src/HOL/Auth/Message.ML
author paulson
Wed, 21 Jul 1999 15:22:11 +0200
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permissions -rw-r--r--
tweaked proofs to handle new freeness reasoning for data c onstructors
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(*  Title:      HOL/Auth/Message
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1996  University of Cambridge
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Datatypes of agents and messages;
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Inductive relations "parts", "analz" and "synth"
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*)
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(*Eliminates a commonly-occurring expression*)
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goal HOL.thy "~ (ALL x. x~=y)";
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by (Blast_tac 1);
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Addsimps [result()];
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AddIffs msg.inject;
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(*Equations hold because constructors are injective; cannot prove for all f*)
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Goal "(Friend x : Friend``A) = (x:A)";
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by Auto_tac;
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qed "Friend_image_eq";
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Goal "(Key x : Key``A) = (x:A)";
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by Auto_tac;
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qed "Key_image_eq";
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Goal "(Nonce x ~: Key``A)";
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by Auto_tac;
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qed "Nonce_Key_image_eq";
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Addsimps [Friend_image_eq, Key_image_eq, Nonce_Key_image_eq];
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(** Inverse of keys **)
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Goal "(invKey K = invKey K') = (K=K')";
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by Safe_tac;
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by (rtac box_equals 1);
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by (REPEAT (rtac invKey 2));
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by (Asm_simp_tac 1);
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qed "invKey_eq";
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Addsimps [invKey, invKey_eq];
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(**** keysFor operator ****)
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Goalw [keysFor_def] "keysFor {} = {}";
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by (Blast_tac 1);
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qed "keysFor_empty";
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Goalw [keysFor_def] "keysFor (H Un H') = keysFor H Un keysFor H'";
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by (Blast_tac 1);
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qed "keysFor_Un";
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Goalw [keysFor_def] "keysFor (UN i:A. H i) = (UN i:A. keysFor (H i))";
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by (Blast_tac 1);
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qed "keysFor_UN";
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(*Monotonicity*)
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Goalw [keysFor_def] "G<=H ==> keysFor(G) <= keysFor(H)";
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by (Blast_tac 1);
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qed "keysFor_mono";
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Goalw [keysFor_def] "keysFor (insert (Agent A) H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_Agent";
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Goalw [keysFor_def] "keysFor (insert (Nonce N) H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_Nonce";
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Goalw [keysFor_def] "keysFor (insert (Number N) H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_Number";
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Goalw [keysFor_def] "keysFor (insert (Key K) H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_Key";
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Goalw [keysFor_def] "keysFor (insert (Hash X) H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_Hash";
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Goalw [keysFor_def] "keysFor (insert {|X,Y|} H) = keysFor H";
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by Auto_tac;
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qed "keysFor_insert_MPair";
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Goalw [keysFor_def]
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    "keysFor (insert (Crypt K X) H) = insert (invKey K) (keysFor H)";
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by Auto_tac;
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qed "keysFor_insert_Crypt";
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Addsimps [keysFor_empty, keysFor_Un, keysFor_UN, 
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          keysFor_insert_Agent, keysFor_insert_Nonce, 
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	  keysFor_insert_Number, keysFor_insert_Key, 
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          keysFor_insert_Hash, keysFor_insert_MPair, keysFor_insert_Crypt];
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AddSEs [keysFor_Un RS equalityD1 RS subsetD RS UnE,
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	keysFor_UN RS equalityD1 RS subsetD RS UN_E];
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Goalw [keysFor_def] "keysFor (Key``E) = {}";
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by Auto_tac;
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qed "keysFor_image_Key";
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Addsimps [keysFor_image_Key];
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Goalw [keysFor_def] "Crypt K X : H ==> invKey K : keysFor H";
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by (Blast_tac 1);
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qed "Crypt_imp_invKey_keysFor";
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(**** Inductive relation "parts" ****)
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val major::prems = 
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Goal "[| {|X,Y|} : parts H;       \
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\            [| X : parts H; Y : parts H |] ==> P  \
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\         |] ==> P";
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by (cut_facts_tac [major] 1);
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by (resolve_tac prems 1);
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by (REPEAT (eresolve_tac [asm_rl, parts.Fst, parts.Snd] 1));
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qed "MPair_parts";
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AddIs  [parts.Inj];
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val partsEs = [MPair_parts, make_elim parts.Body];
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AddSEs partsEs;
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(*NB These two rules are UNSAFE in the formal sense, as they discard the
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     compound message.  They work well on THIS FILE, perhaps because its
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     proofs concern only atomic messages.*)
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Goal "H <= parts(H)";
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by (Blast_tac 1);
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qed "parts_increasing";
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(*Monotonicity*)
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Goalw parts.defs "G<=H ==> parts(G) <= parts(H)";
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by (rtac lfp_mono 1);
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by (REPEAT (ares_tac basic_monos 1));
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qed "parts_mono";
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val parts_insertI = impOfSubs (subset_insertI RS parts_mono);
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Goal "parts{} = {}";
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by Safe_tac;
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by (etac parts.induct 1);
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by (ALLGOALS Blast_tac);
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qed "parts_empty";
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Addsimps [parts_empty];
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Goal "X: parts{} ==> P";
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by (Asm_full_simp_tac 1);
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qed "parts_emptyE";
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AddSEs [parts_emptyE];
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(*WARNING: loops if H = {Y}, therefore must not be repeated!*)
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Goal "X: parts H ==> EX Y:H. X: parts {Y}";
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by (etac parts.induct 1);
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by (ALLGOALS Blast_tac);
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qed "parts_singleton";
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(** Unions **)
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Goal "parts(G) Un parts(H) <= parts(G Un H)";
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by (REPEAT (ares_tac [Un_least, parts_mono, Un_upper1, Un_upper2] 1));
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val parts_Un_subset1 = result();
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Goal "parts(G Un H) <= parts(G) Un parts(H)";
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (ALLGOALS Blast_tac);
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val parts_Un_subset2 = result();
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Goal "parts(G Un H) = parts(G) Un parts(H)";
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by (REPEAT (ares_tac [equalityI, parts_Un_subset1, parts_Un_subset2] 1));
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qed "parts_Un";
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Goal "parts (insert X H) = parts {X} Un parts H";
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by (stac (read_instantiate [("A","H")] insert_is_Un) 1);
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by (simp_tac (HOL_ss addsimps [parts_Un]) 1);
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qed "parts_insert";
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(*TWO inserts to avoid looping.  This rewrite is better than nothing.
