author | paulson |
Fri, 11 Jul 1997 13:26:15 +0200 | |
changeset 3512 | 9dcb4daa15e8 |
parent 3479 | 2aacd6f10654 |
child 3519 | ab0a9fbed4c0 |
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 |
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5 |
||
6 |
Theory of Shared Keys (common to all symmetric-key protocols) |
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Shared, long-term keys; initial states of agents |
2032 | 9 |
*) |
10 |
||
1934 | 11 |
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12 |
open Shared; |
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13 |
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14 |
(*** Basic properties of shrK ***) |
1934 | 15 |
|
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16 |
(*Injectiveness: Agents' long-term keys are distinct.*) |
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17 |
AddIffs [inj_shrK RS inj_eq]; |
2376
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Temporary additions (random) for the nested Otway-Rees protocol
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18 |
|
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19 |
(* invKey(shrK A) = shrK A *) |
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20 |
Addsimps [rewrite_rule [isSymKey_def] isSym_keys]; |
2320 | 21 |
|
1934 | 22 |
(** Rewrites should not refer to initState(Friend i) |
23 |
-- not in normal form! **) |
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24 |
||
2032 | 25 |
goalw thy [keysFor_def] "keysFor (parts (initState lost C)) = {}"; |
1934 | 26 |
by (agent.induct_tac "C" 1); |
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27 |
by (Auto_tac ()); |
1934 | 28 |
qed "keysFor_parts_initState"; |
29 |
Addsimps [keysFor_parts_initState]; |
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30 |
||
2032 | 31 |
|
32 |
(*** Function "sees" ***) |
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33 |
||
1964 | 34 |
(*Agents see their own shared keys!*) |
2032 | 35 |
goal thy "A ~= Spy --> Key (shrK A) : sees lost A evs"; |
1934 | 36 |
by (list.induct_tac "evs" 1); |
37 |
by (agent.induct_tac "A" 1); |
|
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38 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons]))); |
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39 |
by (Blast_tac 1); |
2032 | 40 |
qed_spec_mp "sees_own_shrK"; |
1934 | 41 |
|
2032 | 42 |
(*Spy sees shared keys of lost agents!*) |
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43 |
goal thy "!!A. A: lost ==> Key (shrK A) : sees lost Spy evs"; |
2032 | 44 |
by (list.induct_tac "evs" 1); |
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45 |
by (ALLGOALS (asm_simp_tac (!simpset addsimps [sees_Cons]))); |
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46 |
by (Blast_tac 1); |
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47 |
qed "Spy_sees_lost"; |
1934 | 48 |
|
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49 |
AddSIs [sees_own_shrK, Spy_sees_lost]; |
2032 | 50 |
|
3443 | 51 |
(*For not_lost_tac*) |
52 |
goal thy "!!A. [| Crypt (shrK A) X : analz (sees lost Spy evs); A: lost |] \ |
|
53 |
\ ==> X : analz (sees lost Spy evs)"; |
|
54 |
by (fast_tac (!claset addSDs [analz.Decrypt] addss (!simpset)) 1); |
|
55 |
qed "Crypt_Spy_analz_lost"; |
|
2072 | 56 |
|
3443 | 57 |
(*Prove that the agent is uncompromised by the confidentiality of |
58 |
a component of a message she's said.*) |
|
59 |
fun not_lost_tac s = |
|
60 |
case_tac ("(" ^ s ^ ") : lost") THEN' |
|
61 |
SELECT_GOAL |
|
62 |
(REPEAT_DETERM (dtac (Says_imp_sees_Spy RS analz.Inj) 1) THEN |
|
63 |
REPEAT_DETERM (etac MPair_analz 1) THEN |
|
64 |
THEN_BEST_FIRST |
|
65 |
(dres_inst_tac [("A", s)] Crypt_Spy_analz_lost 1 THEN assume_tac 1) |
|
66 |
(has_fewer_prems 1, size_of_thm) |
|
67 |
(Step_tac 1)); |
|
1934 | 68 |
|
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69 |
|
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70 |
(** Fresh keys never clash with long-term shared keys **) |
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71 |
|
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72 |
goal thy "Key (shrK A) : used evs"; |
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73 |
by (Blast_tac 1); |
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74 |
qed "shrK_in_used"; |
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75 |
AddIffs [shrK_in_used]; |
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76 |
|
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77 |
(*Used in parts_induct_tac and analz_Fake_tac to distinguish session keys |
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78 |
from long-term shared keys*) |
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79 |
goal thy "!!K. Key K ~: used evs ==> K ~: range shrK"; |
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80 |
by (Blast_tac 1); |
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81 |
qed "Key_not_used"; |
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82 |
|
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83 |
(*A session key cannot clash with a long-term shared key*) |
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84 |
goal thy "!!K. K ~: range shrK ==> shrK B ~= K"; |
2891 | 85 |
by (Blast_tac 1); |
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86 |
qed "shrK_neq"; |
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87 |
|
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88 |
Addsimps [Key_not_used, shrK_neq, shrK_neq RS not_sym]; |
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89 |
|
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90 |
|
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91 |
(*** Fresh nonces ***) |
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92 |
|
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93 |
goal thy "Nonce N ~: parts (initState lost B)"; |
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94 |
by (agent.induct_tac "B" 1); |
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95 |
by (Auto_tac ()); |
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96 |
qed "Nonce_notin_initState"; |
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|
97 |
AddIffs [Nonce_notin_initState]; |
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98 |
|
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99 |
goal thy "Nonce N ~: used []"; |
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100 |
by (simp_tac (!simpset addsimps [used_def]) 1); |
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101 |
qed "Nonce_notin_used_empty"; |
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102 |
Addsimps [Nonce_notin_used_empty]; |
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103 |
|
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104 |
|
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105 |
(*** Supply fresh nonces for possibility theorems. ***) |
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106 |
|
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107 |
(*In any trace, there is an upper bound N on the greatest nonce in use.*) |
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108 |
goalw thy [used_def] "EX N. ALL n. N<=n --> Nonce n ~: used evs"; |
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109 |
by (list.induct_tac "evs" 1); |
