--- a/doc-src/TutorialI/Protocol/Event_lemmas.ML Mon Jul 23 14:06:14 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,232 +0,0 @@
-(* Title: HOL/Auth/Event_lemmas
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1996 University of Cambridge
-*)
-
-
-val knows_Cons = thm "knows_Cons";
-val used_Nil = thm "used_Nil";
-val used_Cons = thm "used_Cons";
-
-
-(*Inserted by default but later removed. This declaration lets the file
- be re-loaded.*)
-Addsimps [knows_Cons, used_Nil, used_Cons];
-
-(**** Function "knows" ****)
-
-(** Simplifying parts (insert X (knows Spy evs))
- = parts {X} Un parts (knows Spy evs) -- since general case loops*)
-
-bind_thm ("parts_insert_knows_Spy",
- inst "H" "knows Spy evs" parts_insert);
-
-
-val expand_event_case = thm "event.split";
-
-Goal "knows Spy (Says A B X # evs) = insert X (knows Spy evs)";
-by (Simp_tac 1);
-qed "knows_Spy_Says";
-
-(*The point of letting the Spy see "bad" agents' notes is to prevent
- redundant case-splits on whether A=Spy and whether A:bad*)
-Goal "knows Spy (Notes A X # evs) = \
-\ (if A:bad then insert X (knows Spy evs) else knows Spy evs)";
-by (Simp_tac 1);
-qed "knows_Spy_Notes";
-
-Goal "knows Spy (Gets A X # evs) = knows Spy evs";
-by (Simp_tac 1);
-qed "knows_Spy_Gets";
-
-Goal "knows Spy evs <= knows Spy (Says A B X # evs)";
-by (simp_tac (simpset() addsimps [thm "subset_insertI"]) 1);
-qed "knows_Spy_subset_knows_Spy_Says";
-
-Goal "knows Spy evs <= knows Spy (Notes A X # evs)";
-by (Simp_tac 1);
-by (Fast_tac 1);
-qed "knows_Spy_subset_knows_Spy_Notes";
-
-Goal "knows Spy evs <= knows Spy (Gets A X # evs)";
-by (simp_tac (simpset() addsimps [thm "subset_insertI"]) 1);
-qed "knows_Spy_subset_knows_Spy_Gets";
-
-(*Spy sees what is sent on the traffic*)
-Goal "Says A B X : set evs --> X : knows Spy evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-qed_spec_mp "Says_imp_knows_Spy";
-
-Goal "Notes A X : set evs --> A: bad --> X : knows Spy evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-qed_spec_mp "Notes_imp_knows_Spy";
-
-
-(*Use with addSEs to derive contradictions from old Says events containing
- items known to be fresh*)
-bind_thms ("knows_Spy_partsEs",
- map make_elim [Says_imp_knows_Spy RS parts.Inj, parts.Body]);
-
-Addsimps [knows_Spy_Says, knows_Spy_Notes, knows_Spy_Gets];
-
-
-(*Begin lemmas about agents' knowledge*)
-
-Goal "knows A (Says A B X # evs) = insert X (knows A evs)";
-by (Simp_tac 1);
-qed "knows_Says";
-
-Goal "knows A (Notes A X # evs) = insert X (knows A evs)";
-by (Simp_tac 1);
-qed "knows_Notes";
-
-Goal "A ~= Spy --> knows A (Gets A X # evs) = insert X (knows A evs)";
-by (Simp_tac 1);
-qed "knows_Gets";
-
-
-Goal "knows A evs <= knows A (Says A B X # evs)";
-by (simp_tac (simpset() addsimps [thm "subset_insertI"]) 1);
-qed "knows_subset_knows_Says";
-
-Goal "knows A evs <= knows A (Notes A X # evs)";
-by (simp_tac (simpset() addsimps [thm "subset_insertI"]) 1);
-qed "knows_subset_knows_Notes";
-
-Goal "knows A evs <= knows A (Gets A X # evs)";
-by (simp_tac (simpset() addsimps [thm "subset_insertI"]) 1);
-qed "knows_subset_knows_Gets";
-
-(*Agents know what they say*)
-Goal "Says A B X : set evs --> X : knows A evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-by (Blast_tac 1);
-qed_spec_mp "Says_imp_knows";
-
-(*Agents know what they note*)