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  Not suitable for Addsimps: its behaviour can be strange.*)
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Goal "parts (insert X (insert Y H)) = parts {X} Un parts {Y} Un parts H";
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by (simp_tac (simpset() addsimps [Un_assoc]) 1);
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by (simp_tac (simpset() addsimps [parts_insert RS sym]) 1);
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qed "parts_insert2";
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Goal "(UN x:A. parts(H x)) <= parts(UN x:A. H x)";
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by (REPEAT (ares_tac [UN_least, parts_mono, UN_upper] 1));
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val parts_UN_subset1 = result();
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Goal "parts(UN x:A. H x) <= (UN x:A. parts(H x))";
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by (ALLGOALS Blast_tac);
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val parts_UN_subset2 = result();
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Goal "parts(UN x:A. H x) = (UN x:A. parts(H x))";
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by (REPEAT (ares_tac [equalityI, parts_UN_subset1, parts_UN_subset2] 1));
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qed "parts_UN";
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(*Added to simplify arguments to parts, analz and synth.
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  NOTE: the UN versions are no longer used!*)
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Addsimps [parts_Un, parts_UN];
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AddSEs [parts_Un RS equalityD1 RS subsetD RS UnE,
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	parts_UN RS equalityD1 RS subsetD RS UN_E];
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Goal "insert X (parts H) <= parts(insert X H)";
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by (blast_tac (claset() addIs [impOfSubs parts_mono]) 1);
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qed "parts_insert_subset";
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(** Idempotence and transitivity **)
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Goal "X: parts (parts H) ==> X: parts H";
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by (etac parts.induct 1);
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by (ALLGOALS Blast_tac);
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qed "parts_partsD";
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AddSDs [parts_partsD];
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Goal "parts (parts H) = parts H";
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by (Blast_tac 1);
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qed "parts_idem";
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Addsimps [parts_idem];
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Goal "[| X: parts G;  G <= parts H |] ==> X: parts H";
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by (dtac parts_mono 1);
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by (Blast_tac 1);
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qed "parts_trans";
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(*Cut*)
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Goal "[| Y: parts (insert X G);  X: parts H |] \
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\              ==> Y: parts (G Un H)";
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by (etac parts_trans 1);
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by Auto_tac;
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qed "parts_cut";
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Goal "X: parts H ==> parts (insert X H) = parts H";
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by (fast_tac (claset() addSDs [parts_cut]
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                       addIs  [parts_insertI] 
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                       addss (simpset())) 1);
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qed "parts_cut_eq";
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Addsimps [parts_cut_eq];
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(** Rewrite rules for pulling out atomic messages **)
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fun parts_tac i =
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  EVERY [rtac ([subsetI, parts_insert_subset] MRS equalityI) i,
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         etac parts.induct i,
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         Auto_tac];
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Goal "parts (insert (Agent agt) H) = insert (Agent agt) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Agent";
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Goal "parts (insert (Nonce N) H) = insert (Nonce N) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Nonce";
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Goal "parts (insert (Number N) H) = insert (Number N) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Number";
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Goal "parts (insert (Key K) H) = insert (Key K) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Key";
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Goal "parts (insert (Hash X) H) = insert (Hash X) (parts H)";
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by (parts_tac 1);
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qed "parts_insert_Hash";
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Goal "parts (insert (Crypt K X) H) = \
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\         insert (Crypt K X) (parts (insert X H))";
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by (rtac equalityI 1);
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by (rtac subsetI 1);
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by (etac parts.induct 1);
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by Auto_tac;
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by (etac parts.induct 1);
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by (ALLGOALS (blast_tac (claset() addIs [parts.Body])));
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qed "parts_insert_Crypt";
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Goal "parts (insert {|X,Y|} H) = \
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\         insert {|X,Y|} (parts (insert X (insert Y H)))";
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by (rtac equalityI 1);
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   287
by (rtac subsetI 1);
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by (etac parts.induct 1);
4477
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by Auto_tac;
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   290
by (etac parts.induct 1);
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by (ALLGOALS (blast_tac (claset() addIs [parts.Fst, parts.Snd])));
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qed "parts_insert_MPair";
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   293
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Addsimps [parts_insert_Agent, parts_insert_Nonce, 
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	  parts_insert_Number, parts_insert_Key, 
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          parts_insert_Hash, parts_insert_Crypt, parts_insert_MPair];
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   299
Goal "parts (Key``N) = Key``N";
4477
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by Auto_tac;
2032
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   301
by (etac parts.induct 1);
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by Auto_tac;
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   303
qed "parts_image_Key";
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Addsimps [parts_image_Key];
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   305
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   306
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(*In any message, there is an upper bound N on its greatest nonce.*)
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Goal "EX N. ALL n. N<=n --> Nonce n ~: parts {msg}";
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   309
by (induct_tac "msg" 1);
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   310
by (ALLGOALS (asm_simp_tac (simpset() addsimps [exI, parts_insert2])));
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(*MPair case: blast_tac works out the necessary sum itself!*)
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by (blast_tac (claset() addSEs [add_leE]) 2);
3514
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   313
(*Nonce case*)
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   314
by (res_inst_tac [("x","N + Suc nat")] exI 1);
5983
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nipkow
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   315
by (auto_tac (claset() addSEs [add_leE], simpset()));
3514
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   316
qed "msg_Nonce_supply";
2026
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   317
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   318
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   319
(**** Inductive relation "analz" ****)
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   320
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   321
val major::prems = 
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   322
Goal "[| {|X,Y|} : analz H;       \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   323
\            [| X : analz H; Y : analz H |] ==> P  \
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   324
\         |] ==> P";
