--- 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;