author | paulson |
Fri, 17 Jan 1997 12:49:31 +0100 | |
changeset 2516 | 4d68fbe6378b |
parent 2451 | ce85a2aafc7a |
child 2637 | e9b203f854ae |
permissions | -rw-r--r-- |
2320 | 1 |
(* Title: HOL/Auth/Shared |
1934 | 2 |
ID: $Id$ |
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 |
Copyright 1996 University of Cambridge |
|
5 |
||
6 |
Theory of Shared Keys (common to all symmetric-key protocols) |
|
7 |
||
8 |
Server keys; initial states of agents; new nonces and keys; function "sees" |
|
2032 | 9 |
*) |
10 |
||
1934 | 11 |
|
12 |
open Shared; |
|
13 |
||
1964 | 14 |
(*Holds because Friend is injective: thus cannot prove for all f*) |
15 |
goal thy "(Friend x : Friend``A) = (x:A)"; |
|
16 |
by (Auto_tac()); |
|
17 |
qed "Friend_image_eq"; |
|
18 |
Addsimps [Friend_image_eq]; |
|
19 |
||
1934 | 20 |
Addsimps [Un_insert_left, Un_insert_right]; |
21 |
||
22 |
(*By default only o_apply is built-in. But in the presence of eta-expansion |
|
23 |
this means that some terms displayed as (f o g) will be rewritten, and others |
|
24 |
will not!*) |
|
25 |
Addsimps [o_def]; |
|
26 |
||
1943 | 27 |
(*** Basic properties of shrK and newK ***) |
1934 | 28 |
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(*Injectiveness and freshness of new keys and nonces*) |
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30 |
AddIffs [inj_shrK RS inj_eq, inj_newN RS inj_eq, |
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inj_newK RS inj_eq, inj_nPair RS inj_eq]; |
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32 |
|
1943 | 33 |
(* invKey (shrK A) = shrK A *) |
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34 |
bind_thm ("invKey_id", rewrite_rule [isSymKey_def] isSym_keys); |
1934 | 35 |
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36 |
Addsimps [invKey_id]; |
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38 |
goal thy "!!K. newK i = invKey K ==> newK i = K"; |
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39 |
by (rtac (invKey_eq RS iffD1) 1); |
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by (Full_simp_tac 1); |
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val newK_invKey = result(); |
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43 |
AddSDs [newK_invKey, sym RS newK_invKey]; |
1934 | 44 |
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45 |
Addsimps [newK_neq_shrK, newK_neq_shrK RS not_sym]; |
2320 | 46 |
|
1934 | 47 |
(** Rewrites should not refer to initState(Friend i) |
48 |
-- not in normal form! **) |
|
49 |
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50 |
goal thy "Key (newK i) ~: parts (initState lost B)"; |
2032 | 51 |
by (agent.induct_tac "B" 1); |
1934 | 52 |
by (Auto_tac ()); |
2032 | 53 |
qed "newK_notin_initState"; |
1934 | 54 |
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55 |
AddIffs [newK_notin_initState]; |
1934 | 56 |
|
2032 | 57 |
goalw thy [keysFor_def] "keysFor (parts (initState lost C)) = {}"; |
1934 | 58 |
by (agent.induct_tac "C" 1); |
1993 | 59 |
by (auto_tac (!claset addIs [range_eqI], !simpset)); |
1934 | 60 |
qed "keysFor_parts_initState"; |
61 |
Addsimps [keysFor_parts_initState]; |
|
62 |
||
63 |
goalw thy [keysFor_def] "keysFor (Key``E) = {}"; |
|
64 |
by (Auto_tac ()); |
|
65 |
qed "keysFor_image_Key"; |
|
66 |
Addsimps [keysFor_image_Key]; |
|
67 |
||
1943 | 68 |
goal thy "shrK A ~: newK``E"; |
1934 | 69 |
by (agent.induct_tac "A" 1); |
70 |
by (Auto_tac ()); |
|
1943 | 71 |
qed "shrK_notin_image_newK"; |
72 |
Addsimps [shrK_notin_image_newK]; |
|
1934 | 73 |
|
2032 | 74 |
|
75 |
(*** Function "sees" ***) |
|
76 |
||
77 |
goal thy |
|
78 |
"!!evs. lost' <= lost ==> sees lost' A evs <= sees lost A evs"; |
|
79 |
by (list.induct_tac "evs" 1); |
|
80 |
by (agent.induct_tac "A" 1); |
|
81 |
by (event.induct_tac "a" 2); |
|
82 |
by (Auto_tac ()); |
|
83 |
qed "sees_mono"; |
|
84 |
||
1964 | 85 |
(*Agents see their own shared keys!*) |
2032 | 86 |
goal thy "A ~= Spy --> Key (shrK A) : sees lost A evs"; |
1934 | 87 |
by (list.induct_tac "evs" 1); |
88 |
by (agent.induct_tac "A" 1); |
|
2032 | 89 |
by (Auto_tac ()); |
90 |
qed_spec_mp "sees_own_shrK"; |
|
1934 | 91 |
|
2032 | 92 |
(*Spy sees shared keys of lost agents!*) |
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93 |
goal thy "!!A. A: lost ==> Key (shrK A) : sees lost Spy evs"; |
2032 | 94 |
by (list.induct_tac "evs" 1); |
95 |
by (Auto_tac()); |
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96 |
qed "Spy_sees_lost"; |
1934 | 97 |
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98 |
AddSIs [sees_own_shrK, Spy_sees_lost]; |
2032 | 99 |
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100 |
(*Added for Yahalom/lost_tac*) |
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101 |
goal thy "!!A. [| Crypt (shrK A) X : analz (sees lost Spy evs); A: lost |] \ |
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102 |
\ ==> X : analz (sees lost Spy evs)"; |
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103 |