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   325
by (cut_facts_tac [major] 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   326
by (resolve_tac prems 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   327
by (REPEAT (eresolve_tac [asm_rl, analz.Fst, analz.Snd] 1));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   328
qed "MPair_analz";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   329
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   330
AddIs  [analz.Inj];
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   331
AddSEs [MPair_analz];      (*Perhaps it should NOT be deemed safe!*)
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   332
AddDs  [analz.Decrypt];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   333
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   334
Addsimps [analz.Inj];
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   335
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   336
Goal "H <= analz(H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   337
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   338
qed "analz_increasing";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   339
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   340
Goal "analz H <= parts H";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   341
by (rtac subsetI 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   342
by (etac analz.induct 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   343
by (ALLGOALS Blast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   344
qed "analz_subset_parts";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   345
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   346
bind_thm ("not_parts_not_analz", analz_subset_parts RS contra_subsetD);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   347
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   348
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   349
Goal "parts (analz H) = parts H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   350
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   351
by (rtac (analz_subset_parts RS parts_mono RS subset_trans) 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   352
by (Simp_tac 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   353
by (blast_tac (claset() addIs [analz_increasing RS parts_mono RS subsetD]) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   354
qed "parts_analz";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   355
Addsimps [parts_analz];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   356
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   357
Goal "analz (parts H) = parts H";
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   358
by Auto_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   359
by (etac analz.induct 1);
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   360
by Auto_tac;
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   361
qed "analz_parts";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   362
Addsimps [analz_parts];
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   363
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   364
(*Monotonicity; Lemma 1 of Lowe*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   365
Goalw analz.defs "G<=H ==> analz(G) <= analz(H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   366
by (rtac lfp_mono 1);
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   367
by (REPEAT (ares_tac basic_monos 1));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   368
qed "analz_mono";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   369
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   370
val analz_insertI = impOfSubs (subset_insertI RS analz_mono);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   371
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   372
(** General equational properties **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   373
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   374
Goal "analz{} = {}";
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3714
diff changeset
   375
by Safe_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   376
by (etac analz.induct 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   377
by (ALLGOALS Blast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   378
qed "analz_empty";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   379
Addsimps [analz_empty];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   380
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   381
(*Converse fails: we can analz more from the union than from the 
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   382
  separate parts, as a key in one might decrypt a message in the other*)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   383
Goal "analz(G) Un analz(H) <= analz(G Un H)";
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   384
by (REPEAT (ares_tac [Un_least, analz_mono, Un_upper1, Un_upper2] 1));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   385
qed "analz_Un";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   386
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   387
Goal "insert X (analz H) <= analz(insert X H)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   388
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   389
qed "analz_insert";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   390
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   391
(** Rewrite rules for pulling out atomic messages **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   392
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   393
fun analz_tac i =
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   394
  EVERY [rtac ([subsetI, analz_insert] MRS equalityI) i,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   395
         etac analz.induct i,
7057
b9ddbb925939 tweaked proofs to handle new freeness reasoning for data c onstructors
paulson
parents: 6915
diff changeset
   396
         Auto_tac];
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   397
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   398
Goal "analz (insert (Agent agt) H) = insert (Agent agt) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   399
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   400
qed "analz_insert_Agent";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   401
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   402
Goal "analz (insert (Nonce N) H) = insert (Nonce N) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   403
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   404
qed "analz_insert_Nonce";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   405
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   406
Goal "analz (insert (Number N) H) = insert (Number N) (analz H)";
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   407
by (analz_tac 1);
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   408
qed "analz_insert_Number";
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   409
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   410
Goal "analz (insert (Hash X) H) = insert (Hash X) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   411
by (analz_tac 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   412
qed "analz_insert_Hash";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   413
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   414
(*Can only pull out Keys if they are not needed to decrypt the rest*)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   415
Goalw [keysFor_def]
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   416
    "K ~: keysFor (analz H) ==>  \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   417
\         analz (insert (Key K) H) = insert (Key K) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   418
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   419
qed "analz_insert_Key";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   420
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   421
Goal "analz (insert {|X,Y|} H) = \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   422
\         insert {|X,Y|} (analz (insert X (insert Y H)))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   423
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   424
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   425
by (etac analz.induct 1);
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   426
by Auto_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   427
by (etac analz.induct 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   428
by (ALLGOALS (blast_tac (claset() addIs [analz.Fst, analz.Snd])));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   429
qed "analz_insert_MPair";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   430
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   431
(*Can pull out enCrypted message if the Key is not known*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   432
Goal "Key (invKey K) ~: analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   433
\              analz (insert (Crypt K X) H) = \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   434
\              insert (Crypt K X) (analz H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   435
by (analz_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   436
qed "analz_insert_Crypt";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   437
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   438
Goal "Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   439
\              analz (insert (Crypt K X) H) <= \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   440
\              insert (Crypt K X) (analz (insert X H))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   441
by (rtac subsetI 1);
5102
8c782c25a11e Adapted to new inductive definition package.
