--- a/src/HOL/Auth/OtwayRees_Bad.ML Thu Sep 26 12:47:47 1996 +0200
+++ b/src/HOL/Auth/OtwayRees_Bad.ML Thu Sep 26 12:50:48 1996 +0200
@@ -10,7 +10,7 @@
Proc. Royal Soc. 426 (1989)
This file illustrates the consequences of such errors. We can still prove
-impressive-looking properties such as Enemy_not_see_encrypted_key, yet the
+impressive-looking properties such as Spy_not_see_encrypted_key, yet the
protocol is open to a middleperson attack. Attempting to prove some key lemmas
indicates the possibility of this attack.
*)
@@ -28,7 +28,7 @@
\ Says B A {|Nonce NA, Crypt {|Nonce NA, Key K|} (shrK A)|} \
\ : set_of_list evs";
by (REPEAT (resolve_tac [exI,bexI] 1));
-br (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2;
+by (rtac (otway.Nil RS otway.OR1 RS otway.OR2 RS otway.OR3 RS otway.OR4) 2);
by (ALLGOALS (simp_tac (!simpset setsolver safe_solver)));
by (REPEAT_FIRST (resolve_tac [refl, conjI]));
by (ALLGOALS (fast_tac (!claset addss (!simpset setsolver safe_solver))));
@@ -37,19 +37,19 @@
(**** Inductive proofs about otway ****)
-(*The Enemy can see more than anybody else, except for their initial state*)
+(*The Spy can see more than anybody else, except for their initial state*)
goal thy
"!!evs. evs : otway ==> \
-\ sees A evs <= initState A Un sees Enemy evs";
-be otway.induct 1;
+\ sees A evs <= initState A Un sees Spy evs";
+by (etac otway.induct 1);
by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD]
- addss (!simpset))));
-qed "sees_agent_subset_sees_Enemy";
+ addss (!simpset))));
+qed "sees_agent_subset_sees_Spy";
(*Nobody sends themselves messages*)
goal thy "!!evs. evs : otway ==> ALL A X. Says A A X ~: set_of_list evs";
-be otway.induct 1;
+by (etac otway.induct 1);
by (Auto_tac());
qed_spec_mp "not_Says_to_self";
Addsimps [not_Says_to_self];
@@ -59,69 +59,69 @@
(** For reasoning about the encrypted portion of messages **)
goal thy "!!evs. Says A' B {|N, Agent A, Agent B, X|} : set_of_list evs ==> \
-\ X : analz (sees Enemy evs)";
-by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1);
-qed "OR2_analz_sees_Enemy";
+\ X : analz (sees Spy evs)";
+by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
+qed "OR2_analz_sees_Spy";
goal thy "!!evs. Says S B {|N, X, X'|} : set_of_list evs ==> \
-\ X : analz (sees Enemy evs)";
-by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1);
-qed "OR4_analz_sees_Enemy";
+\ X : analz (sees Spy evs)";
+by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
+qed "OR4_analz_sees_Spy";
goal thy "!!evs. Says B' A {|N, Crypt {|N,K|} K'|} : set_of_list evs ==> \
-\ K : parts (sees Enemy evs)";
+\ K : parts (sees Spy evs)";
by (fast_tac (!claset addSEs partsEs
- addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1);
-qed "Reveal_parts_sees_Enemy";
+ addSDs [Says_imp_sees_Spy RS parts.Inj]) 1);
+qed "Reveal_parts_sees_Spy";
(*OR2_analz... and OR4_analz... let us treat those cases using the same
argument as for the Fake case. This is possible for most, but not all,
proofs: Fake does not invent new nonces (as in OR2), and of course Fake
- messages originate from the Enemy. *)
+ messages originate from the Spy. *)
val parts_Fake_tac =
- dtac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN
- dtac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6 THEN
- dtac Reveal_parts_sees_Enemy 7;
+ dtac (OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts)) 4 THEN
