--- a/src/HOL/Auth/NS_Public_Bad.ML Mon Jan 12 15:47:43 1998 +0100
+++ b/src/HOL/Auth/NS_Public_Bad.ML Mon Jan 12 16:56:39 1998 +0100
@@ -16,6 +16,10 @@
set proof_timing;
HOL_quantifiers := false;
+AddEs spies_partsEs;
+AddDs [impOfSubs analz_subset_parts];
+AddDs [impOfSubs Fake_parts_insert];
+
AddIffs [Spy_in_bad];
(*A "possibility property": there are traces that reach the end*)
@@ -57,13 +61,13 @@
goal thy
"!!A. evs: ns_public ==> (Key (priK A) : parts (spies evs)) = (A : bad)";
by (parts_induct_tac 1);
-by (Fake_parts_insert_tac 1);
+by (Blast_tac 1);
qed "Spy_see_priK";
Addsimps [Spy_see_priK];
goal thy
"!!A. evs: ns_public ==> (Key (priK A) : analz (spies evs)) = (A : bad)";
-by (auto_tac(claset() addDs [impOfSubs analz_subset_parts], simpset()));
+by Auto_tac;
qed "Spy_analz_priK";
Addsimps [Spy_analz_priK];
@@ -82,13 +86,12 @@
by (etac rev_mp 1);
by (etac rev_mp 1);
by (parts_induct_tac 1);
-(*NS3*)
-by (blast_tac (claset() addSEs partsEs) 3);
-(*NS2*)
-by (blast_tac (claset() addSEs partsEs) 2);
-by (Fake_parts_insert_tac 1);
+by (ALLGOALS Blast_tac);
qed "no_nonce_NS1_NS2";
+(*Adding it to the claset slows down proofs...*)
+val nonce_NS1_NS2_E = no_nonce_NS1_NS2 RSN (2, rev_notE);
+
(*Unicity for NS1: nonce NA identifies agents A and B*)
goal thy
@@ -98,15 +101,12 @@
\ A=A' & B=B'";
by (etac rev_mp 1);
by (parts_induct_tac 1);
-by (ALLGOALS
- (asm_simp_tac (simpset() addsimps [all_conj_distrib,
- parts_insert_spies])));
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
(*NS1*)
-by (expand_case_tac "NA = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2);
+by (expand_case_tac "NA = ?y" 2 THEN Blast_tac 2);
(*Fake*)
by (Clarify_tac 1);
-by (ex_strip_tac 1);
-by (Fake_parts_insert_tac 1);
+by (Blast_tac 1);
val lemma = result();
goal thy
@@ -133,15 +133,11 @@
by (etac rev_mp 1);
by (analz_induct_tac 1);
(*NS3*)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj]
- addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]) 4);
+by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 4);
(*NS2*)
-by (blast_tac (claset() addSEs [MPair_parts]
- addDs [Says_imp_spies RS parts.Inj,
- parts.Body, unique_NA]) 3);
+by (blast_tac (claset() addDs [unique_NA]) 3);
(*NS1*)
-by (blast_tac (claset() addSEs spies_partsEs
- addIs [impOfSubs analz_subset_parts]) 2);
+by (Blast_tac 2);
(*Fake*)
by (spy_analz_tac 1);
qed "Spy_not_see_NA";
@@ -161,16 +157,14 @@
by (ALLGOALS Asm_simp_tac);
by (ALLGOALS Clarify_tac);
(*NS2*)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj,
- Spy_not_see_NA, unique_NA]) 3);
+by (blast_tac (claset() addDs [Spy_not_see_NA, unique_NA]) 3);
(*NS1*)
-by (blast_tac (claset() addSEs spies_partsEs) 2);
+by (Blast_tac 2);
(*Fake*)
-by (blast_tac (claset() addSDs [impOfSubs Fake_parts_insert]
- addDs [Spy_not_see_NA,
- impOfSubs analz_subset_parts]) 1);
+by (blast_tac (claset() addDs [Spy_not_see_NA]) 1);
qed "A_trusts_NS2";
+
(*If the encrypted message appears then it originated with Alice in NS1*)
goal thy
"!!evs. [| Crypt (pubK B) {|Nonce NA, Agent A|} : parts (spies evs); \
