lexing: thys/Re1.thy@39cef7b9212a (annotated)

56 5bc72d6d633d updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 55 diff changeset	1
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	2	theory Re1
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	3	imports "Main"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	4	begin
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	5
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	6	section {* Sequential Composition of Sets *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	7
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	8	definition
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	9	Sequ :: "string set \<Rightarrow> string set \<Rightarrow> string set" ("_ ;; _" [100,100] 100)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	10	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	11	"A ;; B = {s1 @ s2 \| s1 s2. s1 \<in> A \<and> s2 \<in> B}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	12
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	13	text {* Two Simple Properties about Sequential Composition *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	14
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	15	lemma seq_empty [simp]:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	16	shows "A ;; {[]} = A"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	17	and "{[]} ;; A = A"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	18	by (simp_all add: Sequ_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	19
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	20	lemma seq_null [simp]:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	21	shows "A ;; {} = {}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	22	and "{} ;; A = {}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	23	by (simp_all add: Sequ_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	24
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	25	section {* Regular Expressions *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	26
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	27	datatype rexp =
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	28	NULL
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	29	\| EMPTY
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	30	\| CHAR char
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	31	\| SEQ rexp rexp
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	32	\| ALT rexp rexp
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	33
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	34	fun SEQS :: "rexp \<Rightarrow> rexp list \<Rightarrow> rexp"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	35	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	36	"SEQS r [] = r"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	37	\| "SEQS r (r'#rs) = SEQ r (SEQS r' rs)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	38
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	39	section {* Semantics of Regular Expressions *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	40
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	41	fun
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	42	L :: "rexp \<Rightarrow> string set"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	43	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	44	"L (NULL) = {}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	45	\| "L (EMPTY) = {[]}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	46	\| "L (CHAR c) = {[c]}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	47	\| "L (SEQ r1 r2) = (L r1) ;; (L r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	48	\| "L (ALT r1 r2) = (L r1) \<union> (L r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	49
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	50	fun
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	51	nullable :: "rexp \<Rightarrow> bool"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	52	where
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	53	"nullable (NULL) = False"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	54	\| "nullable (EMPTY) = True"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	55	\| "nullable (CHAR c) = False"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	56	\| "nullable (ALT r1 r2) = (nullable r1 \<or> nullable r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	57	\| "nullable (SEQ r1 r2) = (nullable r1 \<and> nullable r2)"
70 7b78e093f559 merges fahad parents: 68 diff changeset	58
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	59	fun
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	60	nullable_left :: "rexp \<Rightarrow> bool"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	61	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	62	"nullable_left (NULL) = False"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	63	\| "nullable_left (EMPTY) = True"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	64	\| "nullable_left (CHAR c) = False"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	65	\| "nullable_left (ALT r1 r2) = (nullable_left r1 \<or> nullable_left r2)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	66	\| "nullable_left (SEQ r1 r2) = nullable_left r1"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	67
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	68	lemma nullable_left:
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	69	"nullable r \<Longrightarrow> nullable_left r"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	70	apply(induct r)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	71	apply(auto)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	72	done
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	73
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	74
54 45274393f28c no changes fahad parents: 53 diff changeset	75	value "L(CHAR c)"
45274393f28c no changes fahad parents: 53 diff changeset	76	value "L(SEQ(CHAR c)(CHAR b))"
45274393f28c no changes fahad parents: 53 diff changeset	77
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	78	lemma nullable_correctness:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	79	shows "nullable r \<longleftrightarrow> [] \<in> (L r)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	80	apply (induct r)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	81	apply(auto simp add: Sequ_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	82	done
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	83
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	84	section {* Values *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	85
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	86	datatype val =
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	87	Void
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	88	\| Char char
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	89	\| Seq val val
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	90	\| Right val
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	91	\| Left val
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	92
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	93	fun Seqs :: "val \<Rightarrow> val list \<Rightarrow> val"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	94	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	95	"Seqs v [] = v"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	96	\| "Seqs v (v'#vs) = Seq v (Seqs v' vs)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	97
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	98
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	99	section {* The string behind a value *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	100
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	101	fun flat :: "val \<Rightarrow> string"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	102	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	103	"flat(Void) = []"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	104	\| "flat(Char c) = [c]"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	105	\| "flat(Left v) = flat(v)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	106	\| "flat(Right v) = flat(v)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	107	\| "flat(Seq v1 v2) = flat(v1) @ flat(v2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	108
