--- a/src/HOL/Auth/Shared_lemmas.ML Sat Apr 26 12:38:42 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,260 +0,0 @@
-(* Title: HOL/Auth/Shared
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1996 University of Cambridge
-
-Theory of Shared Keys (common to all symmetric-key protocols)
-
-Shared, long-term keys; initial states of agents
-*)
-
-val inj_shrK = thm "inj_shrK";
-val isSym_keys = thm "isSym_keys";
-val Key_supply_ax = thm "Key_supply_ax";
-
-(*** Basic properties of shrK ***)
-
-(*Injectiveness: Agents' long-term keys are distinct.*)
-AddIffs [inj_shrK RS inj_eq];
-
-Goal "invKey K = K";
-by (cut_facts_tac [rewrite_rule [symKeys_def] isSym_keys] 1);
-by Auto_tac;
-qed "invKey_K";
-Addsimps [invKey_K];
-
-
-Goal "[| Crypt K X \\<in> analz H; Key K \\<in> analz H |] ==> X \\<in> analz H";
-by Auto_tac;
-qed "analz_Decrypt'";
-AddDs [analz_Decrypt'];
-Delrules [analz.Decrypt];
-
-(** Rewrites should not refer to initState(Friend i)
- -- not in normal form! **)
-
-Goalw [keysFor_def] "keysFor (parts (initState C)) = {}";
-by (induct_tac "C" 1);
-by Auto_tac;
-qed "keysFor_parts_initState";
-Addsimps [keysFor_parts_initState];
-
-(*Specialized to shared-key model: no need for addss in protocol proofs*)
-Goal "[| K: keysFor (parts (insert X H)); X : synth (analz H) |] \
-\ ==> K : keysFor (parts H) | Key K : parts H";
-by (force_tac
- (claset() addSDs [impOfSubs (parts_insert_subset_Un RS keysFor_mono),
- impOfSubs (analz_subset_parts RS keysFor_mono)]
- addIs [impOfSubs analz_subset_parts],
- simpset()) 1);
-qed "keysFor_parts_insert";
-
-Goal "Crypt K X : H ==> K : keysFor H";
-by (dtac Crypt_imp_invKey_keysFor 1);
-by (Asm_full_simp_tac 1);
-qed "Crypt_imp_keysFor";
-
-
-(*** Function "knows" ***)
-
-(*Spy sees shared keys of agents!*)
-Goal "A: bad ==> Key (shrK A) : knows Spy evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [imageI, knows_Cons]
- addsplits [expand_event_case])));
-qed "Spy_knows_Spy_bad";
-AddSIs [Spy_knows_Spy_bad];
-
-(*For case analysis on whether or not an agent is compromised*)
-Goal "[| Crypt (shrK A) X : analz (knows Spy evs); A: bad |] \
-\ ==> X : analz (knows Spy evs)";
-by (force_tac (claset() addSDs [analz.Decrypt], simpset()) 1);
-qed "Crypt_Spy_analz_bad";
-
-
-(** Fresh keys never clash with long-term shared keys **)
-
-(*Agents see their own shared keys!*)
-Goal "Key (shrK A) : initState A";
-by (induct_tac "A" 1);
-by Auto_tac;
-qed "shrK_in_initState";
-AddIffs [shrK_in_initState];
-
-Goal "Key (shrK A) : used evs";
-by (rtac initState_into_used 1);
-by (Blast_tac 1);
-qed "shrK_in_used";
-AddIffs [shrK_in_used];
-
-(*Used in parts_induct_tac and analz_Fake_tac to distinguish session keys
- from long-term shared keys*)
-Goal "Key K \\<notin> used evs ==> K \\<notin> range shrK";
-by (Blast_tac 1);
-qed "Key_not_used";
-
-Goal "Key K \\<notin> used evs ==> shrK B \\<noteq> K";
-by (Blast_tac 1);
-qed "shrK_neq";
-
-Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym];
-
-
-(*** Fresh nonces ***)
-
-Goal "Nonce N \\<notin> parts (initState B)";
-by (induct_tac "B" 1);
-by Auto_tac;
-qed "Nonce_notin_initState";
-AddIffs [Nonce_notin_initState];
-
-Goal "Nonce N \\<notin> used []";
-by (simp_tac (simpset() addsimps [used_Nil]) 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.*)
-Goal "EX N. ALL n. N<=n --> Nonce n \\<notin> used evs";
-by (induct_tac "evs" 1);
-by (res_inst_tac [("x","0")] exI 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [used_Cons]
- addsplits [expand_event_case])));
-by Safe_tac;
-by (ALLGOALS (rtac (msg_Nonce_supply RS exE)));
-by (ALLGOALS (blast_tac (claset() addSEs [add_leE])));
-val lemma = result();
-
-Goal "EX N. Nonce N \\<notin> used evs";
-by (rtac (lemma RS exE) 1);
-by (Blast_tac 1);
-qed "Nonce_supply1";
-
-Goal "EX N N'. Nonce N \\<notin> used evs & Nonce N' \\<notin> used evs' & N \\<noteq> N'";
-by (cut_inst_tac [("evs","evs")] lemma 1);
-by (cut_inst_tac [("evs","evs'")] lemma 1);
-by (Clarify_tac 1);
-by (res_inst_tac [("x","N")] exI 1);
-by (res_inst_tac [("x","Suc (N+Na)")] exI 1);
-by (asm_simp_tac (simpset() addsimps [less_not_refl3, le_add1, le_add2,
- less_Suc_eq_le]) 1);
-qed "Nonce_supply2";
-
-Goal "EX N N' N''. Nonce N \\<notin> used evs & Nonce N' \\<notin> used evs' & \