by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); |
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104 |
qed "Crypt_Spy_analz_lost"; |
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105 |
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2032 | 106 |
(** Specialized rewrite rules for (sees lost A (Says...#evs)) **) |
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107 |
|
2078 | 108 |
goal thy "sees lost B (Says A B X # evs) = insert X (sees lost B evs)"; |
1934 | 109 |
by (Simp_tac 1); |
110 |
qed "sees_own"; |
|
111 |
||
2078 | 112 |
goal thy "!!A. Server ~= B ==> \ |
113 |
\ sees lost Server (Says A B X # evs) = sees lost Server evs"; |
|
1934 | 114 |
by (Asm_simp_tac 1); |
115 |
qed "sees_Server"; |
|
116 |
||
2078 | 117 |
goal thy "!!A. Friend i ~= B ==> \ |
118 |
\ sees lost (Friend i) (Says A B X # evs) = sees lost (Friend i) evs"; |
|
1934 | 119 |
by (Asm_simp_tac 1); |
120 |
qed "sees_Friend"; |
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121 |
||
2032 | 122 |
goal thy "sees lost Spy (Says A B X # evs) = insert X (sees lost Spy evs)"; |
1934 | 123 |
by (Simp_tac 1); |
2032 | 124 |
qed "sees_Spy"; |
1934 | 125 |
|
2032 | 126 |
goal thy "sees lost A (Says A' B X # evs) <= insert X (sees lost A evs)"; |
1934 | 127 |
by (simp_tac (!simpset setloop split_tac [expand_if]) 1); |
128 |
by (Fast_tac 1); |
|
129 |
qed "sees_Says_subset_insert"; |
|
130 |
||
2032 | 131 |
goal thy "sees lost A evs <= sees lost A (Says A' B X # evs)"; |
1934 | 132 |
by (simp_tac (!simpset setloop split_tac [expand_if]) 1); |
133 |
by (Fast_tac 1); |
|
134 |
qed "sees_subset_sees_Says"; |
|
135 |
||
2132 | 136 |
(*Pushing Unions into parts. One of the agents A is B, and thus sees Y. |
2160 | 137 |
Once used to prove new_keys_not_seen; now obsolete.*) |
2032 | 138 |
goal thy "(UN A. parts (sees lost A (Says B C Y # evs))) = \ |
139 |
\ parts {Y} Un (UN A. parts (sees lost A evs))"; |
|
1934 | 140 |
by (Step_tac 1); |
2132 | 141 |
by (etac rev_mp 1); (*split_tac does not work on assumptions*) |
142 |
by (ALLGOALS |
|
143 |
(fast_tac (!claset addss (!simpset addsimps [parts_Un, sees_Cons] |
|
144 |
setloop split_tac [expand_if])))); |
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1934 | 145 |
qed "UN_parts_sees_Says"; |
146 |
||
2032 | 147 |
goal thy "Says A B X : set_of_list evs --> X : sees lost Spy evs"; |
1934 | 148 |
by (list.induct_tac "evs" 1); |
149 |
by (Auto_tac ()); |
|
2032 | 150 |
qed_spec_mp "Says_imp_sees_Spy"; |
1934 | 151 |
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152 |
(*Use with addSEs to derive contradictions from old Says events containing |
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153 |
items known to be fresh*) |
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154 |
val sees_Spy_partsEs = make_elim (Says_imp_sees_Spy RS parts.Inj):: partsEs; |
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2064 | 156 |
goal thy |
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157 |
"!!evs. [| Says A B (Crypt (shrK C) X) : set_of_list evs; C : lost |] \ |
2064 | 158 |
\ ==> X : analz (sees lost Spy evs)"; |
159 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj] |
|
160 |
addss (!simpset)) 1); |
|
161 |
qed "Says_Crypt_lost"; |
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162 |
||
2072 | 163 |
goal thy |
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164 |
"!!evs. [| Says A B (Crypt (shrK C) X) : set_of_list evs; \ |
2072 | 165 |
\ X ~: analz (sees lost Spy evs) |] \ |
166 |
\ ==> C ~: lost"; |
|
167 |
by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj] |
|
168 |
addss (!simpset)) 1); |
|
169 |
qed "Says_Crypt_not_lost"; |
|
170 |
||
2320 | 171 |
(*NEEDED??*) |
2032 | 172 |
goal thy "initState lost C <= Key `` range shrK"; |
1934 | 173 |
by (agent.induct_tac "C" 1); |
174 |
by (Auto_tac ()); |
|
175 |
qed "initState_subset"; |
|
176 |
||
2320 | 177 |
(*NEEDED??*) |
2032 | 178 |
goal thy "X : sees lost C evs --> \ |
2078 | 179 |
\ (EX A B. Says A B X : set_of_list evs) | (EX A. X = Key (shrK A))"; |
1934 | 180 |
by (list.induct_tac "evs" 1); |
181 |
by (ALLGOALS Asm_simp_tac); |
|
182 |
by (fast_tac (!claset addDs [impOfSubs initState_subset]) 1); |
|
2032 | 183 |
by (rtac conjI 1); |
1934 | 184 |
by (Fast_tac 2); |
185 |
by (event.induct_tac "a" 1); |
|
186 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [mem_if]))); |
|
187 |
by (ALLGOALS Fast_tac); |
|
188 |
qed_spec_mp "seesD"; |
|
189 |
||
2160 | 190 |
Addsimps [sees_own, sees_Server, sees_Friend, sees_Spy]; |
2032 | 191 |
Delsimps [sees_Cons]; (**** NOTE REMOVAL -- laws above are cleaner ****) |
1934 | 192 |
|
193 |
||
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194 |
(*** Fresh nonces ***) |
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195 |
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196 |
goal thy "Nonce N ~: parts (initState lost B)"; |
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by (agent.induct_tac "B" 1); |
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198 |