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	109	fun flat_left :: "val \<Rightarrow> string"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	110	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	111	"flat_left(Void) = []"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	112	\| "flat_left(Char c) = [c]"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	113	\| "flat_left(Left v) = flat_left(v)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	114	\| "flat_left(Right v) = flat_left(v)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	115	\| "flat_left(Seq v1 v2) = flat_left(v1)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	116
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	117	fun flat_right :: "val \<Rightarrow> string"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	118	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	119	"flat_right(Void) = []"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	120	\| "flat_right(Char c) = [c]"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	121	\| "flat_right(Left v) = flat(v)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	122	\| "flat_right(Right v) = flat(v)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	123	\| "flat_right(Seq v1 v2) = flat(v2)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	124
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	125	fun head :: "val \<Rightarrow> string"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	126	where
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	127	"head(Void) = []"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	128	\| "head(Char c) = [c]"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	129	\| "head(Left v) = head(v)"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	130	\| "head(Right v) = head(v)"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	131	\| "head(Seq v1 v2) = head v1"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	132
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	133	fun flats :: "val \<Rightarrow> string list"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	134	where
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	135	"flats(Void) = [[]]"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	136	\| "flats(Char c) = [[c]]"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	137	\| "flats(Left v) = flats(v)"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	138	\| "flats(Right v) = flats(v)"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	139	\| "flats(Seq v1 v2) = (flats v1) @ (flats v2)"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	140
70 7b78e093f559 merges fahad parents: 68 diff changeset	141	value "flats(Seq(Char c)(Char b))"
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	142
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	143	inductive StrOrd :: "string list \<Rightarrow> string list \<Rightarrow> bool" ("_ \<sqsupset> _" [100, 100] 100)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	144	where
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	145	"[] \<sqsupset> []"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	146	\| "xs \<sqsupset> ys \<Longrightarrow> (x#xs) \<sqsupset> (x#ys)"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	147	\| "length x \<ge> length y \<Longrightarrow> (x#xs) \<sqsupset> (y#xs)"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	148
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	149	lemma StrOrd_append:
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	150	"xs \<sqsupset> ys \<Longrightarrow> (zs @ xs) \<sqsupset> (zs @ ys)"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	151	apply(induct zs)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	152	apply(auto intro: StrOrd.intros)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	153	done
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	154
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	155	section {* Relation between values and regular expressions *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	156
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	157	inductive Prf :: "val \<Rightarrow> rexp \<Rightarrow> bool" ("\<turnstile> _ : _" [100, 100] 100)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	158	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	159	"\<lbrakk>\<turnstile> v1 : r1; \<turnstile> v2 : r2\<rbrakk> \<Longrightarrow> \<turnstile> Seq v1 v2 : SEQ r1 r2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	160	\| "\<turnstile> v1 : r1 \<Longrightarrow> \<turnstile> Left v1 : ALT r1 r2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	161	\| "\<turnstile> v2 : r2 \<Longrightarrow> \<turnstile> Right v2 : ALT r1 r2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	162	\| "\<turnstile> Void : EMPTY"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	163	\| "\<turnstile> Char c : CHAR c"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	164
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	165	inductive Prfs :: "val list \<Rightarrow> rexp list \<Rightarrow> bool" ("\<Turnstile> _ : _" [100, 100] 100)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	166	where
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	167	"\<Turnstile> [] : []"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	168	\| "\<lbrakk>\<turnstile>v : r; \<Turnstile> vs : rs\<rbrakk> \<Longrightarrow> \<Turnstile> (v#vs) : (r#rs)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	169
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	170	fun mkeps :: "rexp \<Rightarrow> val"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	171	where
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	172	"mkeps(EMPTY) = Void"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	173	\| "mkeps(SEQ r1 r2) = Seq (mkeps r1) (mkeps r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	174	\| "mkeps(ALT r1 r2) = (if nullable(r1) then Left (mkeps r1) else Right (mkeps r2))"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	175
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	176	lemma mkeps_nullable:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	177	assumes "nullable(r)" shows "\<turnstile> mkeps r : r"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	178	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	179	apply(induct rule: nullable.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	180	apply(auto intro: Prf.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	181	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	182
54 45274393f28c no changes fahad parents: 53 diff changeset	183	value "flat(Seq(Char c)(Char b))"
45274393f28c no changes fahad parents: 53 diff changeset	184	value "flat(Right(Void))"
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	185
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	186	lemma mkeps_flat:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	187	assumes "nullable(r)" shows "flat (mkeps r) = []"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	188	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	189	apply(induct rule: nullable.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	190	apply(auto)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	191	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	192
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	193	lemma mkeps_flat_left:
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	194	assumes "nullable(r)" shows "flat_left (mkeps r) = []"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	195	using assms
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	196	apply(induct rule: nullable.induct)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	197	apply(auto)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	198	done
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	199
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	200
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	201
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	202	text {*
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	203	The value mkeps returns is always the correct POSIX
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	204	value.