@@ -180,30 +174,27 @@
by (etac rev_mp 1);
by (etac rev_mp 1);
by (parts_induct_tac 1);
-by (Fake_parts_insert_tac 1);
+by (Blast_tac 1);
qed "B_trusts_NS1";
(**** Authenticity properties obtained from NS2 ****)
-(*Unicity for NS2: nonce NB identifies agent A and nonce NA
+(*Unicity for NS2: nonce NB identifies nonce NA and agent A
[proof closely follows that for unique_NA] *)
goal thy
- "!!evs. [| Nonce NB ~: analz (spies evs); evs : ns_public |] \
-\ ==> EX A' NA'. ALL A NA. \
-\ Crypt (pubK A) {|Nonce NA, Nonce NB|} \
-\ : parts (spies evs) --> A=A' & NA=NA'";
+ "!!evs. [| Nonce NB ~: analz (spies evs); evs : ns_public |] \
+\ ==> EX A' NA'. ALL A NA. \
+\ Crypt (pubK A) {|Nonce NA, Nonce NB|} : parts (spies evs) \
+\ --> A=A' & NA=NA'";
by (etac rev_mp 1);
by (parts_induct_tac 1);
-by (ALLGOALS
- (asm_simp_tac (simpset() addsimps [all_conj_distrib, parts_insert_spies])));
+by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
(*NS2*)
-by (expand_case_tac "NB = ?y" 2 THEN blast_tac (claset() addSEs partsEs) 2);
+by (expand_case_tac "NB = ?y" 2 THEN Blast_tac 2);
(*Fake*)
-by (Clarify_tac 1);
-by (ex_strip_tac 1);
-by (Fake_parts_insert_tac 1);
+by (Blast_tac 1);
val lemma = result();
goal thy
@@ -228,14 +219,11 @@
by (ALLGOALS (asm_simp_tac (simpset() addsimps [all_conj_distrib])));
by (ALLGOALS Clarify_tac);
(*NS3: because NB determines A*)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, unique_NB]) 4);
+by (blast_tac (claset() addDs [unique_NB]) 4);
(*NS2: by freshness and unicity of NB*)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj]
- addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]
- addEs partsEs
- addIs [impOfSubs analz_subset_parts]) 3);
+by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3);
(*NS1: by freshness*)
-by (blast_tac (claset() addSEs spies_partsEs) 2);
+by (Blast_tac 2);
(*Fake*)
by (spy_analz_tac 1);
qed "Spy_not_see_NB";
@@ -256,14 +244,12 @@
by (ALLGOALS (asm_simp_tac (simpset() addsimps [ex_disj_distrib])));
by (ALLGOALS Clarify_tac);
(*NS3: because NB determines A (this use of unique_NB is more robust) *)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj, Spy_not_see_NB]
+by (blast_tac (claset() addDs [Spy_not_see_NB]
addIs [unique_NB RS conjunct1]) 3);
(*NS1: by freshness*)
-by (blast_tac (claset() addSEs spies_partsEs) 2);
+by (Blast_tac 2);
(*Fake*)
-by (blast_tac (claset() addSDs [impOfSubs Fake_parts_insert]
- addDs [Spy_not_see_NB,
- impOfSubs analz_subset_parts]) 1);
+by (blast_tac (claset() addDs [Spy_not_see_NB]) 1);
qed "B_trusts_NS3";
@@ -275,12 +261,9 @@
by (analz_induct_tac 1);
by (ALLGOALS Clarify_tac);
(*NS2: by freshness and unicity of NB*)
-by (blast_tac (claset() addDs [Says_imp_spies RS parts.Inj]
- addEs [no_nonce_NS1_NS2 RSN (2, rev_notE)]
- addEs partsEs
- addIs [impOfSubs analz_subset_parts]) 3);
+by (blast_tac (claset() addEs [nonce_NS1_NS2_E]) 3);
(*NS1: by freshness*)
-by (blast_tac (claset() addSEs spies_partsEs) 2);
+by (Blast_tac 2);
(*Fake*)
by (spy_analz_tac 1);
(*NS3: unicity of NB identifies A and NA, but not B*)