berghofe
parents: 5076
diff changeset
   442
by (eres_inst_tac [("xa","x")] analz.induct 1);
7057
b9ddbb925939 tweaked proofs to handle new freeness reasoning for data c onstructors
paulson
parents: 6915
diff changeset
   443
by Auto_tac;
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   444
val lemma1 = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   445
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   446
Goal "Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   447
\              insert (Crypt K X) (analz (insert X H)) <= \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   448
\              analz (insert (Crypt K X) H)";
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   449
by Auto_tac;
5102
8c782c25a11e Adapted to new inductive definition package.
berghofe
parents: 5076
diff changeset
   450
by (eres_inst_tac [("xa","x")] analz.induct 1);
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   451
by Auto_tac;
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   452
by (blast_tac (claset() addIs [analz_insertI, analz.Decrypt]) 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   453
val lemma2 = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   454
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   455
Goal "Key (invKey K) : analz H ==>  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   456
\              analz (insert (Crypt K X) H) = \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   457
\              insert (Crypt K X) (analz (insert X H))";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   458
by (REPEAT (ares_tac [equalityI, lemma1, lemma2] 1));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   459
qed "analz_insert_Decrypt";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   460
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   461
(*Case analysis: either the message is secure, or it is not!
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   462
  Effective, but can cause subgoals to blow up!
5055
546d6d62aeab fixed comment
paulson
parents: 4735
diff changeset
   463
  Use with split_if;  apparently split_tac does not cope with patterns
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   464
  such as "analz (insert (Crypt K X) H)" *)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   465
Goal "analz (insert (Crypt K X) H) =                \
2154
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   466
\         (if (Key (invKey K) : analz H)                \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   467
\          then insert (Crypt K X) (analz (insert X H)) \
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   468
\          else insert (Crypt K X) (analz H))";
2102
41a667d2c3fa Replaced excluded_middle_tac by case_tac
paulson
parents: 2068
diff changeset
   469
by (case_tac "Key (invKey K)  : analz H " 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   470
by (ALLGOALS (asm_simp_tac (simpset() addsimps [analz_insert_Crypt, 
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   471
						analz_insert_Decrypt])));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   472
qed "analz_Crypt_if";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   473
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   474
Addsimps [analz_insert_Agent, analz_insert_Nonce, 
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   475
	  analz_insert_Number, analz_insert_Key, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   476
          analz_insert_Hash, analz_insert_MPair, analz_Crypt_if];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   477
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   478
(*This rule supposes "for the sake of argument" that we have the key.*)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   479
Goal  "analz (insert (Crypt K X) H) <=  \
2284
80ebd1a213fd Swapped arguments of Crypt (for clarity and because it is conventional)
paulson
parents: 2170
diff changeset
   480
\          insert (Crypt K X) (analz (insert X H))";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   481
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   482
by (etac analz.induct 1);
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   483
by Auto_tac;
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   484
qed "analz_insert_Crypt_subset";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   485
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   486
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   487
Goal "analz (Key``N) = Key``N";
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   488
by Auto_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   489
by (etac analz.induct 1);
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   490
by Auto_tac;
2026
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   491
qed "analz_image_Key";
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   492
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   493
Addsimps [analz_image_Key];
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   494
0df5a96bf77e Last working version prior to introduction of "lost"
paulson
parents: 2011
diff changeset
   495
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   496
(** Idempotence and transitivity **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   497
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   498
Goal "X: analz (analz H) ==> X: analz H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   499
by (etac analz.induct 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   500
by (ALLGOALS Blast_tac);
2922
580647a879cf Using Blast_tac
paulson
parents: 2891
diff changeset
   501
qed "analz_analzD";
580647a879cf Using Blast_tac
paulson
parents: 2891
diff changeset
   502
AddSDs [analz_analzD];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   503
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   504
Goal "analz (analz H) = analz H";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   505
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   506
qed "analz_idem";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   507
Addsimps [analz_idem];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   508
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   509
Goal "[| X: analz G;  G <= analz H |] ==> X: analz H";
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   510
by (dtac analz_mono 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   511
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   512
qed "analz_trans";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   513
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   514
(*Cut; Lemma 2 of Lowe*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   515
Goal "[| Y: analz (insert X H);  X: analz H |] ==> Y: analz H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   516
by (etac analz_trans 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   517
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   518
qed "analz_cut";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   519
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   520
(*Cut can be proved easily by induction on
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   521
   "Y: analz (insert X H) ==> X: analz H --> Y: analz H"
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   522
*)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   523
3449
6b17f82bbf01 New comments; a tidied proof
paulson
parents: 3431
diff changeset
   524
(*This rewrite rule helps in the simplification of messages that involve
6b17f82bbf01 New comments; a tidied proof
paulson
parents: 3431
diff changeset
   525
  the forwarding of unknown components (X).  Without it, removing occurrences
6b17f82bbf01 New comments; a tidied proof
paulson
parents: 3431
diff changeset
   526
  of X can be very complicated. *)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   527
Goal "X: analz H ==> analz (insert X H) = analz H";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   528
by (blast_tac (claset() addIs [analz_cut, analz_insertI]) 1);
3431
05b397185e1d Useful new lemma
paulson
parents: 3121
diff changeset
   529
qed "analz_insert_eq";
05b397185e1d Useful new lemma
paulson
parents: 3121
diff changeset
   530
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   531
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   532
(** A congruence rule for "analz" **)
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   533
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   534
Goal "[| analz G <= analz G'; analz H <= analz H' \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   535
\              |] ==> analz (G Un H) <= analz (G' Un H')";
3714
ab3b4ceb61dc Deleted obsolete version of clarify_tac
paulson
parents: 3702
diff changeset
   536
by (Clarify_tac 1);
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   537
by (etac analz.induct 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   538
by (ALLGOALS (best_tac (claset() addIs [analz_mono RS subsetD])));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   539
qed "analz_subset_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   540
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   541
Goal "[| analz G = analz G'; analz H = analz H' \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   542
\              |] ==> analz (G Un H) = analz (G' Un H')";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   543
by (REPEAT_FIRST (ares_tac [equalityI, analz_subset_cong]
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   544
          ORELSE' etac equalityE));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   545
qed "analz_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   546
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   547
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   548