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	205	*}
70 7b78e093f559 merges fahad parents: 68 diff changeset	206
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	207
70 7b78e093f559 merges fahad parents: 68 diff changeset	208
7b78e093f559 merges fahad parents: 68 diff changeset	209
54 45274393f28c no changes fahad parents: 53 diff changeset	210
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	211	lemma Prf_flat_L:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	212	assumes "\<turnstile> v : r" shows "flat v \<in> L r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	213	using assms
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	214	apply(induct v r rule: Prf.induct)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	215	apply(auto simp add: Sequ_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	216	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	217
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	218	lemma L_flat_Prf:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	219	"L(r) = {flat v \| v. \<turnstile> v : r}"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	220	apply(induct r)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	221	apply(auto dest: Prf_flat_L simp add: Sequ_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	222	apply (metis Prf.intros(4) flat.simps(1))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	223	apply (metis Prf.intros(5) flat.simps(2))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	224	apply (metis Prf.intros(1) flat.simps(5))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	225	apply (metis Prf.intros(2) flat.simps(3))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	226	apply (metis Prf.intros(3) flat.simps(4))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	227	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	228	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	229	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	230
70 7b78e093f559 merges fahad parents: 68 diff changeset	231	definition prefix :: "string \<Rightarrow> string \<Rightarrow> bool" ("_ \<sqsubset> _" [100, 100] 100)
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	232	where
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	233	"s1 \<sqsubset> s2 \<equiv> \<exists>s3. s1 @ s3 = s2"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	234
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	235	section {* Ordering of values *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	236
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	237	inductive ValOrd :: "val \<Rightarrow> rexp \<Rightarrow> val \<Rightarrow> bool" ("_ \<succ>_ _" [100, 100, 100] 100)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	238	where
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	239	"v2 \<succ>r2 v2' \<Longrightarrow> (Seq v1 v2) \<succ>(SEQ r1 r2) (Seq v1 v2')"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	240	\| "\<lbrakk>v1 \<succ>r1 v1'; v1 \<noteq> v1'\<rbrakk> \<Longrightarrow> (Seq v1 v2) \<succ>(SEQ r1 r2) (Seq v1' v2')"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	241	\| "length (flat v1) \<ge> length (flat v2) \<Longrightarrow> (Left v1) \<succ>(ALT r1 r2) (Right v2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	242	\| "length (flat v2) > length (flat v1) \<Longrightarrow> (Right v2) \<succ>(ALT r1 r2) (Left v1)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	243	\| "v2 \<succ>r2 v2' \<Longrightarrow> (Right v2) \<succ>(ALT r1 r2) (Right v2')"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	244	\| "v1 \<succ>r1 v1' \<Longrightarrow> (Left v1) \<succ>(ALT r1 r2) (Left v1')"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	245	\| "Void \<succ>EMPTY Void"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	246	\| "(Char c) \<succ>(CHAR c) (Char c)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	247
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	248	inductive ValOrd2 :: "val \<Rightarrow> val \<Rightarrow> bool" ("_ 2\<succ> _" [100, 100] 100)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	249	where
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	250	"v2 2\<succ> v2' \<Longrightarrow> (Seq v1 v2) 2\<succ> (Seq v1 v2')"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	251	\| "\<lbrakk>v1 2\<succ> v1'; v1 \<noteq> v1'\<rbrakk> \<Longrightarrow> (Seq v1 v2) 2\<succ> (Seq v1' v2')"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	252	\| "length (flat v1) \<ge> length (flat v2) \<Longrightarrow> (Left v1) 2\<succ> (Right v2)"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	253	\| "length (flat v2) > length (flat v1) \<Longrightarrow> (Right v2) 2\<succ> (Left v1)"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	254	\| "v2 2\<succ> v2' \<Longrightarrow> (Right v2) 2\<succ> (Right v2')"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	255	\| "v1 2\<succ> v1' \<Longrightarrow> (Left v1) 2\<succ> (Left v1')"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	256	\| "Void 2\<succ> Void"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	257	\| "(Char c) 2\<succ> (Char c)"
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	258
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	259	lemma Ord1:
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	260	"v1 \<succ>r v2 \<Longrightarrow> v1 2\<succ> v2"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	261	apply(induct rule: ValOrd.induct)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	262	apply(auto intro: ValOrd2.intros)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	263	done
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	264
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	265	lemma Ord2:
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	266	"v1 2\<succ> v2 \<Longrightarrow> \<exists>r. v1 \<succ>r v2"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	267	apply(induct v1 v2 rule: ValOrd2.induct)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	268	apply(auto intro: ValOrd.intros)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	269	done
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	270
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	271	lemma Ord3:
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	272	"\<lbrakk>v1 2\<succ> v2; \<turnstile> v1 : r\<rbrakk> \<Longrightarrow> v1 \<succ>r v2"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	273	apply(induct v1 v2 arbitrary: r rule: ValOrd2.induct)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	274	apply(auto intro: ValOrd.intros elim: Prf.cases)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	275	done
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	276
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	277
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	278	lemma ValOrd_refl:
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	279	assumes "\<turnstile> v : r"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	280	shows "v \<succ>r v"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	281	using assms
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	282	apply(induct)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	283	apply(auto intro: ValOrd.intros)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	284	done
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	285
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	286	section {* Posix definition *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	287
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	288	definition POSIX :: "val \<Rightarrow> rexp \<Rightarrow> bool"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	289	where
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	290	"POSIX v r \<equiv> (\<turnstile> v : r \<and> (\<forall>v'. (\<turnstile> v' : r \<and> flat v = flat v') \<longrightarrow> v \<succ>r v'))"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	291
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	292	definition POSIX2 :: "val \<Rightarrow> rexp \<Rightarrow> bool"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	293	where
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	294	"POSIX2 v r \<equiv> (\<turnstile> v : r \<and> (\<forall>v'. (\<turnstile> v' : r \<and> flat v = flat v') \<longrightarrow> v 2\<succ> v'))"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	295
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	296	lemma "POSIX v r = POSIX2 v r"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	297	unfolding POSIX_def POSIX2_def
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	298	apply(auto)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	299	apply(rule Ord1)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	300	apply(auto)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	301	apply(rule Ord3)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	302	apply(auto)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	303	done
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	304
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	305	(*
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	306	an alternative definition: might cause problems
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	307	with theorem mkeps_POSIX
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	308	*)
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	309
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	310	(*
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	311	definition POSIX2 :: "val \<Rightarrow> rexp \<Rightarrow> bool"
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	312	where
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	313	"POSIX2 v r \<equiv> \<turnstile> v : r \<and> (\<forall>v'. \<turnstile> v' : r \<longrightarrow> v \<succ>r v')"
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	314	*)
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	315
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	316	(*
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	317	definition POSIX3 :: "val \<Rightarrow> rexp \<Rightarrow> bool"
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	318	where
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	319	"POSIX3 v r \<equiv> \<turnstile> v : r \<and> (\<forall>v'. (\<turnstile> v' : r \<and> length (flat v') \<le> length(flat v)) \<longrightarrow> v \<succ>r v')"
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	320	*)
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	321