+ dtac (OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)) 6 THEN
+ dtac Reveal_parts_sees_Spy 7;
-(** Theorems of the form X ~: parts (sees Enemy evs) imply that NOBODY
+(** Theorems of the form X ~: parts (sees Spy evs) imply that NOBODY
sends messages containing X! **)
-(*Enemy never sees another agent's shared key! (unless it is leaked at start)*)
+(*Spy never sees another agent's shared key! (unless it is leaked at start)*)
goal thy
"!!evs. [| evs : otway; A ~: bad |] \
-\ ==> Key (shrK A) ~: parts (sees Enemy evs)";
-be otway.induct 1;
+\ ==> Key (shrK A) ~: parts (sees Spy evs)";
+by (etac otway.induct 1);
by parts_Fake_tac;
by (Auto_tac());
(*Deals with Fake message*)
by (best_tac (!claset addDs [impOfSubs analz_subset_parts,
- impOfSubs Fake_parts_insert]) 1);
-qed "Enemy_not_see_shrK";
+ impOfSubs Fake_parts_insert]) 1);
+qed "Spy_not_see_shrK";
-bind_thm ("Enemy_not_analz_shrK",
- [analz_subset_parts, Enemy_not_see_shrK] MRS contra_subsetD);
+bind_thm ("Spy_not_analz_shrK",
+ [analz_subset_parts, Spy_not_see_shrK] MRS contra_subsetD);
-Addsimps [Enemy_not_see_shrK, Enemy_not_analz_shrK];
+Addsimps [Spy_not_see_shrK, Spy_not_analz_shrK];
(*We go to some trouble to preserve R in the 3rd and 4th subgoals
As usual fast_tac cannot be used because it uses the equalities too soon*)
val major::prems =
-goal thy "[| Key (shrK A) : parts (sees Enemy evs); \
+goal thy "[| Key (shrK A) : parts (sees Spy evs); \
\ evs : otway; \
\ A:bad ==> R \
\ |] ==> R";
-br ccontr 1;
-br ([major, Enemy_not_see_shrK] MRS rev_notE) 1;
+by (rtac ccontr 1);
+by (rtac ([major, Spy_not_see_shrK] MRS rev_notE) 1);
by (swap_res_tac prems 2);
by (ALLGOALS (fast_tac (!claset addIs prems)));
-qed "Enemy_see_shrK_E";
+qed "Spy_see_shrK_E";
-bind_thm ("Enemy_analz_shrK_E",
- analz_subset_parts RS subsetD RS Enemy_see_shrK_E);
+bind_thm ("Spy_analz_shrK_E",
+ analz_subset_parts RS subsetD RS Spy_see_shrK_E);
-AddSEs [Enemy_see_shrK_E, Enemy_analz_shrK_E];
+AddSEs [Spy_see_shrK_E, Spy_analz_shrK_E];
(*** Future keys can't be seen or used! ***)
@@ -134,14 +134,14 @@
goal thy "!!evs. evs : otway ==> \
\ length evs <= length evs' --> \
\ Key (newK evs') ~: (UN C. parts (sees C evs))";
-be otway.induct 1;
+by (etac otway.induct 1);
by parts_Fake_tac;
(*auto_tac does not work here, as it performs safe_tac first*)
by (ALLGOALS Asm_simp_tac);
by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts,
- impOfSubs parts_insert_subset_Un,
- Suc_leD]
- addss (!simpset))));
+ impOfSubs parts_insert_subset_Un,
+ Suc_leD]
+ addss (!simpset))));
val lemma = result();
(*Variant needed for the main theorem below*)
@@ -158,9 +158,9 @@
\ Key (newK evt) : parts {X}; \
\ evs : otway \
\ |] ==> length evt < length evs";
-br ccontr 1;
-by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy]
- addIs [impOfSubs parts_mono, leI]) 1);
+by (rtac ccontr 1);
+by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy]
+ addIs [impOfSubs parts_mono, leI]) 1);
qed "Says_imp_old_keys";
@@ -169,17 +169,17 @@
goal thy "!!evs. evs : otway ==> \
\ length evs <= length evs' --> \
\ Nonce (newN evs') ~: (UN C. parts (sees C evs))";
-be otway.induct 1;
+by (etac otway.induct 1);
(*auto_tac does not work here, as it performs safe_tac first*)
by (ALLGOALS (asm_simp_tac (!simpset addsimps [de_Morgan_disj]
addcongs [conj_cong])));
by (REPEAT_FIRST (fast_tac (!claset (*60 seconds???*)