by (Auto_tac ()); |
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199 |
qed "Nonce_notin_initState"; |
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200 |
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201 |
AddIffs [Nonce_notin_initState]; |
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202 |
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203 |
goalw thy [used_def] "!!X. X: parts (sees lost B evs) ==> X: used evs"; |
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204 |
by (etac (impOfSubs parts_mono) 1); |
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by (Fast_tac 1); |
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206 |
qed "usedI"; |
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207 |
|
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208 |
AddIs [usedI]; |
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209 |
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210 |
(** Fresh keys never clash with long-term shared keys **) |
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211 |
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212 |
goal thy "Key (shrK A) : used evs"; |
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213 |
by (Best_tac 1); |
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214 |
qed "shrK_in_used"; |
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215 |
AddIffs [shrK_in_used]; |
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216 |
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217 |
(*Used in parts_Fake_tac and analz_Fake_tac to distinguish session keys |
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218 |
from long-term shared keys*) |
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219 |
goal thy "!!K. Key K ~: used evs ==> K ~: range shrK"; |
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220 |
by (Best_tac 1); |
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221 |
qed "Key_not_used"; |
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222 |
|
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223 |
(*A session key cannot clash with a long-term shared key*) |
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224 |
goal thy "!!K. K ~: range shrK ==> shrK B ~= K"; |
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225 |
by (Fast_tac 1); |
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226 |
qed "shrK_neq"; |
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227 |
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228 |
Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym]; |
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changeset
|
230 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
231 |
goal thy "used (Says A B X # evs) = parts{X} Un used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
232 |
by (simp_tac (!simpset addsimps [used_def, UN_parts_sees_Says]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
233 |
qed "used_Says"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
234 |
Addsimps [used_Says]; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
235 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
236 |
goal thy "used [] <= used l"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
237 |
by (list.induct_tac "l" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
238 |
by (event.induct_tac "a" 2); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
239 |
by (ALLGOALS Asm_simp_tac); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
240 |
by (Best_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
241 |
qed "used_nil_subset"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
242 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
243 |
goal thy "used l <= used (l@l')"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
244 |
by (list.induct_tac "l" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
245 |
by (simp_tac (!simpset addsimps [used_nil_subset]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
246 |
by (event.induct_tac "a" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
247 |
by (Asm_simp_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
248 |
by (Best_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
249 |
qed "used_subset_append"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
250 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
251 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
252 |
(*** Supply fresh nonces for possibility theorems. ***) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
253 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
254 |
goalw thy [used_def] "EX N. ALL n. N<=n --> Nonce n ~: used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
255 |
by (list.induct_tac "evs" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
256 |
by (res_inst_tac [("x","0")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
257 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
258 |
by (Full_simp_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