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	322	lemma POSIX_SEQ1:
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	323	assumes "POSIX (Seq v1 v2) (SEQ r1 r2)" "\<turnstile> v1 : r1" "\<turnstile> v2 : r2"
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	324	shows "POSIX v1 r1"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	325	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	326	unfolding POSIX_def
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	327	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	328	apply(drule_tac x="Seq v' v2" in spec)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	329	apply(simp)
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	330	apply(erule impE)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	331	apply(rule Prf.intros)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	332	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	333	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	334	apply(erule ValOrd.cases)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	335	apply(simp_all)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	336	apply(clarify)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	337	by (metis ValOrd_refl)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	338
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	339	lemma POSIX_SEQ2:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	340	assumes "POSIX (Seq v1 v2) (SEQ r1 r2)" "\<turnstile> v1 : r1" "\<turnstile> v2 : r2"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	341	shows "POSIX v2 r2"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	342	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	343	unfolding POSIX_def
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	344	apply(auto)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	345	apply(drule_tac x="Seq v1 v'" in spec)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	346	apply(simp)
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	347	apply(erule impE)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	348	apply(rule Prf.intros)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	349	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	350	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	351	apply(erule ValOrd.cases)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	352	apply(simp_all)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	353	done
12 232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	354
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	355	lemma POSIX_ALT2:
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	356	assumes "POSIX (Left v1) (ALT r1 r2)"
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	357	shows "POSIX v1 r1"
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	358	using assms
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	359	unfolding POSIX_def
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	360	apply(auto)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	361	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	362	apply(simp_all)[5]
12 232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	363	apply(drule_tac x="Left v'" in spec)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	364	apply(simp)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	365	apply(drule mp)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	366	apply(rule Prf.intros)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	367	apply(auto)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	368	apply(erule ValOrd.cases)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	369	apply(simp_all)
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	370	done
232ea10bed6f Delete POSIX_ALT2 fahadausaf <fahad.ausaf@icloud.com> parents: 11 diff changeset	371
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	372	lemma POSIX_ALT1a:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	373	assumes "POSIX (Right v2) (ALT r1 r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	374	shows "POSIX v2 r2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	375	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	376	unfolding POSIX_def
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	377	apply(auto)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	378	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	379	apply(simp_all)[5]
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	380	apply(drule_tac x="Right v'" in spec)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	381	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	382	apply(drule mp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	383	apply(rule Prf.intros)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	384	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	385	apply(erule ValOrd.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	386	apply(simp_all)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	387	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	388
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	389	lemma POSIX_ALT1b:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	390	assumes "POSIX (Right v2) (ALT r1 r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	391	shows "(\<forall>v'. (\<turnstile> v' : r2 \<and> flat v' = flat v2) \<longrightarrow> v2 \<succ>r2 v')"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	392	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	393	apply(drule_tac POSIX_ALT1a)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	394	unfolding POSIX_def
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	395	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	396	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	397
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	398	lemma POSIX_ALT_I1:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	399	assumes "POSIX v1 r1"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	400	shows "POSIX (Left v1) (ALT r1 r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	401	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	402	unfolding POSIX_def
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	403	apply(auto)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	404	apply (metis Prf.intros(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	405	apply(rotate_tac 2)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	406	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	407	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	408	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	409	apply(rule ValOrd.intros)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	410	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	411	apply(rule ValOrd.intros)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	412	by simp
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	413
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	414
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	415	lemma POSIX_ALT_I2:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	416	assumes "POSIX v2 r2" "\<forall>v'. \<turnstile> v' : r1 \<longrightarrow> length (flat v2) > length (flat v')"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	417	shows "POSIX (Right v2) (ALT r1 r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	418	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	419	unfolding POSIX_def
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	420	apply(auto)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	421	apply (metis Prf.intros)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	422	apply(rotate_tac 3)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	423	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	424	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	425	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	426	apply(rule ValOrd.intros)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	427	apply metis
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	428	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	429
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	430
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	431	lemma
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	432	"\<lbrakk>POSIX (mkeps r2) r2; nullable r2; \<not> nullable r1\<rbrakk>
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	433	\<Longrightarrow> POSIX (val.Right (mkeps r2)) (ALT r1 r2)"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	434	apply(auto simp add: POSIX_def)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	435	apply(rule Prf.intros(3))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	436	apply(auto)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	437	apply(rotate_tac 3)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	438	apply(erule Prf.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	439	apply(simp_all)[5]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	440	apply(simp add: mkeps_flat)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	441	apply(auto)[1]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	442	apply (metis Prf_flat_L nullable_correctness)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	443	apply(rule ValOrd.intros)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	444	apply(auto)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	445	done
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	446
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	447	lemma mkeps_POSIX:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	448	assumes "nullable r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	449	shows "POSIX (mkeps r) r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	450	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	451	apply(induct r)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	452	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	453	apply(simp add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	454	apply(auto)[1]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	455	apply (metis Prf.intros(4))
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	456	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	457	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	458	apply (metis ValOrd.intros)
66 eb97e8361211 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 63 diff changeset	459	apply(simp)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	460	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	461	apply(simp add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	462	apply(auto)[1]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	463	apply (metis mkeps.simps(2) mkeps_nullable nullable.simps(5))