Goal "analz H = analz H' ==> analz(insert X H) = analz(insert X H')";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   549
by (asm_simp_tac (simpset() addsimps [insert_def] delsimps [singleton_conv]
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   550
                            setloop (rtac analz_cong)) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   551
qed "analz_insert_cong";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   552
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   553
(*If there are no pairs or encryptions then analz does nothing*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   554
Goal "[| ALL X Y. {|X,Y|} ~: H;  ALL X K. Crypt K X ~: H |] ==> \
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   555
\         analz H = H";
3730
6933d20f335f Step_tac -> Safe_tac
paulson
parents: 3714
diff changeset
   556
by Safe_tac;
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   557
by (etac analz.induct 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   558
by (ALLGOALS Blast_tac);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   559
qed "analz_trivial";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   560
4157
200f897f0858 generalized UNION1 to UNION
paulson
parents: 4091
diff changeset
   561
(*These two are obsolete (with a single Spy) but cost little to prove...*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   562
Goal "X: analz (UN i:A. analz (H i)) ==> X: analz (UN i:A. H i)";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   563
by (etac analz.induct 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   564
by (ALLGOALS (blast_tac (claset() addIs [impOfSubs analz_mono])));
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   565
val lemma = result();
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   566
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   567
Goal "analz (UN i:A. analz (H i)) = analz (UN i:A. H i)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   568
by (blast_tac (claset() addIs [lemma, impOfSubs analz_mono]) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   569
qed "analz_UN_analz";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   570
Addsimps [analz_UN_analz];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   571
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   572
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   573
(**** Inductive relation "synth" ****)
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   574
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   575
AddIs  synth.intrs;
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   576
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   577
(*NO Agent_synth, as any Agent name can be synthesized.  Ditto for Number*)
6141
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 5983
diff changeset
   578
val Nonce_synth = synth.mk_cases "Nonce n : synth H";
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 5983
diff changeset
   579
val Key_synth   = synth.mk_cases "Key K : synth H";
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 5983
diff changeset
   580
val Hash_synth  = synth.mk_cases "Hash X : synth H";
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 5983
diff changeset
   581
val MPair_synth = synth.mk_cases "{|X,Y|} : synth H";
a6922171b396 removal of the (thm list) argument of mk_cases
paulson
parents: 5983
diff changeset
   582
val Crypt_synth = synth.mk_cases "Crypt K X : synth H";
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   583
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   584
AddSEs [Nonce_synth, Key_synth, Hash_synth, MPair_synth, Crypt_synth];
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   585
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   586
Goal "H <= synth(H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   587
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   588
qed "synth_increasing";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   589
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   590
(*Monotonicity*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   591
Goalw synth.defs "G<=H ==> synth(G) <= synth(H)";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   592
by (rtac lfp_mono 1);
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   593
by (REPEAT (ares_tac basic_monos 1));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   594
qed "synth_mono";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   595
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   596
(** Unions **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   597
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   598
(*Converse fails: we can synth more from the union than from the 
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   599
  separate parts, building a compound message using elements of each.*)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   600
Goal "synth(G) Un synth(H) <= synth(G Un H)";
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   601
by (REPEAT (ares_tac [Un_least, synth_mono, Un_upper1, Un_upper2] 1));
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   602
qed "synth_Un";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   603
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   604
Goal "insert X (synth H) <= synth(insert X H)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   605
by (blast_tac (claset() addIs [impOfSubs synth_mono]) 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   606
qed "synth_insert";
1885
a18a6dc14f76 Auth proofs work up to the XXX...
paulson
parents: 1852
diff changeset
   607
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   608
(** Idempotence and transitivity **)
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   609
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   610
Goal "X: synth (synth H) ==> X: synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   611
by (etac synth.induct 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   612
by (ALLGOALS Blast_tac);
2922
580647a879cf Using Blast_tac
paulson
parents: 2891
diff changeset
   613
qed "synth_synthD";
580647a879cf Using Blast_tac
paulson
parents: 2891
diff changeset
   614
AddSDs [synth_synthD];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   615
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   616
Goal "synth (synth H) = synth H";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   617
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   618
qed "synth_idem";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   619
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   620
Goal "[| X: synth G;  G <= synth H |] ==> X: synth H";
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   621
by (dtac synth_mono 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   622
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   623
qed "synth_trans";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   624
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   625
(*Cut; Lemma 2 of Lowe*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   626
Goal "[| Y: synth (insert X H);  X: synth H |] ==> Y: synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   627
by (etac synth_trans 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   628
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   629
qed "synth_cut";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   630
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   631
Goal "Agent A : synth H";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   632
by (Blast_tac 1);
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   633
qed "Agent_synth";
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   634
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   635
Goal "Number n : synth H";
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   636
by (Blast_tac 1);
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   637
qed "Number_synth";
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   638
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   639
Goal "(Nonce N : synth H) = (Nonce N : H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   640
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   641
qed "Nonce_synth_eq";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   642
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   643
Goal "(Key K : synth H) = (Key K : H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   644
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   645
qed "Key_synth_eq";
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   646
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   647
Goal "Key K ~: H ==> (Crypt K X : synth H) = (Crypt K X : H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   648
by (Blast_tac 1);
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   649
qed "Crypt_synth_eq";
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   650
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   651
Addsimps [Agent_synth, Number_synth, 
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   652
	  Nonce_synth_eq, Key_synth_eq, Crypt_synth_eq];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   653
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   654
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   655
Goalw [keysFor_def]
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   656
    "keysFor (synth H) = keysFor H Un invKey``{K. Key K : H}";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   657
by (Blast_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   658
qed "keysFor_synth";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   659
Addsimps [keysFor_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   660
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   661
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   662
(*** Combinations of parts, analz and synth ***)