-Goal "Notes A X : set evs --> X : knows A evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-by (Blast_tac 1);
-qed_spec_mp "Notes_imp_knows";
-
-(*Agents know what they receive*)
-Goal "A ~= Spy --> Gets A X : set evs --> X : knows A evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-qed_spec_mp "Gets_imp_knows_agents";
-
-
-(*What agents DIFFERENT FROM Spy know
- was either said, or noted, or got, or known initially*)
-Goal "[| X : knows A evs; A ~= Spy |] ==> EX B. \
-\ Says A B X : set evs | Gets A X : set evs | Notes A X : set evs | X : initState A";
-by (etac rev_mp 1);
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-by (Blast_tac 1);
-qed_spec_mp "knows_imp_Says_Gets_Notes_initState";
-
-(*What the Spy knows -- for the time being --
- was either said or noted, or known initially*)
-Goal "[| X : knows Spy evs |] ==> EX A B. \
-\ Says A B X : set evs | Notes A X : set evs | X : initState Spy";
-by (etac rev_mp 1);
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac (simpset() addsplits [expand_event_case])));
-by (Blast_tac 1);
-qed_spec_mp "knows_Spy_imp_Says_Notes_initState";
-
-(*END lemmas about agents' knowledge*)
-
-
-
-(**** NOTE REMOVAL--laws above are cleaner, as they don't involve "case" ****)
-Delsimps [knows_Cons];
-
-
-(*** Fresh nonces ***)
-
-Goal "parts (knows Spy evs) <= used evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [parts_insert_knows_Spy]
- addsplits [expand_event_case])));
-by (ALLGOALS Blast_tac);
-qed "parts_knows_Spy_subset_used";
-
-bind_thm ("usedI", impOfSubs parts_knows_Spy_subset_used);
-AddIs [usedI];
-
-Goal "parts (initState B) <= used evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [parts_insert_knows_Spy]
- addsplits [expand_event_case])));
-by (ALLGOALS Blast_tac);
-bind_thm ("initState_into_used", impOfSubs (result()));
-
-Goal "used (Says A B X # evs) = parts{X} Un used evs";
-by (Simp_tac 1);
-qed "used_Says";
-Addsimps [used_Says];
-
-Goal "used (Notes A X # evs) = parts{X} Un used evs";
-by (Simp_tac 1);
-qed "used_Notes";
-Addsimps [used_Notes];
-
-Goal "used (Gets A X # evs) = used evs";
-by (Simp_tac 1);
-qed "used_Gets";
-Addsimps [used_Gets];
-
-Goal "used [] <= used evs";
-by (Simp_tac 1);
-by (blast_tac (claset() addIs [initState_into_used]) 1);
-qed "used_nil_subset";
-
-(**** NOTE REMOVAL--laws above are cleaner, as they don't involve "case" ****)
-Delsimps [used_Nil, used_Cons];
-
-
-(*For proving theorems of the form X ~: analz (knows 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.*)
-
-bind_thms ("analz_mono_contra",
- [knows_Spy_subset_knows_Spy_Says RS analz_mono RS contra_subsetD,
- knows_Spy_subset_knows_Spy_Notes RS analz_mono RS contra_subsetD,
- knows_Spy_subset_knows_Spy_Gets RS analz_mono RS contra_subsetD]);
-
-val analz_mono_contra_tac =
- let val analz_impI = inst "P" "?Y ~: analz (knows Spy ?evs)" impI
- in
- rtac analz_impI THEN'
- REPEAT1 o
- (dresolve_tac
- [knows_Spy_subset_knows_Spy_Says RS analz_mono RS contra_subsetD,
- knows_Spy_subset_knows_Spy_Notes RS analz_mono RS contra_subsetD,
- knows_Spy_subset_knows_Spy_Gets RS analz_mono RS contra_subsetD])
- THEN'
- mp_tac
- end;
-
-fun Reception_tac i =
- blast_tac (claset() addDs [Says_imp_knows_Spy RS parts.Inj,
- impOfSubs (parts_insert RS equalityD1),
- parts_trans,
- Says_imp_knows_Spy RS analz.Inj,
- impOfSubs analz_mono, analz_cut]
- addIs [@{thm less_SucI}]) i;
-
-