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	464	apply(rotate_tac 6)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	465	apply(erule Prf.cases)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	466	apply(simp_all)[5]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	467	apply (simp add: mkeps_flat)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	468	apply(case_tac "mkeps r1a = v1")
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	469	apply(simp)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	470	apply (metis ValOrd.intros(1))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	471	apply (rule ValOrd.intros(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	472	apply metis
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	473	apply(simp)
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	474	(* ALT case *)
72 9128b9440e93 updated R1 and notes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 71 diff changeset	475	thm mkeps.simps
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	476	apply(simp)
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	477	apply(erule disjE)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	478	apply(simp)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	479	apply (metis POSIX_ALT_I1)
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	480	(* *)
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	481	apply(auto)[1]
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	482	thm POSIX_ALT_I1
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	483	apply (metis POSIX_ALT_I1)
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	484	apply(simp (no_asm) add: POSIX_def)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	485	apply(auto)[1]
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	486	apply(rule Prf.intros(3))
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	487	apply(simp only: POSIX_def)
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	488	apply(rotate_tac 4)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	489	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	490	apply(simp_all)[5]
72 9128b9440e93 updated R1 and notes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 71 diff changeset	491	thm mkeps_flat
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	492	apply(simp add: mkeps_flat)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	493	apply(auto)[1]
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	494	thm Prf_flat_L nullable_correctness
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	495	apply (metis Prf_flat_L nullable_correctness)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	496	apply(rule ValOrd.intros)
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	497	apply(subst (asm) POSIX_def)
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	498	apply(clarify)
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	499	apply(drule_tac x="v2" in spec)
72 9128b9440e93 updated R1 and notes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 71 diff changeset	500	by simp
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	501
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	502
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	503	section {* Derivatives *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	504
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	505	fun
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	506	der :: "char \<Rightarrow> rexp \<Rightarrow> rexp"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	507	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	508	"der c (NULL) = NULL"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	509	\| "der c (EMPTY) = NULL"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	510	\| "der c (CHAR c') = (if c = c' then EMPTY else NULL)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	511	\| "der c (ALT r1 r2) = ALT (der c r1) (der c r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	512	\| "der c (SEQ r1 r2) =
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	513	(if nullable r1
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	514	then ALT (SEQ (der c r1) r2) (der c r2)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	515	else SEQ (der c r1) r2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	516
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	517	fun
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	518	ders :: "string \<Rightarrow> rexp \<Rightarrow> rexp"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	519	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	520	"ders [] r = r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	521	\| "ders (c # s) r = ders s (der c r)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	522
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	523	section {* Injection function *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	524
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	525	fun injval :: "rexp \<Rightarrow> char \<Rightarrow> val \<Rightarrow> val"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	526	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	527	"injval (CHAR d) c Void = Char d"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	528	\| "injval (ALT r1 r2) c (Left v1) = Left(injval r1 c v1)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	529	\| "injval (ALT r1 r2) c (Right v2) = Right(injval r2 c v2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	530	\| "injval (SEQ r1 r2) c (Seq v1 v2) = Seq (injval r1 c v1) v2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	531	\| "injval (SEQ r1 r2) c (Left (Seq v1 v2)) = Seq (injval r1 c v1) v2"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	532	\| "injval (SEQ r1 r2) c (Right v2) = Seq (mkeps r1) (injval r2 c v2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	533
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	534
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	535	section {* Projection function *}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	536
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	537	fun projval :: "rexp \<Rightarrow> char \<Rightarrow> val \<Rightarrow> val"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	538	where
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	539	"projval (CHAR d) c _ = Void"
71 2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	540	\| "projval (ALT r1 r2) c (Left v1) = Left (projval r1 c v1)"
2d30c74ba67f added a section about a nullable proof Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 70 diff changeset	541	\| "projval (ALT r1 r2) c (Right v2) = Right (projval r2 c v2)"
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	542	\| "projval (SEQ r1 r2) c (Seq v1 v2) =
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	543	(if flat v1 = [] then Right(projval r2 c v2)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	544	else if nullable r1 then Left (Seq (projval r1 c v1) v2)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	545	else Seq (projval r1 c v1) v2)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	546
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	547	text {*
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	548	Injection value is related to r
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	549	*}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	550
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	551	lemma v3:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	552	assumes "\<turnstile> v : der c r" shows "\<turnstile> (injval r c v) : r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	553	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	554	apply(induct arbitrary: v rule: der.induct)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	555	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	556	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	557	apply(simp_all)[5]
49 c616ec6b1e3c updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 48 diff changeset	558	apply(simp)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	559	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	560	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	561	apply(case_tac "c = c'")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	562	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	563	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	564	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	565	apply (metis Prf.intros(5))
49 c616ec6b1e3c updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 48 diff changeset	566	apply(simp)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	567	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	568	apply(simp_all)[5]
49 c616ec6b1e3c updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 48 diff changeset	569	apply(simp)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	570	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	571	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	572	apply (metis Prf.intros(2))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	573	apply (metis Prf.intros(3))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	574	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	575	apply(case_tac "nullable r1")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	576	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	577	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	578	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	579	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	580	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	581	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	582	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	583	apply (metis Prf.intros(1))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	584	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	585	apply (metis Prf.intros(1) mkeps_nullable)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	586	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	587	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	588	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	589	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	590	apply(rule Prf.intros)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	591	apply(auto)[2]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	592	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	593