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|
110 |
by (res_inst_tac [("x","0")] exI 1); |
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|
111 |
by (Step_tac 1); |
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|
112 |
by (Full_simp_tac 1); |
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113 |
(*Inductive step*) |
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114 |
by (event.induct_tac "a" 1); |
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115 |
by (ALLGOALS (full_simp_tac |
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116 |
(!simpset delsimps [sees_Notes] |
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117 |
addsimps [UN_parts_sees_Says, |
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118 |
UN_parts_sees_Notes]))); |
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|
119 |
by (ALLGOALS (rtac (msg_Nonce_supply RS exE))); |
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120 |
by (ALLGOALS (blast_tac (!claset addSEs [add_leE]))); |
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121 |
val lemma = result(); |
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122 |
|
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123 |
goal thy "EX N. Nonce N ~: used evs"; |
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124 |
by (rtac (lemma RS exE) 1); |
2891 | 125 |
by (Blast_tac 1); |
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126 |
qed "Nonce_supply1"; |
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127 |
|
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128 |
goal thy "EX N N'. Nonce N ~: used evs & Nonce N' ~: used evs' & N ~= N'"; |
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|
129 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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|
130 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
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131 |
by (Step_tac 1); |
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132 |
by (res_inst_tac [("x","N")] exI 1); |
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|
133 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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|
134 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
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135 |
le_add2, le_add1, |
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|
136 |
le_eq_less_Suc RS sym]) 1); |
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137 |
qed "Nonce_supply2"; |
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138 |
|
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139 |
goal thy "EX N N' N''. Nonce N ~: used evs & Nonce N' ~: used evs' & \ |
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140 |
\ Nonce N'' ~: used evs'' & N ~= N' & N' ~= N'' & N ~= N''"; |
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|
141 |
by (cut_inst_tac [("evs","evs")] lemma 1); |
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|
142 |
by (cut_inst_tac [("evs","evs'")] lemma 1); |
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|
143 |
by (cut_inst_tac [("evs","evs''")] lemma 1); |
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|
144 |
by (Step_tac 1); |
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|
145 |
by (res_inst_tac [("x","N")] exI 1); |
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|
146 |
by (res_inst_tac [("x","Suc (N+Na)")] exI 1); |
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|
147 |
by (res_inst_tac [("x","Suc (Suc (N+Na+Nb))")] exI 1); |
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|
148 |
by (asm_simp_tac (!simpset addsimps [less_not_refl2 RS not_sym, |
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149 |
le_add2, le_add1, |
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150 |
le_eq_less_Suc RS sym]) 1); |
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|
151 |
by (rtac (less_trans RS less_not_refl2 RS not_sym) 1); |
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|
152 |
by (stac (le_eq_less_Suc RS sym) 1); |
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|
153 |
by (asm_simp_tac (!simpset addsimps [le_eq_less_Suc RS sym]) 2); |
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|
154 |
by (REPEAT (rtac le_add1 1)); |
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|
155 |
qed "Nonce_supply3"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
156 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
157 |
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
|
158 |
by (rtac (lemma RS exE) 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
159 |
by (rtac selectI 1); |
2891 | 160 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
161 |
qed "Nonce_supply"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
162 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
163 |
(*** Supply fresh keys for possibility theorems. ***) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
164 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
165 |
goal thy "EX K. Key K ~: used evs"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
166 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
2891 | 167 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
168 |
qed "Key_supply1"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
169 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
170 |
goal thy "EX K K'. Key K ~: used evs & Key K' ~: used evs' & K ~= K'"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
171 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
172 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
173 |
by (cut_inst_tac [("evs","evs'")] |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
174 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
175 |
by (Auto_tac()); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
176 |
qed "Key_supply2"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
177 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
178 |
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
|
179 |
\ Key K'' ~: used evs'' & K ~= K' & K' ~= K'' & K ~= K''"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
180 |
by (cut_inst_tac [("evs","evs")] (Finites.emptyI RS Key_supply_ax) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
181 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
182 |
by (cut_inst_tac [("evs","evs'")] |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
183 |
(Finites.emptyI RS Finites.insertI RS Key_supply_ax) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
184 |
by (etac exE 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
185 |
by (cut_inst_tac [("evs","evs''")] |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
186 |
(Finites.emptyI RS Finites.insertI RS Finites.insertI RS Key_supply_ax) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
187 |
by (Step_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
188 |
by (Full_simp_tac 1); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
189 |
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
|
190 |
qed "Key_supply3"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
191 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
192 |
goal thy "Key (@ K. Key K ~: used evs) ~: used evs"; |
3414
804c8a178a7f
Modified a few defs and proofs because of the changes to theory Finite.thy.