- addSEs [MPair_parts]
- addDs [Says_imp_sees_Enemy RS parts.Inj,
- impOfSubs analz_subset_parts,
- impOfSubs parts_insert_subset_Un,
- Suc_leD]
- addss (!simpset))));
+ addSEs [MPair_parts]
+ addDs [Says_imp_sees_Spy RS parts.Inj,
+ impOfSubs analz_subset_parts,
+ impOfSubs parts_insert_subset_Un,
+ Suc_leD]
+ addss (!simpset))));
val lemma = result();
(*Variant needed for the main theorem below*)
@@ -196,9 +196,9 @@
\ Nonce (newN evt) : parts {X}; \
\ evs : otway \
\ |] ==> length evt < length evs";
-br ccontr 1;
-by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Enemy]
- addIs [impOfSubs parts_mono, leI]) 1);
+by (rtac ccontr 1);
+by (fast_tac (!claset addSDs [new_nonces_not_seen, Says_imp_sees_Spy]
+ addIs [impOfSubs parts_mono, leI]) 1);
qed "Says_imp_old_nonces";
@@ -207,7 +207,7 @@
goal thy "!!evs. evs : otway ==> \
\ length evs <= length evs' --> \
\ newK evs' ~: keysFor (UN C. parts (sees C evs))";
-be otway.induct 1;
+by (etac otway.induct 1);
by parts_Fake_tac;
by (ALLGOALS Asm_simp_tac);
(*OR1 and OR3*)
@@ -217,15 +217,15 @@
(map
(best_tac
(!claset addDs [impOfSubs (analz_subset_parts RS keysFor_mono),
- impOfSubs (parts_insert_subset_Un RS keysFor_mono),
- Suc_leD]
- addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)]
- addss (!simpset)))
+ impOfSubs (parts_insert_subset_Un RS keysFor_mono),
+ Suc_leD]
+ addEs [new_keys_not_seen RS not_parts_not_analz RSN(2,rev_notE)]
+ addss (!simpset)))
[3,2,1]));
(*Reveal: dummy message*)
by (best_tac (!claset addEs [new_keys_not_seen RSN(2,rev_notE)]
- addIs [less_SucI, impOfSubs keysFor_mono]
- addss (!simpset addsimps [le_def])) 1);
+ addIs [less_SucI, impOfSubs keysFor_mono]
+ addss (!simpset addsimps [le_def])) 1);
val lemma = result();
goal thy
@@ -235,8 +235,8 @@
qed "new_keys_not_used";
bind_thm ("new_keys_not_analzd",
- [analz_subset_parts RS keysFor_mono,
- new_keys_not_used] MRS contra_subsetD);
+ [analz_subset_parts RS keysFor_mono,
+ new_keys_not_used] MRS contra_subsetD);
Addsimps [new_keys_not_used, new_keys_not_analzd];
@@ -247,8 +247,8 @@
(****
The following is to prove theorems of the form
- Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) ==>
- Key K : analz (sees Enemy evs)
+ Key K : analz (insert (Key (newK evt)) (sees Spy evs)) ==>
+ Key K : analz (sees Spy evs)
A more general formula must be proved inductively.
@@ -260,14 +260,14 @@
We require that agents should behave like this subsequently also.*)
goal thy
"!!evs. evs : otway ==> \
-\ (Crypt X (newK evt)) : parts (sees Enemy evs) & \
-\ Key K : parts {X} --> Key K : parts (sees Enemy evs)";
-be otway.induct 1;
+\ (Crypt X (newK evt)) : parts (sees Spy evs) & \
+\ Key K : parts {X} --> Key K : parts (sees Spy evs)";
+by (etac otway.induct 1);
by parts_Fake_tac;
by (ALLGOALS (asm_simp_tac (!simpset addsimps pushes)));
(*Deals with Faked messages*)
by (best_tac (!claset addSEs partsEs
- addDs [impOfSubs analz_subset_parts,
+ addDs [impOfSubs analz_subset_parts,
impOfSubs parts_insert_subset_Un]
addss (!simpset)) 2);
(*Base case and Reveal*)
@@ -296,10 +296,10 @@
(*This lets us avoid analyzing the new message -- unless we have to!*)
(*NEEDED??*)
-goal thy "synth (analz (sees Enemy evs)) <= \
-\ synth (analz (sees Enemy (Says A B X # evs)))";
+goal thy "synth (analz (sees Spy evs)) <= \
+\ synth (analz (sees Spy (Says A B X # evs)))";
by (Simp_tac 1);