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   663
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   664
Goal "parts (synth H) = parts H Un synth H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   665
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   666
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   667
by (etac parts.induct 1);
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   668
by (ALLGOALS
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   669
    (blast_tac (claset() addIs ((synth_increasing RS parts_mono RS subsetD)
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   670
				::parts.intrs))));
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   671
qed "parts_synth";
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   672
Addsimps [parts_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   673
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   674
Goal "analz (analz G Un H) = analz (G Un H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   675
by (REPEAT_FIRST (resolve_tac [equalityI, analz_subset_cong]));
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   676
by (ALLGOALS Simp_tac);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   677
qed "analz_analz_Un";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   678
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   679
Goal "analz (synth G Un H) = analz (G Un H) Un synth G";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   680
by (rtac equalityI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   681
by (rtac subsetI 1);
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   682
by (etac analz.induct 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   683
by (blast_tac (claset() addIs [impOfSubs analz_mono]) 5);
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   684
by (ALLGOALS (blast_tac (claset() addIs analz.intrs)));
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   685
qed "analz_synth_Un";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   686
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   687
Goal "analz (synth H) = analz H Un synth H";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   688
by (cut_inst_tac [("H","{}")] analz_synth_Un 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   689
by (Full_simp_tac 1);
1913
2809adb15eb0 Renaming of functions, and tidying
paulson
parents: 1893
diff changeset
   690
qed "analz_synth";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   691
Addsimps [analz_analz_Un, analz_synth_Un, analz_synth];
1839
199243afac2b Proving safety properties of authentication protocols
paulson
parents:
diff changeset
   692
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   693
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   694
(** For reasoning about the Fake rule in traces **)
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   695
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   696
Goal "X: G ==> parts(insert X H) <= parts G Un parts H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   697
by (rtac ([parts_mono, parts_Un_subset2] MRS subset_trans) 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   698
by (Blast_tac 1);
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   699
qed "parts_insert_subset_Un";
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   700
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   701
(*More specifically for Fake.  Very occasionally we could do with a version
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   702
  of the form  parts{X} <= synth (analz H) Un parts H *)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   703
Goal "X: synth (analz H) ==> \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   704
\     parts (insert X H) <= synth (analz H) Un parts H";
2032
1bbf1bdcaf56 Introduction of "lost" argument
paulson
parents: 2028
diff changeset
   705
by (dtac parts_insert_subset_Un 1);
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   706
by (Full_simp_tac 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   707
by (Blast_tac 1);
1946
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   708
qed "Fake_parts_insert";
b59a3d686436 New theorems for Fake case
paulson
parents: 1929
diff changeset
   709
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   710
(*H is sometimes (Key `` KK Un spies evs), so can't put G=H*)
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   711
Goal "X: synth (analz G) ==> \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   712
\     analz (insert X H) <= synth (analz G) Un analz (G Un H)";
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   713
by (rtac subsetI 1);
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   714
by (subgoal_tac "x : analz (synth (analz G) Un H)" 1);
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   715
by (blast_tac (claset() addIs [impOfSubs analz_mono,
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   716
			       impOfSubs (analz_mono RS synth_mono)]) 2);
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   717
by (Full_simp_tac 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   718
by (Blast_tac 1);
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   719
qed "Fake_analz_insert";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   720
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   721
Goal "(X: analz H & X: parts H) = (X: analz H)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   722
by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   723
val analz_conj_parts = result();
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   724
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   725
Goal "(X: analz H | X: parts H) = (X: parts H)";
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   726
by (blast_tac (claset() addIs [impOfSubs analz_subset_parts]) 1);
2011
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   727
val analz_disj_parts = result();
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   728
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   729
AddIffs [analz_conj_parts, analz_disj_parts];
d9af64c26be6 New laws for messages
paulson
parents: 1998
diff changeset
   730
1998
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   731
(*Without this equation, other rules for synth and analz would yield
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   732
  redundant cases*)
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   733
Goal "({|X,Y|} : synth (analz H)) = \
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   734
\     (X : synth (analz H) & Y : synth (analz H))";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   735
by (Blast_tac 1);
1998
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   736
qed "MPair_synth_analz";
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   737
f8230821f1e8 Reordering of premises for cut theorems, and new law MPair_synth_analz
paulson
parents: 1994
diff changeset
   738
AddIffs [MPair_synth_analz];
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   739
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   740
Goal "[| Key K : analz H;  Key (invKey K) : analz H |] \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   741
\      ==> (Crypt K X : synth (analz H)) = (X : synth (analz H))";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   742
by (Blast_tac 1);
2154
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   743
qed "Crypt_synth_analz";
913b4fc7670a New, purely illustrative result Crypt_synth_analz
paulson
parents: 2102
diff changeset
   744
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   745
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   746
Goal "X ~: synth (analz H) \
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   747
\     ==> (Hash{|X,Y|} : synth (analz H)) = (Hash{|X,Y|} : analz H)";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   748
by (Blast_tac 1);
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   749
qed "Hash_synth_analz";
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   750
Addsimps [Hash_synth_analz];
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   751
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   752
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   753
(**** HPair: a combination of Hash and MPair ****)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   754
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   755
(*** Freeness ***)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   756
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   757
Goalw [HPair_def] "Agent A ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   758
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   759
qed "Agent_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   760
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   761
Goalw [HPair_def] "Nonce N ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   762
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   763
qed "Nonce_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   764
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   765
Goalw [HPair_def] "Number N ~= Hash[X] Y";
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   766
by (Simp_tac 1);
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   767
qed "Number_neq_HPair";
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   768
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   769
Goalw [HPair_def] "Key K ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   770
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   771
qed "Key_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   772
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   773
Goalw [HPair_def] "Hash Z ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   774
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   775