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	594	lemma v3_proj:
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	595	assumes "\<turnstile> v : r" and "\<exists>s. (flat v) = c # s"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	596	shows "\<turnstile> (projval r c v) : der c r"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	597	using assms
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	598	apply(induct rule: Prf.induct)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	599	prefer 4
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	600	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	601	prefer 4
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	602	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	603	apply (metis Prf.intros(4))
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	604	prefer 2
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	605	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	606	apply (metis Prf.intros(2))
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	607	prefer 2
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	608	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	609	apply (metis Prf.intros(3))
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	610	apply(auto)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	611	apply(rule Prf.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	612	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	613	apply (metis Prf_flat_L nullable_correctness)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	614	apply(rule Prf.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	615	apply(rule Prf.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	616	apply (metis Cons_eq_append_conv)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	617	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	618	apply(rule Prf.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	619	apply (metis Cons_eq_append_conv)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	620	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	621	done
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	622
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	623	text {*
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	624	The string behind the injection value is an added c
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	625	*}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	626
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	627	lemma v4:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	628	assumes "\<turnstile> v : der c r" shows "flat (injval r c v) = c # (flat v)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	629	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	630	apply(induct arbitrary: v rule: der.induct)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	631	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	632	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	633	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	634	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	635	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	636	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	637	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	638	apply(case_tac "c = c'")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	639	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	640	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	641	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	642	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	643	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	644	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	645	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	646	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	647	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	648	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	649	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	650	apply(case_tac "nullable r1")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	651	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	652	apply(erule Prf.cases)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	653	apply(simp_all (no_asm_use))[5]
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	654	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	655	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	656	apply(simp_all)[5]
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	657	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	658	apply(simp only: injval.simps flat.simps)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	659	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	660	apply (metis mkeps_flat)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	661	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	662	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	663	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	664	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	665
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	666	lemma v4_flat_left:
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	667	assumes "\<turnstile> v : der c r" "\<not>(nullable_left r)" shows "flat_left (injval r c v) = c # (flat_left v)"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	668	using assms
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	669	apply(induct arbitrary: v rule: der.induct)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	670	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	671	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	672	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	673	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	674	apply(case_tac "c = c'")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	675	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	676	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	677	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	678	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	679	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	680	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	681	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	682	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	683	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	684	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	685	apply(case_tac "nullable r1")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	686	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	687	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	688	apply(simp_all (no_asm_use))[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	689	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	690	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	691	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	692	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	693	apply(simp only: injval.simps)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	694	apply (metis nullable_left)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	695	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	696	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	697	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	698	done
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	699
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	700
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	701	lemma v4_proj:
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	702	assumes "\<turnstile> v : r" and "\<exists>s. (flat v) = c # s"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	703	shows "c # flat (projval r c v) = flat v"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	704	using assms
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	705	apply(induct rule: Prf.induct)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	706	prefer 4
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	707	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	708	prefer 4
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	709	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	710	prefer 2
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	711	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	712	prefer 2
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	713	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	714	apply(auto)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	715	by (metis Cons_eq_append_conv)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	716
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	717	lemma v4_proj2:
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	718	assumes "\<turnstile> v : r" and "(flat v) = c # s"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	719	shows "flat (projval r c v) = s"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	720	using assms
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	721	by (metis list.inject v4_proj)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	722
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	723	lemma injval_inj: "inj_on (injval r c) {v. \<turnstile> v : der c r}"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	724	apply(induct c r rule: der.induct)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	725	unfolding inj_on_def
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	726	apply(auto)[1]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	727	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	728	apply(simp_all)[5]
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	729	apply(auto)[1]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	730	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	731	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	732	apply(auto)[1]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	733	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	734	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	735	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	736	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	737	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	738	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	739	apply(auto)[1]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	740	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	741	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	742	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	743	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	744	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	745	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	746	apply(auto)[1]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	747	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	748	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	749	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	750	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	751	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	752	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	753	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	754	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	755	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	756	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	757	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	758	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	759	apply(clarify)