-(*Compatibility for the old "spies" function*)
-bind_thms ("spies_partsEs", knows_Spy_partsEs);
-bind_thm ("Says_imp_spies", Says_imp_knows_Spy);
-bind_thm ("parts_insert_spies", parts_insert_knows_Spy);
--- a/doc-src/TutorialI/Protocol/Message_lemmas.ML Mon Jul 23 14:06:14 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,899 +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"
-*)
-
-(*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 symKeys_def = thm "symKeys_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 \\<in> Friend`A) = (x:A)";
-by Auto_tac;
-qed "Friend_image_eq";
-
-Goal "(Key x \\<in> Key`A) = (x\\<in>A)";
-by Auto_tac;
-qed "Key_image_eq";
-
-Goal "(Nonce x \\<notin> 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 (\\<Union>i\\<in>A. H i) = (\\<Union>i\\<in>A. keysFor (H i))";
-by (Blast_tac 1);
-qed "keysFor_UN";
-
-(*Monotonicity*)
-Goalw [keysFor_def] "G\\<subseteq>H ==> keysFor(G) \\<subseteq> 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 thm "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 \\<in> H ==> invKey K \\<in> keysFor H";
-by (Blast_tac 1);
-qed "Crypt_imp_invKey_keysFor";
-
-
-(**** Inductive relation "parts" ****)
-
-val major::prems =
-Goal "[| {|X,Y|} \\<in> parts H; \
-\ [| X \\<in> parts H; Y \\<in> 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 \\<subseteq> parts(H)";
-by (Blast_tac 1);
-qed "parts_increasing";
-
-val parts_insertI = impOfSubs (thm "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\\<in> 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\\<in> parts H ==> \\<exists>Y\\<in>H. X\\<in> parts {Y}";
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-qed "parts_singleton";
-
-
-(** Unions **)
-
-Goal "parts(G) Un parts(H) \\<subseteq> parts(G Un H)";
-by (REPEAT (ares_tac [thm "Un_least", parts_mono, thm "Un_upper1", thm "Un_upper2"] 1));
-val parts_Un_subset1 = result();
-
-Goal "parts(G Un H) \\<subseteq> 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")] (thm "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 [thm "Un_assoc"]) 1);
-by (simp_tac (simpset() addsimps [parts_insert RS sym]) 1);
-qed "parts_insert2";
-
-Goal "(\\<Union>x\\<in>A. parts(H x)) \\<subseteq> parts(\\<Union>x\\<in>A. H x)";
-by (REPEAT (ares_tac [thm "UN_least", parts_mono, thm "UN_upper"] 1));
-val parts_UN_subset1 = result();
-
-Goal "parts(\\<Union>x\\<in>A. H x) \\<subseteq> (\\<Union>x\\<in>A. parts(H x))";
-by (rtac subsetI 1);
-by (etac parts.induct 1);
-by (ALLGOALS Blast_tac);
-val parts_UN_subset2 = result();
-
-Goal "parts(\\<Union>x\\<in>A. H x) = (\\<Union>x\\<in>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 thm "UN_E"];
-
-Goal "insert X (parts H) \\<subseteq> parts(insert X H)";
-by (blast_tac (claset() addIs [impOfSubs parts_mono]) 1);
-qed "parts_insert_subset";
-
-(** Idempotence and transitivity **)
-
-Goal "X\\<in> parts (parts H) ==> X\\<in> 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\\<in> parts G; G \\<subseteq> parts H |] ==> X\\<in> parts H";
-by (dtac parts_mono 1);
-by (Blast_tac 1);
-qed "parts_trans";
-
-(*Cut*)
-Goal "[| Y\\<in> parts (insert X G); X\\<in> parts H |] \
-\ ==> Y\\<in> parts (G Un H)";
-by (etac parts_trans 1);
-by Auto_tac;
-qed "parts_cut";
-
-Goal "X\\<in> 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 "\\<exists>N. \\<forall>n. N\\<le>n --> Nonce n \\<notin> 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 [@{thm add_leE}]) 2);