qed "Hash_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   776
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   777
Goalw [HPair_def] "Crypt K X' ~= Hash[X] Y";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   778
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   779
qed "Crypt_neq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   780
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   781
val HPair_neqs = [Agent_neq_HPair, Nonce_neq_HPair, Number_neq_HPair, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   782
                  Key_neq_HPair, Hash_neq_HPair, Crypt_neq_HPair];
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   783
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   784
AddIffs HPair_neqs;
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   785
AddIffs (HPair_neqs RL [not_sym]);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   786
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   787
Goalw [HPair_def] "(Hash[X'] Y' = Hash[X] Y) = (X' = X & Y'=Y)";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   788
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   789
qed "HPair_eq";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   790
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   791
Goalw [HPair_def] "({|X',Y'|} = Hash[X] Y) = (X' = Hash{|X,Y|} & Y'=Y)";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   792
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   793
qed "MPair_eq_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   794
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   795
Goalw [HPair_def] "(Hash[X] Y = {|X',Y'|}) = (X' = Hash{|X,Y|} & Y'=Y)";
4477
b3e5857d8d99 New Auto_tac (by Oheimb), and new syntax (without parens), and expandshort
paulson
parents: 4422
diff changeset
   796
by Auto_tac;
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   797
qed "HPair_eq_MPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   798
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   799
AddIffs [HPair_eq, MPair_eq_HPair, HPair_eq_MPair];
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   800
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   801
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   802
(*** Specialized laws, proved in terms of those for Hash and MPair ***)
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   803
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   804
Goalw [HPair_def] "keysFor (insert (Hash[X] Y) H) = keysFor H";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   805
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   806
qed "keysFor_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   807
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   808
Goalw [HPair_def]
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   809
    "parts (insert (Hash[X] Y) H) = \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   810
\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (parts (insert Y H)))";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   811
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   812
qed "parts_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   813
5076
fbc9d95b62ba Ran isatool fixgoal
paulson
parents: 5055
diff changeset
   814
Goalw [HPair_def]
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   815
    "analz (insert (Hash[X] Y) H) = \
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   816
\    insert (Hash[X] Y) (insert (Hash{|X,Y|}) (analz (insert Y H)))";
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   817
by (Simp_tac 1);
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   818
qed "analz_insert_HPair";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   819
5114
c729d4c299c1 Deleted leading parameters thanks to new Goal command
paulson
parents: 5102
diff changeset
   820
Goalw [HPair_def] "X ~: synth (analz H) \
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   821
\   ==> (Hash[X] Y : synth (analz H)) = \
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   822
\       (Hash {|X, Y|} : analz H & Y : synth (analz H))";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   823
by (Simp_tac 1);
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   824
by (Blast_tac 1);
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   825
qed "HPair_synth_analz";
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   826
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   827
Addsimps [keysFor_insert_HPair, parts_insert_HPair, analz_insert_HPair, 
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   828
          HPair_synth_analz, HPair_synth_analz];
2484
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   829
596a5b5a68ff Incorporation of HPair into Message
paulson
parents: 2415
diff changeset
   830
1929
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   831
(*We do NOT want Crypt... messages broken up in protocols!!*)
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   832
Delrules partsEs;
f0839bab4b00 Working version of NS, messages 1-3, WITH INTERLEAVING
paulson
parents: 1913
diff changeset
   833
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   834
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   835
(** Rewrites to push in Key and Crypt messages, so that other messages can
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   836
    be pulled out using the analz_insert rules **)
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   837
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   838
fun insComm thy x y = read_instantiate_sg (sign_of thy) [("x",x), ("y",y)] 
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   839
                          insert_commute;
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   840
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   841
val pushKeys = map (insComm thy "Key ?K") 
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   842
                   ["Agent ?C", "Nonce ?N", "Number ?N", 
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   843
		    "Hash ?X", "MPair ?X ?Y", "Crypt ?X ?K'"];
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   844
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   845
val pushCrypts = map (insComm thy "Crypt ?X ?K") 
3668
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   846
                     ["Agent ?C", "Nonce ?N", "Number ?N", 
a39baf59ea47 Split base cases from "msg" to "atomic" in order
paulson
parents: 3650
diff changeset
   847
		      "Hash ?X'", "MPair ?X' ?Y"];
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   848
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   849
(*Cannot be added with Addsimps -- we don't always want to re-order messages*)
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   850
val pushes = pushKeys@pushCrypts;
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   851
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   852
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   853
(*** Tactics useful for many protocol proofs ***)
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   854
3470
8160cc3f6d40 Added a comment
paulson
parents: 3449
diff changeset
   855
(*Prove base case (subgoal i) and simplify others.  A typical base case
3683
aafe719dff14 Global change: lost->bad and sees Spy->spies
paulson
parents: 3668
diff changeset
   856
  concerns  Crypt K X ~: Key``shrK``bad  and cannot be proved by rewriting
3470
8160cc3f6d40 Added a comment
paulson
parents: 3449
diff changeset
   857
  alone.*)
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   858
fun prove_simple_subgoals_tac i = 
5421
01fc8d6a40f2 small simplification to not_Says_to_self
paulson
parents: 5223
diff changeset
   859
    Force_tac i THEN ALLGOALS Asm_simp_tac;
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   860
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   861
fun Fake_parts_insert_tac i = 
4556
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   862
    blast_tac (claset() addIs [parts_insertI]
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   863
			addDs [impOfSubs analz_subset_parts,
e7a4683c0026 Tidying, mostly to do with handling a more specific version of Fake_parts_insert
paulson
parents: 4477
diff changeset
   864
			       impOfSubs Fake_parts_insert]) i;
3121
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   865
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   866
(*Apply rules to break down assumptions of the form
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   867
  Y : parts(insert X H)  and  Y : analz(insert X H)
cbb6c0c1c58a Conversion to use blast_tac (with other improvements)
paulson
parents: 3102
diff changeset
   868
*)
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   869
val Fake_insert_tac = 
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   870
    dresolve_tac [impOfSubs Fake_analz_insert,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   871
                  impOfSubs Fake_parts_insert] THEN'
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   872
    eresolve_tac [asm_rl, synth.Inj];
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   873
3702
0fc9bf467f95 clarify_tac and a new simprule
paulson
parents: 3684
diff changeset
   874
fun Fake_insert_simp_tac i = 
0fc9bf467f95 clarify_tac and a new simprule
paulson
parents: 3684
diff changeset
   875
    REPEAT (Fake_insert_tac i) THEN Asm_full_simp_tac i;
0fc9bf467f95 clarify_tac and a new simprule
paulson
parents: 3684
diff changeset
   876
0fc9bf467f95 clarify_tac and a new simprule
paulson
parents: 3684
diff changeset
   877
3449
6b17f82bbf01 New comments; a tidied proof
paulson
parents: 3431
diff changeset
   878
(*Analysis of Fake cases.  Also works for messages that forward unknown parts,
6b17f82bbf01 New comments; a tidied proof
paulson
parents: 3431
diff changeset
   879
  but this application is no longer necessary if analz_insert_eq is used.
