 +0200
+++ b/src/HOL/Auth/Shared.thy	Fri Jul 11 13:26:15 1997 +0200
@@ -5,10 +5,10 @@
 
 Theory of Shared Keys (common to all symmetric-key protocols)
 
-Server keys; initial states of agents; new nonces and keys; function "sees" 
+Shared, long-term keys; initial states of agents
 *)
 
-Shared = Message + List + Finite +
+Shared = Event + Finite +
 
 consts
   shrK    :: agent => key  (*symmetric keys*)
@@ -17,9 +17,6 @@
   isSym_keys "isSymKey K"	(*All keys are symmetric*)
   inj_shrK   "inj shrK"		(*No two agents have the same long-term key*)
 
-consts  (*Initial states of agents -- parameter of the construction*)
-  initState :: [agent set, agent] => msg set
-
 primrec initState agent
         (*Server knows all long-term keys; other agents know only their own*)
   initState_Server  "initState lost Server     = Key `` range shrK"
@@ -27,31 +24,6 @@
   initState_Spy     "initState lost Spy        = Key``shrK``lost"
 
 
-datatype  (*Messages, and components of agent stores*)
-  event = Says agent agent msg
-
-consts  
-  sees1 :: [agent, event] => msg set
-
-primrec sees1 event
-           (*Spy reads all traffic whether addressed to him or not*)
-  sees1_Says  "sees1 A (Says A' B X)  = (if A:{B,Spy} then {X} else {})"
-
-consts  
-  sees :: [agent set, agent, event list] => msg set
-
-primrec sees list
-  sees_Nil  "sees lost A []       = initState lost A"
-  sees_Cons "sees lost A (ev#evs) = sees1 A ev Un sees lost A evs"
-
-
-constdefs
-  (*Set of items that might be visible to somebody: complement of the set
-        of fresh items*)
-  used :: event list => msg set
-    "used evs == parts (UN lost B. sees lost B evs)"
-
-
 rules
   (*Unlike the corresponding property of nonces, this cannot be proved.
     We have infinitely many agents and there is nothing to stop their