-br (subset_insertI RS analz_mono RS synth_mono) 1;
+by (rtac (subset_insertI RS analz_mono RS synth_mono) 1);
qed "synth_analz_thin";
AddIs [impOfSubs synth_analz_thin];
@@ -314,15 +314,15 @@
on NS_Shared/Says_S_message_form) *)
goal thy
"!!evs. evs: otway ==> \
-\ Crypt {|N, Key K|} (shrK A) : parts (sees Enemy evs) & \
+\ Crypt {|N, Key K|} (shrK A) : parts (sees Spy evs) & \
\ A ~: bad --> \
\ (EX evt:otway. K = newK evt)";
-be otway.induct 1;
+by (etac otway.induct 1);
by parts_Fake_tac;
by (Auto_tac());
(*Deals with Fake message*)
by (best_tac (!claset addDs [impOfSubs analz_subset_parts,
- impOfSubs Fake_parts_insert]) 1);
+ impOfSubs Fake_parts_insert]) 1);
val lemma = result() RS mp;
@@ -331,13 +331,13 @@
goal thy
"!!evs. [| Says B' A {|N, Crypt {|N, Key K|} (shrK A)|} : set_of_list evs; \
\ evs : otway |] \
-\ ==> (EX evt:otway. K = newK evt) | Key K : analz (sees Enemy evs)";
+\ ==> (EX evt:otway. K = newK evt) | Key K : analz (sees Spy evs)";
by (excluded_middle_tac "A : bad" 1);
-by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]
- addss (!simpset)) 2);
+by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]
+ addss (!simpset)) 2);
by (forward_tac [lemma] 1);
by (fast_tac (!claset addEs partsEs
- addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1);
+ addSDs [Says_imp_sees_Spy RS parts.Inj]) 1);
by (Fast_tac 1);
qed "Reveal_message_form";
@@ -354,22 +354,22 @@
(*The equality makes the induction hypothesis easier to apply*)
goal thy
"!!evs. evs : otway ==> \
-\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees Enemy evs))) = \
-\ (K : newK``E | Key K : analz (sees Enemy evs))";
-be otway.induct 1;
-bd OR2_analz_sees_Enemy 4;
-bd OR4_analz_sees_Enemy 6;
-bd Reveal_message_form 7;
+\ ALL K E. (Key K : analz (Key``(newK``E) Un (sees Spy evs))) = \
+\ (K : newK``E | Key K : analz (sees Spy evs))";
+by (etac otway.induct 1);
+by (dtac OR2_analz_sees_Spy 4);
+by (dtac OR4_analz_sees_Spy 6);
+by (dtac Reveal_message_form 7);
by (REPEAT_FIRST (ares_tac [allI, lemma]));
by (REPEAT ((eresolve_tac [bexE, disjE] ORELSE' hyp_subst_tac) 7));
by (ALLGOALS (*Takes 28 secs*)
(asm_simp_tac
(!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK]
- @ pushes)
+ @ pushes)
setloop split_tac [expand_if])));
(** LEVEL 7 **)
(*Reveal case 2, OR4, OR2, Fake*)
-by (EVERY (map enemy_analz_tac [7,5,3,2]));
+by (EVERY (map spy_analz_tac [7,5,3,2]));
(*Reveal case 1, OR3, Base*)
by (Auto_tac());
qed_spec_mp "analz_image_newK";
@@ -377,10 +377,10 @@
goal thy
"!!evs. evs : otway ==> \
-\ Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) = \
-\ (K = newK evt | Key K : analz (sees Enemy evs))";
+\ Key K : analz (insert (Key (newK evt)) (sees Spy evs)) = \
+\ (K = newK evt | Key K : analz (sees Spy evs))";
by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK,
- insert_Key_singleton]) 1);
+ insert_Key_singleton]) 1);
by (Fast_tac 1);
qed "analz_insert_Key_newK";
@@ -393,8 +393,8 @@
\ evs : otway |] \
\ ==> (EX evt:otway. K = Key(newK evt)) & \
\ (EX i. NA = Nonce i)";
-be rev_mp 1;
-be otway.induct 1;
+by (etac rev_mp 1);
+by (etac otway.induct 1);
by (ALLGOALS (fast_tac (!claset addIs [less_SucI] addss (!simpset))));
qed "Says_Server_message_form";
@@ -402,34 +402,34 @@
(*Crucial security property, but not itself enough to guarantee correctness!
The need for quantification over N, C seems to indicate the problem.