-(*Nonce case*)
-by (res_inst_tac [("x","N + Suc nat")] exI 1);
-by (auto_tac (claset() addSEs [@{thm add_leE}], simpset()));
-qed "msg_Nonce_supply";
-
-
-(**** Inductive relation "analz" ****)
-
-val major::prems =
-Goal "[| {|X,Y|} \\<in> analz H; \
-\ [| X \\<in> analz H; Y \\<in> 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 \\<subseteq> analz(H)";
-by (Blast_tac 1);
-qed "analz_increasing";
-
-Goal "analz H \\<subseteq> 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 (thm "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) \\<subseteq> analz(G Un H)";
-by (REPEAT (ares_tac [thm "Un_least", analz_mono, thm "Un_upper1", thm "Un_upper2"] 1));
-qed "analz_Un";
-
-Goal "insert X (analz H) \\<subseteq> 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 \\<notin> 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) \\<notin> 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) \\<in> analz H ==> \
-\ analz (insert (Crypt K X) H) \\<subseteq> \
-\ insert (Crypt K X) (analz (insert X H))";
-by (rtac subsetI 1);
-by (eres_inst_tac [("x","x")] analz.induct 1);
-by Auto_tac;
-val lemma1 = result();
-
-Goal "Key (invKey K) \\<in> analz H ==> \
-\ insert (Crypt K X) (analz (insert X H)) \\<subseteq> \
-\ analz (insert (Crypt K X) H)";
-by Auto_tac;
-by (eres_inst_tac [("x","x")] analz.induct 1);
-by Auto_tac;
-by (blast_tac (claset() addIs [analz_insertI, analz.Decrypt]) 1);
-val lemma2 = result();
-
-Goal "Key (invKey K) \\<in> 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) \\<in> analz H) \
-\ then insert (Crypt K X) (analz (insert X H)) \
-\ else insert (Crypt K X) (analz H))";
-by (case_tac "Key (invKey K) \\<in> 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) \\<subseteq> \
-\ 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\\<in> analz (analz H) ==> X\\<in> 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\\<in> analz G; G \\<subseteq> analz H |] ==> X\\<in> analz H";
-by (dtac analz_mono 1);
-by (Blast_tac 1);
-qed "analz_trans";
-
-(*Cut; Lemma 2 of Lowe*)
-Goal "[| Y\\<in> analz (insert X H); X\\<in> analz H |] ==> Y\\<in> 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\\<in> 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 \\<subseteq> analz G'; analz H \\<subseteq> analz H' \
-\ |] ==> analz (G Un H) \\<subseteq> 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 [thm "insert_def"] delsimps [thm "singleton_conv"]
- setloop (rtac analz_cong)) 1);
-qed "analz_insert_cong";
-
-(*If there are no pairs or encryptions then analz does nothing*)
-Goal "[| \\<forall>X Y. {|X,Y|} \\<notin> H; \\<forall>X K. Crypt K X \\<notin> 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\\<in> analz (\\<Union>i\\<in>A. analz (H i)) ==> X\\<in> analz (\\<Union>i\\<in>A. H i)";
-by (etac analz.induct 1);
-by (ALLGOALS (blast_tac (claset() addIs [impOfSubs analz_mono])));
-val lemma = result();
-
-Goal "analz (\\<Union>i\\<in>A. analz (H i)) = analz (\\<Union>i\\<in>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 \\<subseteq> 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) \\<subseteq> synth(G Un H)";
-by (REPEAT (ares_tac [thm "Un_least", synth_mono, thm "Un_upper1", thm "Un_upper2"] 1));
-qed "synth_Un";
-
-Goal "insert X (synth H) \\<subseteq> synth(insert X H)";