259 |
(*Inductive step*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
260 |
by (event.induct_tac "a" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
261 |
by (full_simp_tac (!simpset addsimps [UN_parts_sees_Says]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
262 |
by (msg.induct_tac "msg" 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
263 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [exI, parts_insert2]))); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
264 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
265 |
(*MPair case*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
266 |
by (res_inst_tac [("x","Na+Nb")] exI 2); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
267 |
by (fast_tac (!claset addSEs [add_leE]) 2); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
268 |
(*Nonce case*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
269 |
by (res_inst_tac [("x","N + Suc nat")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
270 |
by (fast_tac (!claset addSEs [add_leE] addafter (TRYALL trans_tac)) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
271 |
val lemma = result(); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
272 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
273 |
goal thy "EX N. Nonce N ~: used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
274 |
by (rtac (lemma RS exE) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
275 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
276 |
qed "Nonce_supply1"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
277 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
278 |
goal thy "EX N N'. Nonce N ~: used evs & Nonce N' ~: used evs' & N ~= N'"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
279 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
280 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
281 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
282 |
by (res_inst_tac [("x","N")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
283 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
284 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
285 |
le_add2, le_add1, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
286 |
le_eq_less_Suc RS sym]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
287 |
qed "Nonce_supply2"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
288 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
289 |
goal thy "EX N N' N''. Nonce N ~: used evs & Nonce N' ~: used evs' & \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
290 |
\ Nonce N'' ~: used evs'' & N ~= N' & N' ~= N'' & N ~= N''"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
291 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
292 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
293 |
by (cut_inst_tac [("evs","evs''")] lemma 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
294 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
295 |
by (res_inst_tac [("x","N")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
296 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
297 |
by (res_inst_tac [("x","Suc (Suc (N+Na+Nb))")] exI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
298 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
299 |
le_add2, le_add1, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
300 |
le_eq_less_Suc RS sym]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
301 |
by (rtac (less_trans RS less_not_refl2 RS not_sym) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
302 |
by (stac (le_eq_less_Suc RS sym) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
303 |
by (asm_simp_tac (!simpset addsimps [le_eq_less_Suc RS sym]) 2); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
304 |
by (REPEAT (rtac le_add1 1)); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
305 |
qed "Nonce_supply3"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
306 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
307 |
goal thy "Nonce (@ N. Nonce N ~: used evs) ~: used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
308 |
by (rtac (lemma RS exE) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
309 |
by (rtac selectI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
310 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
311 |
qed "Nonce_supply"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
312 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
313 |
(*** Supply fresh keys for possibility theorems. ***) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
314 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
315 |
goal thy "EX K. Key K ~: used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
316 |
by (rtac (Fin.emptyI RS Key_supply_ax RS exE) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
317 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
318 |
qed "Key_supply1"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
319 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
