--- a/src/HOL/Auth/Message.thy Fri Mar 02 13:26:55 2001 +0100
+++ b/src/HOL/Auth/Message.thy Mon Mar 05 12:31:31 2001 +0100
@@ -11,7 +11,7 @@
files ("Message_lemmas.ML"):
(*Eliminates a commonly-occurring expression*)
-lemma [simp] : "~ (ALL x. x~=y)"
+lemma [simp] : "~ (\<forall> x. x\<noteq>y)"
by blast
(*Needed occasionally with spy_analz_tac, e.g. in analz_insert_Key_newK*)
@@ -66,17 +66,17 @@
(*Keys useful to decrypt elements of a message set*)
keysFor :: "msg set => key set"
- "keysFor H == invKey ` {K. EX X. Crypt K X : H}"
+ "keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
(** Inductive definition of all "parts" of a message. **)
consts parts :: "msg set => msg set"
inductive "parts H"
intros
- Inj [intro] : "X: H ==> X : parts H"
- Fst: "{|X,Y|} : parts H ==> X : parts H"
- Snd: "{|X,Y|} : parts H ==> Y : parts H"
- Body: "Crypt K X : parts H ==> X : parts H"
+ Inj [intro]: "X \<in> H ==> X \<in> parts H"
+ Fst: "{|X,Y|} \<in> parts H ==> X \<in> parts H"
+ Snd: "{|X,Y|} \<in> parts H ==> Y \<in> parts H"
+ Body: "Crypt K X \<in> parts H ==> X \<in> parts H"
(*Monotonicity*)
@@ -94,11 +94,11 @@
consts analz :: "msg set => msg set"
inductive "analz H"
intros
- Inj [intro,simp] : "X: H ==> X: analz H"
- Fst: "{|X,Y|} : analz H ==> X : analz H"
- Snd: "{|X,Y|} : analz H ==> Y : analz H"
+ Inj [intro,simp] : "X \<in> H ==> X \<in> analz H"
+ Fst: "{|X,Y|} \<in> analz H ==> X \<in> analz H"
+ Snd: "{|X,Y|} \<in> analz H ==> Y \<in> analz H"
Decrypt [dest]:
- "[|Crypt K X : analz H; Key(invKey K): analz H|] ==> X : analz H"
+ "[|Crypt K X \<in> analz H; Key(invKey K): analz H|] ==> X \<in> analz H"
(*Monotonicity; Lemma 1 of Lowe's paper*)
@@ -116,12 +116,12 @@
consts synth :: "msg set => msg set"
inductive "synth H"
intros
- Inj [intro]: "X: H ==> X: synth H"
- Agent [intro]: "Agent agt : synth H"
- Number [intro]: "Number n : synth H"
- Hash [intro]: "X: synth H ==> Hash X : synth H"
- MPair [intro]: "[|X: synth H; Y: synth H|] ==> {|X,Y|} : synth H"
- Crypt [intro]: "[|X: synth H; Key(K) : H|] ==> Crypt K X : synth H"
+ Inj [intro]: "X \<in> H ==> X \<in> synth H"
+ Agent [intro]: "Agent agt \<in> synth H"
+ Number [intro]: "Number n \<in> synth H"
+ Hash [intro]: "X \<in> synth H ==> Hash X \<in> synth H"
+ MPair [intro]: "[|X \<in> synth H; Y \<in> synth H|] ==> {|X,Y|} \<in> synth H"
+ Crypt [intro]: "[|X \<in> synth H; Key(K) \<in> H|] ==> Crypt K X \<in> synth H"
(*Monotonicity*)
lemma synth_mono: "G<=H ==> synth(G) <= synth(H)"
@@ -131,11 +131,11 @@
done
(*NO Agent_synth, as any Agent name can be synthesized. Ditto for Number*)
-inductive_cases Nonce_synth [elim!]: "Nonce n : synth H"
-inductive_cases Key_synth [elim!]: "Key K : synth H"
-inductive_cases Hash_synth [elim!]: "Hash X : synth H"
-inductive_cases MPair_synth [elim!]: "{|X,Y|} : synth H"
-inductive_cases Crypt_synth [elim!]: "Crypt K X : synth H"
+inductive_cases Nonce_synth [elim!]: "Nonce n \<in> synth H"
+inductive_cases Key_synth [elim!]: "Key K \<in> synth H"
+inductive_cases Hash_synth [elim!]: "Hash X \<in> synth H"
+inductive_cases MPair_synth [elim!]: "{|X,Y|} \<in> synth H"
+inductive_cases Crypt_synth [elim!]: "Crypt K X \<in> synth H"
use "Message_lemmas.ML"