Omitting the Reveal message from the description deprives us of even
- this clue. *)
+ this clue. *)
goal thy
"!!evs. [| A ~: bad; B ~: bad; evs : otway; evt : otway |] \
\ ==> Says Server B \
\ {|Nonce NA, Crypt {|Nonce NA, Key(newK evt)|} (shrK A), \
\ Crypt {|NB, Key(newK evt)|} (shrK B)|} : set_of_list evs --> \
-\ (ALL N C. Says C Enemy {|N, Key(newK evt)|} ~: set_of_list evs) --> \
-\ Key(newK evt) ~: analz (sees Enemy evs)";
-be otway.induct 1;
-bd OR2_analz_sees_Enemy 4;
-bd OR4_analz_sees_Enemy 6;
-bd Reveal_message_form 7;
+\ (ALL N C. Says C Spy {|N, Key(newK evt)|} ~: set_of_list evs) --> \
+\ Key(newK evt) ~: analz (sees Spy evs)";
+by (etac otway.induct 1);
+by (dtac OR2_analz_sees_Spy 4);
+by (dtac OR4_analz_sees_Spy 6);
+by (dtac Reveal_message_form 7);
by (REPEAT_FIRST (eresolve_tac [asm_rl, bexE, disjE] ORELSE' hyp_subst_tac));
by (ALLGOALS
(asm_full_simp_tac
(!simpset addsimps ([analz_subset_parts RS contra_subsetD,
- analz_insert_Key_newK] @ pushes)
+ analz_insert_Key_newK] @ pushes)
setloop split_tac [expand_if])));
(** LEVEL 6 **)
(*Reveal case 1*)
by (Fast_tac 5);
(*OR3*)
by (fast_tac (!claset addSIs [parts_insertI]
- addEs [Says_imp_old_keys RS less_irrefl]
- addss (!simpset)) 3);
+ addEs [Says_imp_old_keys RS less_irrefl]
+ addss (!simpset)) 3);
(*Reveal case 2, OR4, OR2, Fake*)
-br conjI 3;
-by (REPEAT (enemy_analz_tac 1));
+by (rtac conjI 3);
+by (REPEAT (spy_analz_tac 1));
val lemma = result() RS mp RS mp RSN(2,rev_notE);
@@ -439,12 +439,12 @@
"!!evs. [| Says Server B \
\ {|NA, Crypt {|NA, K|} (shrK A), \
\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs; \
-\ (ALL N C. Says C Enemy {|N, K|} ~: set_of_list evs); \
+\ (ALL N C. Says C Spy {|N, K|} ~: set_of_list evs); \
\ A ~: bad; B ~: bad; evs : otway |] \
-\ ==> K ~: analz (sees Enemy evs)";
+\ ==> K ~: analz (sees Spy evs)";
by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
by (fast_tac (!claset addSEs [lemma]) 1);
-qed "Enemy_not_see_encrypted_key";
+qed "Spy_not_see_encrypted_key";
(*** Attempting to prove stronger properties ***)
@@ -460,7 +460,7 @@
\ {|NA, Crypt {|NA, K|} (shrK A), \
\ Crypt {|NB, K|} (shrK B)|} : set_of_list evs --> \
\ A=A' & B=B' & NA=NA' & NB=NB'";
-be otway.induct 1;
+by (etac otway.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset addsimps [all_conj_distrib])));
by (Step_tac 1);
(*Remaining cases: OR3 and OR4*)
@@ -471,8 +471,8 @@
by (REPEAT (ares_tac [refl,exI,impI,conjI] 1));
(*...we assume X is a very new message, and handle this case by contradiction*)
by (fast_tac (!claset addEs [Says_imp_old_keys RS less_irrefl]
- delrules [conjI] (*prevent split-up into 4 subgoals*)
- addss (!simpset addsimps [parts_insertI])) 1);
+ delrules [conjI] (*prevent split-up into 4 subgoals*)
+ addss (!simpset addsimps [parts_insertI])) 1);
val lemma = result();
@@ -487,7 +487,7 @@
\ : set_of_list evs; \
\ evs : otway |] \
\ ==> A=A' & B=B' & NA=NA' & NB=NB'";
-bd lemma 1;
+by (dtac lemma 1);
by (REPEAT (etac exE 1));
(*Duplicate the assumption*)