-\ Nonce N'' \\<notin> used evs'' & N \\<noteq> N' & N' \\<noteq> N'' & N \\<noteq> N''";
-by (cut_inst_tac [("evs","evs")] lemma 1);
-by (cut_inst_tac [("evs","evs'")] lemma 1);
-by (cut_inst_tac [("evs","evs''")] lemma 1);
-by (Clarify_tac 1);
-by (res_inst_tac [("x","N")] exI 1);
-by (res_inst_tac [("x","Suc (N+Na)")] exI 1);
-by (res_inst_tac [("x","Suc (Suc (N+Na+Nb))")] exI 1);
-by (asm_simp_tac (simpset() addsimps [less_not_refl3, le_add1, le_add2,
- less_Suc_eq_le]) 1);
-qed "Nonce_supply3";
-
-Goal "Nonce (@ N. Nonce N \\<notin> used evs) \\<notin> used evs";
-by (rtac (lemma RS exE) 1);
-by (rtac someI 1);
-by (Blast_tac 1);
-qed "Nonce_supply";
-
-(*** Supply fresh keys for possibility theorems. ***)
-
-Goal "EX K. Key K \\<notin> used evs";
-by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1);
-by (Blast_tac 1);
-qed "Key_supply1";
-
-Goal "EX K K'. Key K \\<notin> used evs & Key K' \\<notin> used evs' & K \\<noteq> K'";
-by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1);
-by (etac exE 1);
-by (cut_inst_tac [("evs","evs'")]
- (Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1);
-by (Asm_full_simp_tac 1 THEN depth_tac (claset()) 2 1); (* replaces Auto_tac *)
-qed "Key_supply2";
-
-Goal "EX K K' K''. Key K \\<notin> used evs & Key K' \\<notin> used evs' & \
-\ Key K'' \\<notin> used evs'' & K \\<noteq> K' & K' \\<noteq> K'' & K \\<noteq> K''";
-by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1);
-by (etac exE 1);
-(*Blast_tac requires instantiation of the keys for some reason*)
-by (cut_inst_tac [("evs","evs'"), ("a1","K")]
- (Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1);
-by (etac exE 1);
-by (cut_inst_tac [("evs","evs''"), ("a1","Ka"), ("a2","K")]
- (Finites.emptyI RS Finites.insertI RS Finites.insertI RS Key_supply_ax) 1);
-by (Blast_tac 1);
-qed "Key_supply3";
-
-Goal "Key (@ K. Key K \\<notin> used evs) \\<notin> used evs";
-by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1);
-by (rtac someI 1);
-by (Blast_tac 1);
-qed "Key_supply";
-
-(*** Tactics for possibility theorems ***)
-
-(*Omitting used_Says makes the tactic much faster: it leaves expressions
- such as Nonce ?N \\<notin> used evs that match Nonce_supply*)
-fun gen_possibility_tac ss state = state |>
- (REPEAT
- (ALLGOALS (simp_tac (ss delsimps [used_Says, used_Notes, used_Gets]
- setSolver safe_solver))
- THEN
- REPEAT_FIRST (eq_assume_tac ORELSE'
- resolve_tac [refl, conjI, Nonce_supply, Key_supply])));
-
-(*Tactic for possibility theorems (ML script version)*)
-fun possibility_tac state = gen_possibility_tac (simpset()) state;
-
-(*For harder protocols (such as Recur) where we have to set up some
- nonces and keys initially*)
-fun basic_possibility_tac st = st |>
- REPEAT
- (ALLGOALS (asm_simp_tac (simpset() setSolver safe_solver))
- THEN
- REPEAT_FIRST (resolve_tac [refl, conjI]));
-
-
-(*** Specialized rewriting for analz_insert_freshK ***)
-
-Goal "A <= - (range shrK) ==> shrK x \\<notin> A";
-by (Blast_tac 1);
-qed "subset_Compl_range";
-
-Goal "insert (Key K) H = Key ` {K} Un H";
-by (Blast_tac 1);
-qed "insert_Key_singleton";
-
-Goal "insert (Key K) (Key`KK Un C) = Key ` (insert K KK) Un C";
-by (Blast_tac 1);
-qed "insert_Key_image";
-
-(** Reverse the normal simplification of "image" to build up (not break down)
- the set of keys. Use analz_insert_eq with (Un_upper2 RS analz_mono) to
- erase occurrences of forwarded message components (X). **)
-
-bind_thms ("analz_image_freshK_simps",
- simp_thms @ mem_simps @ (*these two allow its use with only:*)
- disj_comms @
- [image_insert RS sym, image_Un RS sym, empty_subsetI, insert_subset,
- analz_insert_eq, impOfSubs (Un_upper2 RS analz_mono),
- insert_Key_singleton, subset_Compl_range,
- Key_not_used, insert_Key_image, Un_assoc RS sym]);
-
-val analz_image_freshK_ss =
- simpset() delsimps [image_insert, image_Un]
- delsimps [imp_disjL] (*reduces blow-up*)
- addsimps analz_image_freshK_simps;
-
-(*Lemma for the trivial direction of the if-and-only-if*)
-Goal "(Key K : analz (Key`nE Un H)) --> (K : nE | Key K : analz H) ==> \
-\ (Key K : analz (Key`nE Un H)) = (K : nE | Key K : analz H)";
-by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1);
-qed "analz_image_freshK_lemma";
-