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	760	apply (metis list.distinct(1) mkeps_flat v4)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	761	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	762	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	763	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	764	apply(rotate_tac 6)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	765	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	766	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	767	apply (metis list.distinct(1) mkeps_flat v4)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	768	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	769	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	770	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	771	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	772	done
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	773
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	774	lemma t: "(c#xs = c#ys) \<Longrightarrow> xs = ys"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	775	by (metis list.sel(3))
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	776
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	777	lemma t2: "(xs = ys) \<Longrightarrow> (c#xs) = (c#ys)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	778	by (metis)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	779
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	780	fun zeroable where
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	781	"zeroable NULL = True"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	782	\| "zeroable EMPTY = False"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	783	\| "zeroable (CHAR c) = False"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	784	\| "zeroable (ALT r1 r2) = (zeroable r1 \<and> zeroable r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	785	\| "zeroable (SEQ r1 r2) = (zeroable r1 \<or> zeroable r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	786
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	787	lemma "\<not>(nullable r) \<Longrightarrow> \<not>(\<exists>v. \<turnstile> v : r \<and> flat v = [])"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	788	by (metis Prf_flat_L nullable_correctness)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	789
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	790	lemma proj_inj_id:
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	791	assumes "\<turnstile> v : der c r"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	792	shows "projval r c (injval r c v) = v"
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	793	using assms
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	794	apply(induct c r arbitrary: v rule: der.induct)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	795	apply(simp)
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	796	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	797	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	798	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	799	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	800	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	801	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	802	apply(case_tac "c = c'")
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	803	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	804	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	805	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	806	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	807	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	808	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	809	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	810	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	811	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	812	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	813	apply(case_tac "nullable r1")
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	814	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	815	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	816	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	817	apply(auto)[1]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	818	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	819	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	820	apply(auto)[1]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	821	apply (metis list.distinct(1) v4)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	822	apply(auto)[1]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	823	apply (metis mkeps_flat)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	824	apply(auto)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	825	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	826	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	827	apply(auto)[1]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	828	apply(simp add: v4)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	829	done
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	830
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	831	lemma LeftRight:
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	832	assumes "(Left v1) \<succ>(der c (ALT r1 r2)) (Right v2)"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	833	and "\<turnstile> v1 : der c r1" "\<turnstile> v2 : der c r2"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	834	shows "(injval (ALT r1 r2) c (Left v1)) \<succ>(ALT r1 r2) (injval (ALT r1 r2) c (Right v2))"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	835	using assms
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	836	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	837	apply(erule ValOrd.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	838	apply(simp_all)[8]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	839	apply(rule ValOrd.intros)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	840	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	841	apply(subst v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	842	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	843	apply(subst v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	844	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	845	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	846	done
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	847
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	848	lemma RightLeft:
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	849	assumes "(Right v1) \<succ>(der c (ALT r1 r2)) (Left v2)"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	850	and "\<turnstile> v1 : der c r2" "\<turnstile> v2 : der c r1"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	851	shows "(injval (ALT r1 r2) c (Right v1)) \<succ>(ALT r1 r2) (injval (ALT r1 r2) c (Left v2))"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	852	using assms
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	853	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	854	apply(erule ValOrd.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	855	apply(simp_all)[8]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	856	apply(rule ValOrd.intros)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	857	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	858	apply(subst v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	859	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	860	apply(subst v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	861	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	862	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	863	done
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	864
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	865	lemma h:
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	866	assumes "nullable r1" "\<turnstile> v1 : der c r1"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	867	shows "injval r1 c v1 \<succ>r1 mkeps r1"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	868	using assms
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	869	apply(induct r1 arbitrary: v1 rule: der.induct)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	870	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	871	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	872	apply(erule Prf.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	873	apply(simp_all)[5]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	874	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	875	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	876	apply(erule Prf.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	877	apply(simp_all)[5]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	878	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	879	apply(auto)[1]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	880	apply (metis ValOrd.intros(6))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	881	apply (metis ValOrd.intros(6))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	882	apply (metis ValOrd.intros(3) le_add2 list.size(3) mkeps_flat monoid_add_class.add.right_neutral)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	883	apply(auto)[1]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	884	apply (metis ValOrd.intros(4) length_greater_0_conv list.distinct(1) list.size(3) mkeps_flat v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	885	apply (metis ValOrd.intros(4) length_greater_0_conv list.distinct(1) list.size(3) mkeps_flat v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	886	apply (metis ValOrd.intros(5))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	887	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	888	apply(erule Prf.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	889	apply(simp_all)[5]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	890	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	891	apply(erule Prf.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	892	apply(simp_all)[5]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	893	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	894	apply (metis ValOrd.intros(2) list.distinct(1) mkeps_flat v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	895	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	896	by (metis ValOrd.intros(1))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	897