nipkow
parents:
3207
diff
changeset
|
193 |
by (rtac (Finites.emptyI RS Key_supply_ax RS exE) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
194 |
by (rtac selectI 1); |
2891 | 195 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
196 |
qed "Key_supply"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
197 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
198 |
(*** Tactics for possibility theorems ***) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
199 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
200 |
val possibility_tac = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
201 |
REPEAT (*omit used_Says so that Nonces, Keys start from different traces!*) |
3512
9dcb4daa15e8
Moving common declarations and proofs from theories "Shared"
paulson
parents:
3479
diff
changeset
|
202 |
(ALLGOALS (simp_tac (!simpset delsimps [used_Says] setSolver safe_solver)) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
203 |
THEN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
204 |
REPEAT_FIRST (eq_assume_tac ORELSE' |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
205 |
resolve_tac [refl, conjI, Nonce_supply, Key_supply])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
206 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
207 |
(*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:
2451
diff
changeset
|
208 |
nonces and keys initially*) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
209 |
val basic_possibility_tac = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
210 |
REPEAT |
2637
e9b203f854ae
reflecting my recent changes of the simplifier and classical reasoner
oheimb
parents:
2516
diff
changeset
|
211 |
(ALLGOALS (asm_simp_tac (!simpset setSolver safe_solver)) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
212 |
THEN |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
213 |
REPEAT_FIRST (resolve_tac [refl, conjI])); |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
214 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
215 |
|
3472
fb3c38c88c08
Deleted the obsolete operators newK, newN and nPair
paulson
parents:
3465
diff
changeset
|
216 |
(*** Specialized rewriting for analz_insert_freshK ***) |
2320 | 217 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
218 |
goal thy "!!A. A <= Compl (range shrK) ==> shrK x ~: A"; |
2891 | 219 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
220 |
qed "subset_Compl_range"; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
221 |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
222 |
goal thy "insert (Key K) H = Key `` {K} Un H"; |
2891 | 223 |
by (Blast_tac 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
224 |
qed "insert_Key_singleton"; |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
225 |
|
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
226 |
goal thy "insert (Key K) (Key``KK Un C) = Key `` (insert K KK) Un C"; |
2891 | 227 |
by (Blast_tac 1); |
228 |
qed "insert_Key_image"; |
|
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
229 |
|
3451
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
230 |
(*Reverse the normal simplification of "image" to build up (not break down) |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
231 |
the set of keys. Use analz_insert_eq with (Un_upper2 RS analz_mono) to |
d10f100676d8
Made proofs more concise by replacing calls to spy_analz_tac by uses of
paulson
parents:
3443
diff
changeset
|
232 |
erase occurrences of forwarded message components (X).*) |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
233 |
val analz_image_freshK_ss = |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
234 |
!simpset delsimps [image_insert, image_Un] |
3479
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
235 |
addsimps ([image_insert RS sym, image_Un RS sym, |
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
236 |
analz_insert_eq, impOfSubs (Un_upper2 RS analz_mono), |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
237 |
insert_Key_singleton, subset_Compl_range, |
3479
2aacd6f10654
Reordered rules in analz_image_freshK_ss to improve clarity
paulson
parents:
3472
diff
changeset
|
238 |
Key_not_used, insert_Key_image, Un_assoc RS sym] |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
239 |
@disj_comms) |
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
240 |
setloop split_tac [expand_if]; |
2045
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
241 |
|
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
242 |
(*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
|
243 |
goal thy |
ae1030e66745
Removed some dead wood. Transferred lemmas used to prove analz_image_newK
paulson
parents:
2032
diff
changeset
|
244 |
"!!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
|
245 |
\ (Key K : analz (Key``nE Un H)) = (K : nE | Key K : analz H)"; |
2922 | 246 |
by (blast_tac (!claset addIs [impOfSubs analz_mono]) 1); |
2516
4d68fbe6378b
Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents:
2451
diff
changeset
|
247 |
qed "analz_image_freshK_lemma"; |