-by (blast_tac (claset() addIs [impOfSubs synth_mono]) 1);
-qed "synth_insert";
-
-(** Idempotence and transitivity **)
-
-Goal "X\\<in> synth (synth H) ==> X\\<in> 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\\<in> synth G; G \\<subseteq> synth H |] ==> X\\<in> synth H";
-by (dtac synth_mono 1);
-by (Blast_tac 1);
-qed "synth_trans";
-
-(*Cut; Lemma 2 of Lowe*)
-Goal "[| Y\\<in> synth (insert X H); X\\<in> synth H |] ==> Y\\<in> synth H";
-by (etac synth_trans 1);
-by (Blast_tac 1);
-qed "synth_cut";
-
-Goal "Agent A \\<in> synth H";
-by (Blast_tac 1);
-qed "Agent_synth";
-
-Goal "Number n \\<in> synth H";
-by (Blast_tac 1);
-qed "Number_synth";
-
-Goal "(Nonce N \\<in> synth H) = (Nonce N \\<in> H)";
-by (Blast_tac 1);
-qed "Nonce_synth_eq";
-
-Goal "(Key K \\<in> synth H) = (Key K \\<in> H)";
-by (Blast_tac 1);
-qed "Key_synth_eq";
-
-Goal "Key K \\<notin> H ==> (Crypt K X \\<in> synth H) = (Crypt K X \\<in> 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 \\<in> 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\\<in> G ==> parts(insert X H) \\<subseteq> 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} \\<subseteq> synth (analz H) Un parts H *)
-Goal "X\\<in> synth (analz H) ==> \
-\ parts (insert X H) \\<subseteq> 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\\<in> synth (analz G) ==> \
-\ analz (insert X H) \\<subseteq> synth (analz G) Un analz (G Un H)";
-by (rtac subsetI 1);
-by (subgoal_tac "x \\<in> 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\\<in> analz H & X\\<in> parts H) = (X\\<in> analz H)";
-by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
-val analz_conj_parts = result();
-
-Goal "(X\\<in> analz H | X\\<in> parts H) = (X\\<in> 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|} \\<in> synth (analz H)) = \
-\ (X \\<in> synth (analz H) & Y \\<in> synth (analz H))";
-by (Blast_tac 1);
-qed "MPair_synth_analz";
-
-AddIffs [MPair_synth_analz];
-
-Goal "[| Key K \\<in> analz H; Key (invKey K) \\<in> analz H |] \
-\ ==> (Crypt K X \\<in> synth (analz H)) = (X \\<in> synth (analz H))";
-by (Blast_tac 1);
-qed "Crypt_synth_analz";
-
-
-Goal "X \\<notin> synth (analz H) \
-\ ==> (Hash{|X,Y|} \\<in> synth (analz H)) = (Hash{|X,Y|} \\<in> 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 \\<notin> synth (analz H) \
-\ ==> (Hash[X] Y \\<in> synth (analz H)) = \
-\ (Hash {|X, Y|} \\<in> analz H & Y \\<in> 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 \\<notin> Key`shrK`bad and cannot be proved by rewriting
- alone.*)
-fun prove_simple_subgoals_tac i =
- force_tac (claset(), simpset() addsimps [@{thm 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 \\<in> parts(insert X H) and Y \\<in> 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];
--- a/doc-src/TutorialI/Protocol/Public_lemmas.ML Mon Jul 23 14:06:14 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,170 +0,0 @@
-(* Title: HOL/Auth/Public_lemmas
- ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
- Copyright 1996 University of Cambridge
-
-Theory of Public Keys (common to all symmetric-key protocols)
-
-Server keys; initial states of agents; new nonces and keys; function "sees"
-*)
-
-val inj_pubK = thm "inj_pubK";
-val priK_neq_pubK = thm "priK_neq_pubK";
-
-(*** Basic properties of pubK & priK ***)
-
-AddIffs [inj_pubK RS @{thm inj_eq}];
-
-Goal "(priK A = priK B) = (A=B)";