by (forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl 1);
@@ -499,16 +499,16 @@
goal thy
"!!evs. [| A ~: bad; A ~= B; evs : otway |] \
\ ==> Crypt {|NA, Agent A, Agent B|} (shrK A) \
-\ : parts (sees Enemy evs) --> \
+\ : parts (sees Spy evs) --> \
\ Says A B {|NA, Agent A, Agent B, \
\ Crypt {|NA, Agent A, Agent B|} (shrK A)|} \
\ : set_of_list evs";
-be otway.induct 1;
+by (etac otway.induct 1);
by parts_Fake_tac;
by (ALLGOALS Asm_simp_tac);
(*Fake*)
by (best_tac (!claset addSDs [impOfSubs analz_subset_parts,
- impOfSubs Fake_parts_insert]) 2);
+ impOfSubs Fake_parts_insert]) 2);
by (Auto_tac());
qed_spec_mp "Crypt_imp_OR1";
@@ -517,7 +517,7 @@
substituting some other nonce NA' for NB.*)
goal thy
"!!evs. [| A ~: bad; evs : otway |] \
-\ ==> Crypt {|Nonce NA, Key K|} (shrK A) : parts (sees Enemy evs) --> \
+\ ==> Crypt {|Nonce NA, Key K|} (shrK A) : parts (sees Spy evs) --> \
\ Says A B {|Nonce NA, Agent A, Agent B, \
\ Crypt {|Nonce NA, Agent A, Agent B|} (shrK A)|} \
\ : set_of_list evs --> \
@@ -526,23 +526,23 @@
\ Crypt {|Nonce NA, Key K|} (shrK A), \
\ Crypt {|Nonce NB, Key K|} (shrK B)|} \
\ : set_of_list evs)";
-be otway.induct 1;
+by (etac otway.induct 1);
fun ftac rl = forward_tac [rl];
by (
- ftac (OR2_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 4 THEN
- ftac (OR4_analz_sees_Enemy RS (impOfSubs analz_subset_parts)) 6 THEN
- ftac Reveal_parts_sees_Enemy 7);
+ ftac (OR2_analz_sees_Spy RS (impOfSubs analz_subset_parts)) 4 THEN
+ ftac (OR4_analz_sees_Spy RS (impOfSubs analz_subset_parts)) 6 THEN
+ ftac Reveal_parts_sees_Spy 7);
(* by parts_Fake_tac; ?*)
by (ALLGOALS Asm_simp_tac);
(*Fake*)
by (best_tac (!claset addSDs [impOfSubs analz_subset_parts,
- impOfSubs Fake_parts_insert]) 1);
+ impOfSubs Fake_parts_insert]) 1);
(*OR1: it cannot be a new Nonce, contradiction.*)
by (fast_tac (!claset addSIs [parts_insertI]
- addSEs partsEs
- addEs [Says_imp_old_nonces RS less_irrefl]
- addss (!simpset)) 1);
+ addSEs partsEs
+ addEs [Says_imp_old_nonces RS less_irrefl]
+ addss (!simpset)) 1);
(*OR3 and OR4*) (** LEVEL 5 **)
(*OR4*)
by (REPEAT (Safe_step_tac 2));
@@ -550,7 +550,7 @@
by (best_tac (!claset addSDs [parts_cut]) 3);
by (forward_tac [Crypt_imp_OR1] 2);
by (fast_tac (!claset addEs partsEs
- addSDs [Says_imp_sees_Enemy RS parts.Inj]) 4);
+ addSDs [Says_imp_sees_Spy RS parts.Inj]) 4);
by (REPEAT (Fast_tac 2));
(*OR3*) (** LEVEL 11 **)
by (ALLGOALS (asm_simp_tac (!simpset addsimps [ex_disj_distrib])));
@@ -577,14 +577,14 @@
\ Crypt {|Nonce NA, Key K|} (shrK A), \
\ Crypt {|Nonce NB, Key K|} (shrK B)|} \
\ : set_of_list evs)";
-be otway.induct 1;
+by (etac otway.induct 1);
by (ALLGOALS (asm_simp_tac (!simpset addcongs [conj_cong])));
(*OR2*)
by (Fast_tac 3);
(*OR1: it cannot be a new Nonce, contradiction.*)
by (fast_tac (!claset addSIs [parts_insertI]
- addEs [Says_imp_old_nonces RS less_irrefl]
- addss (!simpset)) 2);
+ addEs [Says_imp_old_nonces RS less_irrefl]
+ addss (!simpset)) 2);
by (ALLGOALS
(asm_simp_tac (!simpset addsimps [all_conj_distrib, de_Morgan_disj, de_Morgan_conj])));