320 |
val Fin_UNIV_insertI = UNIV_I RS Fin.insertI; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
321 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
322 |
goal thy "EX K K'. Key K ~: used evs & Key K' ~: used evs' & K ~= K'"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
323 |
by (cut_inst_tac [("evs","evs")] (Fin.emptyI RS Key_supply_ax) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
324 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
325 |
by (cut_inst_tac [("evs","evs'")] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
326 |
(Fin.emptyI RS Fin_UNIV_insertI RS Key_supply_ax) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
327 |
by (Auto_tac()); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
328 |
qed "Key_supply2"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
329 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
330 |
goal thy "EX K K' K''. Key K ~: used evs & Key K' ~: used evs' & \ |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
331 |
\ Key K'' ~: used evs'' & K ~= K' & K' ~= K'' & K ~= K''"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
332 |
by (cut_inst_tac [("evs","evs")] (Fin.emptyI RS Key_supply_ax) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
333 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
334 |
by (cut_inst_tac [("evs","evs'")] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
335 |
(Fin.emptyI RS Fin_UNIV_insertI RS Key_supply_ax) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
336 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
337 |
by (cut_inst_tac [("evs","evs''")] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
338 |
(Fin.emptyI RS Fin_UNIV_insertI RS Fin_UNIV_insertI RS Key_supply_ax) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
339 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
340 |
by (Full_simp_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
341 |
by (fast_tac (!claset addSEs [allE]) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
342 |
qed "Key_supply3"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
343 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
344 |
goal thy "Key (@ K. Key K ~: used evs) ~: used evs"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
345 |
by (rtac (Fin.emptyI RS Key_supply_ax RS exE) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
346 |
by (rtac selectI 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
347 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
348 |
qed "Key_supply"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
349 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
350 |
(*** Tactics for possibility theorems ***) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
351 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
352 |
val possibility_tac = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
353 |
REPEAT (*omit used_Says so that Nonces, Keys start from different traces!*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
354 |
(ALLGOALS (simp_tac |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
355 |
(!simpset delsimps [used_Says] setsolver safe_solver)) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
356 |
THEN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
357 |
REPEAT_FIRST (eq_assume_tac ORELSE' |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
358 |
resolve_tac [refl, conjI, Nonce_supply, Key_supply])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
359 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
360 |
(*For harder protocols (such as Recur) where we have to set up some |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
361 |
nonces and keys initially*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
362 |
val basic_possibility_tac = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
363 |
REPEAT |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
364 |
(ALLGOALS (asm_simp_tac (!simpset setsolver safe_solver)) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
365 |
THEN |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
366 |
REPEAT_FIRST (resolve_tac [refl, conjI])); |
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Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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changeset
|
367 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
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diff
changeset
|
368 |
|
2049
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
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diff
changeset
|
369 |
(** Power of the Spy **) |
1934 | 370 |
|
2049
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
371 |
(*The Spy can see more than anybody else, except for their initial state*) |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
372 |
goal thy "sees lost A evs <= initState lost A Un sees lost Spy evs"; |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
373 |