-by Safe_tac;
-by (dres_inst_tac [("f","invKey")] arg_cong 1);
-by (Full_simp_tac 1);
-qed "priK_inj_eq";
-
-AddIffs [priK_inj_eq];
-AddIffs [priK_neq_pubK, priK_neq_pubK RS not_sym];
-
-Goalw [symKeys_def] "pubK A \\<notin> symKeys";
-by (Simp_tac 1);
-qed "not_symKeys_pubK";
-
-Goalw [symKeys_def] "priK A \\<notin> symKeys";
-by (Simp_tac 1);
-qed "not_symKeys_priK";
-
-AddIffs [not_symKeys_pubK, not_symKeys_priK];
-
-Goal "(K \\<in> symKeys) \\<noteq> (K' \\<in> symKeys) ==> K \\<noteq> K'";
-by (Blast_tac 1);
-qed "symKeys_neq_imp_neq";
-
-Goal "[| Crypt K X \\<in> analz H; K \\<in> symKeys; Key K \\<in> analz H |] \
-\ ==> X \\<in> analz H";
-by (auto_tac(claset(), simpset() addsimps [symKeys_def]));
-qed "analz_symKeys_Decrypt";
-
-
-(** "Image" equations that hold for injective functions **)
-
-Goal "(invKey x : invKey`A) = (x:A)";
-by Auto_tac;
-qed "invKey_image_eq";
-
-(*holds because invKey is injective*)
-Goal "(pubK x : pubK`A) = (x:A)";
-by Auto_tac;
-qed "pubK_image_eq";
-
-Goal "(priK x ~: pubK`A)";
-by Auto_tac;
-qed "priK_pubK_image_eq";
-Addsimps [invKey_image_eq, pubK_image_eq, priK_pubK_image_eq];
-
-
-(** 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 (claset() addIs [range_eqI], simpset()));
-qed "keysFor_parts_initState";
-Addsimps [keysFor_parts_initState];
-
-
-(*** Function "spies" ***)
-
-(*Agents see their own private keys!*)
-Goal "Key (priK A) : initState A";
-by (induct_tac "A" 1);
-by Auto_tac;
-qed "priK_in_initState";
-AddIffs [priK_in_initState];
-
-(*All public keys are visible*)
-Goal "Key (pubK A) : spies evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [imageI, knows_Cons]
- addsplits [expand_event_case])));
-qed_spec_mp "spies_pubK";
-
-(*Spy sees private keys of bad agents!*)
-Goal "A: bad ==> Key (priK A) : spies evs";
-by (induct_tac "evs" 1);
-by (ALLGOALS (asm_simp_tac
- (simpset() addsimps [imageI, knows_Cons]
- addsplits [expand_event_case])));
-qed "Spy_spies_bad";
-
-AddIffs [spies_pubK, spies_pubK RS analz.Inj];
-AddSIs [Spy_spies_bad];
-
-
-(*** Fresh nonces ***)
-
-Goal "Nonce N ~: parts (initState B)";
-by (induct_tac "B" 1);
-by Auto_tac;
-qed "Nonce_notin_initState";
-AddIffs [Nonce_notin_initState];
-
-Goal "Nonce N ~: 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 ~: 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 [@{thm add_leE}])));
-val lemma = result();
-
-Goal "EX N. Nonce N ~: used evs";
-by (rtac (lemma RS exE) 1);
-by (Blast_tac 1);
-qed "Nonce_supply1";
-
-Goal "Nonce (@ N. Nonce N ~: used evs) ~: used evs";
-by (rtac (lemma RS exE) 1);
-by (rtac someI 1);
-by (Fast_tac 1);
-qed "Nonce_supply";
-
-(*Tactic for possibility theorems*)
-fun possibility_tac st = st |>
- REPEAT (*omit used_Says so that Nonces start from different traces!*)
- (ALLGOALS (simp_tac (simpset() delsimps [used_Says]))
- THEN
- REPEAT_FIRST (eq_assume_tac ORELSE'
- resolve_tac [refl, conjI, Nonce_supply]));
-
-
-(*** Specialized rewriting for the analz_image_... theorems ***)
-
-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. Based on analz_image_freshK_ss, but simpler.*)
-val analz_image_keys_ss =
- simpset() delsimps [image_insert, image_Un]
- delsimps [thm "imp_disjL"] (*reduces blow-up*)
- addsimps [image_insert RS sym, image_Un RS sym,
- rangeI,
- insert_Key_singleton,
- insert_Key_image, thm "Un_assoc" RS sym];
-