(*Fake, OR4*) (** LEVEL 5 **)
@@ -593,7 +593,7 @@
by (fast_tac (!claset addSDs [spec]) 4);
by (forward_tac [Crypt_imp_OR1] 3);
by (fast_tac (!claset addEs partsEs
- addSDs [Says_imp_sees_Enemy RS parts.Inj]) 5);
+ addSDs [Says_imp_sees_Spy RS parts.Inj]) 5);
by (REPEAT (Fast_tac 3));
(** LEVEL 11 **)
(*Fake (??) and OR4*)
@@ -607,12 +607,12 @@
(** First, two lemmas for the Fake, OR2 and OR4 cases **)
goal thy
- "!!evs. [| X : synth (analz (sees Enemy evs)); \
+ "!!evs. [| X : synth (analz (sees Spy evs)); \
\ Crypt X' (shrK C) : parts{X}; \
\ C ~: bad; evs : otway |] \
-\ ==> Crypt X' (shrK C) : parts (sees Enemy evs)";
+\ ==> Crypt X' (shrK C) : parts (sees Spy evs)";
by (best_tac (!claset addSEs [impOfSubs analz_subset_parts]
- addDs [impOfSubs parts_insert_subset_Un]
+ addDs [impOfSubs parts_insert_subset_Un]
addss (!simpset)) 1);
qed "Crypt_Fake_parts";
@@ -620,12 +620,12 @@
"!!evs. [| Crypt X' K : parts (sees A evs); evs : otway |] \
\ ==> EX S S' Y. Says S S' Y : set_of_list evs & \
\ Crypt X' K : parts {Y}";
-bd parts_singleton 1;
+by (dtac parts_singleton 1);
by (fast_tac (!claset addSDs [seesD] addss (!simpset)) 1);
qed "Crypt_parts_singleton";
(*The Key K uniquely identifies a pair of senders in the message encrypted by
- C, but if C=Enemy then he could send all sorts of nonsense.*)
+ C, but if C=Spy then he could send all sorts of nonsense.*)
goal thy
"!!evs. evs : otway ==> \
\ EX A B. ALL C. \
@@ -633,33 +633,33 @@
\ (ALL S S' X. Says S S' X : set_of_list evs --> \
\ (EX NA. Crypt {|NA, Key K|} (shrK C) : parts{X}) --> C=A | C=B)";
by (Simp_tac 1);
-be otway.induct 1;
-bd OR2_analz_sees_Enemy 4;
-bd OR4_analz_sees_Enemy 6;
+by (etac otway.induct 1);
+by (dtac OR2_analz_sees_Spy 4);
+by (dtac OR4_analz_sees_Spy 6);
by (ALLGOALS
(asm_simp_tac (!simpset addsimps [all_conj_distrib, imp_conj_distrib])));
by (REPEAT_FIRST (etac exE));
(*OR4*)
by (ex_strip_tac 4);
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts,
- Crypt_parts_singleton]) 4);
+ Crypt_parts_singleton]) 4);
(*OR3: Case split propagates some context to other subgoal...*)
- (** LEVEL 8 **)
+ (** LEVEL 8 **)
by (excluded_middle_tac "K = newK evsa" 3);
by (Asm_simp_tac 3);
by (REPEAT (ares_tac [exI] 3));
(*...we prove this case by contradiction: the key is too new!*)
by (fast_tac (!claset addIs [parts_insertI]
- addSEs partsEs
- addEs [Says_imp_old_keys RS less_irrefl]
- addss (!simpset)) 3);
+ addSEs partsEs
+ addEs [Says_imp_old_keys RS less_irrefl]
+ addss (!simpset)) 3);
(*OR2*) (** LEVEL 12 **)
-(*enemy_analz_tac just does not work here: it is an entirely different proof!*)
+(*spy_analz_tac just does not work here: it is an entirely different proof!*)
by (ex_strip_tac 2);
by (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 2);
by (Simp_tac 2);
by (fast_tac (!claset addSDs [synth.Inj RS Crypt_Fake_parts,
- Crypt_parts_singleton]) 2);
+ Crypt_parts_singleton]) 2);
(*Fake*) (** LEVEL 16 **)
by (ex_strip_tac 1);
by (fast_tac (!claset addSDs [Crypt_Fake_parts, Crypt_parts_singleton]) 1);