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   880
  Abstraction over i is ESSENTIAL: it delays the dereferencing of claset
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   881
  DEPENDS UPON "X" REFERRING TO THE FRADULENT MESSAGE *)
4735
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   882
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   883
val atomic_spy_analz_tac = SELECT_GOAL
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   884
    (Fake_insert_simp_tac 1
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   885
     THEN
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   886
     IF_UNSOLVED (Blast.depth_tac
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   887
		  (claset() addIs [analz_insertI,
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   888
				   impOfSubs analz_subset_parts]) 4 1));
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   889
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   890
fun spy_analz_tac i =
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   891
  DETERM
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   892
   (SELECT_GOAL
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   893
     (EVERY 
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   894
      [  (*push in occurrences of X...*)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   895
       (REPEAT o CHANGED)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   896
           (res_inst_tac [("x1","X")] (insert_commute RS ssubst) 1),
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   897
       (*...allowing further simplifications*)
4686
74a12e86b20b Removed `addsplits [expand_if]'
nipkow
parents: 4651
diff changeset
   898
       Simp_tac 1,
3476
1be4fee7606b spy_analz_tac: Restored iffI to the list of rules used to break down
paulson
parents: 3470
diff changeset
   899
       REPEAT (FIRSTGOAL (resolve_tac [allI,impI,notI,conjI,iffI])),
4735
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   900
       DEPTH_SOLVE (atomic_spy_analz_tac 1)]) i);
6d544b44a70e spy_analz_tac now handles individual conjuncts properly
paulson
parents: 4686
diff changeset
   901
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   902
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   903
(** Useful in many uniqueness proofs **)
2327
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   904
fun ex_strip_tac i = REPEAT (swap_res_tac [exI, conjI] i) THEN 
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   905
                     assume_tac (i+1);
00ac25b2791d Moved much common material to Message.ML
paulson
parents: 2284
diff changeset
   906
6915
4ab8e31a8421 Now if_weak_cong is a standard congruence rule
paulson
parents: 6141
diff changeset
   907
(*Apply the EX-ALL quantification to prove uniqueness theorems in 
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   908
  their standard form*)
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   909
fun prove_unique_tac lemma = 
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   910
  EVERY' [dtac lemma,
2516
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   911
          REPEAT o (mp_tac ORELSE' eresolve_tac [asm_rl,exE]),
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   912
          (*Duplicate the assumption*)
4d68fbe6378b Now with Andy Gordon's treatment of freshness to replace newN/K
paulson
parents: 2484
diff changeset
   913
          forw_inst_tac [("psi", "ALL C.?P(C)")] asm_rl,
4091
771b1f6422a8 isatool fixclasimp;
wenzelm
parents: 3919
diff changeset
   914
          Blast.depth_tac (claset() addSDs [spec]) 0];
2415
46de4b035f00 New tactic: prove_unique_tac
paulson
parents: 2373
diff changeset
   915
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   916
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   917
(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*)
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   918
goal Set.thy "A Un (B Un A) = B Un A";
2891
d8f254ad1ab9 Calls Blast_tac
paulson
parents: 2637
diff changeset
   919
by (Blast_tac 1);
2373
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   920
val Un_absorb3 = result();
490ffa16952e Addition of the Hash constructor
paulson
parents: 2327
diff changeset
   921
Addsimps [Un_absorb3];
3514
eb16b8e8d872 Moved some declarations to Message from Public and Shared
paulson
parents: 3476
diff changeset
   922
eb16b8e8d872 Moved some declarations to Message from Public and Shared
paulson
parents: 3476
diff changeset
   923
(*By default only o_apply is built-in.  But in the presence of eta-expansion
eb16b8e8d872 Moved some declarations to Message from Public and Shared
paulson
parents: 3476
diff changeset
   924
  this means that some terms displayed as (f o g) will be rewritten, and others
eb16b8e8d872 Moved some declarations to Message from Public and Shared
paulson
parents: 3476
diff changeset
   925
  will not!*)
eb16b8e8d872 Moved some declarations to Message from Public and Shared
paulson
parents: 3476
diff changeset
   926
Addsimps [o_def];