by (list.induct_tac "evs" 1); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
374 |
by (event.induct_tac "a" 2); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
375 |
by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
376 |
addss (!simpset)))); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
377 |
qed "sees_agent_subset_sees_Spy"; |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
378 |
|
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
379 |
(*The Spy can see more than anybody else who's lost their key!*) |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
380 |
goal thy "A: lost --> A ~= Server --> sees lost A evs <= sees lost Spy evs"; |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
381 |
by (list.induct_tac "evs" 1); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
382 |
by (event.induct_tac "a" 2); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
383 |
by (agent.induct_tac "A" 1); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
384 |
by (auto_tac (!claset addDs [sees_Says_subset_insert RS subsetD], (!simpset))); |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
385 |
qed_spec_mp "sees_lost_agent_subset_sees_Spy"; |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
386 |
|
1934 | 387 |
|
2032 | 388 |
(** Simplifying parts (insert X (sees lost A evs)) |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
389 |
= parts {X} Un parts (sees lost A evs) -- since general case loops*) |
2012 | 390 |
|
391 |
val parts_insert_sees = |
|
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
392 |
parts_insert |> read_instantiate_sg (sign_of thy) |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
393 |
[("H", "sees lost A evs")] |
2012 | 394 |
|> standard; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
395 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
396 |
|
2049
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
397 |
(*** Specialized rewriting for analz_insert_Key_newK ***) |
d3b93e1765bc
Moved sees_lost_agent_subset_sees_Spy to common file
paulson
parents:
2045
diff
changeset
|
398 |
|
2320 | 399 |
(*Push newK applications in, allowing other keys to be pulled out*) |
400 |
val pushKey_newK = insComm thy "Key (newK ?evs)" "Key (shrK ?C)"; |
|
401 |
||
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
402 |
goal thy "!!A. A <= Compl (range shrK) ==> shrK x ~: A"; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
403 |
by (Fast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
404 |
qed "subset_Compl_range"; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
405 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
406 |
goal thy "insert (Key (f x)) (Key``(f``E) Un C) = \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
407 |
\ Key `` (f `` (insert x E)) Un C"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
408 |
by (Fast_tac 1); |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
409 |
qed "insert_Key_image"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
410 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
411 |
goal thy "insert (Key K) H = Key `` {K} Un H"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
412 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
413 |
qed "insert_Key_singleton"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
414 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
415 |
goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
416 |
by (Fast_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
417 |
qed "insert_Key_image'"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
418 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
419 |
val analz_image_freshK_ss = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
420 |
!simpset delsimps [image_insert, image_Un] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
421 |
addsimps ([image_insert RS sym, image_Un RS sym, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
422 |
Key_not_used, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
423 |
insert_Key_singleton, subset_Compl_range, |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
424 |
insert_Key_image', Un_assoc RS sym] |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
425 |
@disj_comms) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
426 |
setloop split_tac [expand_if]; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
427 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
428 |
(*Lemma for the trivial direction of the if-and-only-if*) |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
429 |
goal thy |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
430 |
"!!evs. (Key K : analz (Key``nE Un H)) --> (K : nE | Key K : analz H) ==> \ |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
431 |
\ (Key K : analz (Key``nE Un H)) = (K : nE | Key K : analz H)"; |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
432 |
by (fast_tac (!claset addSEs [impOfSubs analz_mono]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
433 |
qed "analz_image_freshK_lemma"; |