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	898	lemma LeftRightSeq:
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	899	assumes "(Left (Seq v1 v2)) \<succ>(der c (SEQ r1 r2)) (Right v3)"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	900	and "nullable r1" "\<turnstile> v1 : der c r1"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	901	shows "(injval (SEQ r1 r2) c (Seq v1 v2)) \<succ>(SEQ r1 r2) (injval (SEQ r1 r2) c (Right v2))"
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	902	using assms
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	903	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	904	apply(erule ValOrd.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	905	apply(simp_all)[8]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	906	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	907	apply(simp)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	908	apply(rule ValOrd.intros(2))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	909	prefer 2
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	910	apply (metis list.distinct(1) mkeps_flat v4)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	911	by (metis h)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	912
76 39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	913	lemma POSIX_der:
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	914	assumes "POSIX2 v (der c r)" "\<turnstile> v : der c r"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	915	shows "POSIX2 (injval r c v) r"
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	916	using assms
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	917	unfolding POSIX2_def
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	918	apply(auto)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	919	thm v3
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	920	apply (erule v3)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	921	thm v4
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	922	apply(subst (asm) v4)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	923	apply(assumption)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	924	apply(drule_tac x="projval r c v'" in spec)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	925	apply(drule mp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	926	apply(rule conjI)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	927	thm v3_proj
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	928	apply(rule v3_proj)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	929	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	930	apply(rule_tac x="flat v" in exI)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	931	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	932	thm t
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	933	apply(rule_tac c="c" in t)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	934	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	935	thm v4_proj
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	936	apply(subst v4_proj)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	937	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	938	apply(rule_tac x="flat v" in exI)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	939	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	940	apply(simp)
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	941	oops
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	942
39cef7b9212a added an equivalent slightly simpler POSIX definition Christian Urban <urbanc@in.tum.de> parents: 75 diff changeset	943
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	944	lemma Prf_inj_test:
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	945	assumes "v1 \<succ>(der c r) v2" "\<turnstile> v1 : der c r" "\<turnstile> v2 : der c r" "\<Turnstile> vs : rs" "flat v1 = flat v2"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	946	shows "Seqs (injval r c v1) vs \<succ>(SEQS r rs) Seqs (injval r c v2) vs"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	947	using assms
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	948	apply(induct arbitrary: v1 v2 vs rs rule: der.induct)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	949	(* NULL case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	950	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	951	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	952	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	953	(* EMPTY case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	954	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	955	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	956	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	957	(* CHAR case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	958	apply(case_tac "c = c'")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	959	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	960	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	961	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	962	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	963	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	964	apply (metis ValOrd.intros(8))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	965	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	966	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	967	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	968	(* ALT case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	969	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	970	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	971	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	972	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	973	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	974	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	975	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	976	apply (metis ValOrd.intros(6))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	977	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	978	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	979	apply (metis LeftRight ValOrd.intros(3) der.simps(4) injval.simps(2) injval.simps(3))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	980	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	981	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	982	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	983	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	984	apply (metis RightLeft ValOrd.intros(4) der.simps(4) injval.simps(2) injval.simps(3))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	985	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	986	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	987	apply (metis ValOrd.intros(5))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	988	(* SEQ case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	989	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	990	apply(case_tac "nullable r1")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	991	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	992	defer
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	993	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	994	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	995	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	996	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	997	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	998	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	999	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1000	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1001	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1002	apply(rule ValOrd.intros)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1003	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1004	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1005	apply(rule ValOrd.intros(2))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1006	apply(rotate_tac 2)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1007	apply(drule_tac x="v1c" in meta_spec)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1008	apply(rotate_tac 10)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1009	apply(drule_tac x="v1'" in meta_spec)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1010	apply(drule_tac meta_mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1011	apply(assumption)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1012	apply(drule_tac meta_mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1013	apply(assumption)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1014	apply(drule_tac meta_mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1015	apply(assumption)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1016	apply(drule_tac meta_mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1017	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1018	apply(subst v4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1019	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1020	apply(subst (asm) v4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1021	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1022	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1023	apply(simp add: prefix_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1024	oops
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1025
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1026	lemma Prf_inj:
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1027	assumes "v1 \<succ>(der c r) v2" "\<turnstile> v1 : der c r" "\<turnstile> v2 : der c r" ("flat v1 = flat v2")
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1028	shows "(injval r c v1) \<succ>r (injval r c v2)"
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1029	using assms
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1030	apply(induct c r arbitrary: v1 v2 rule: der.induct)
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1031	(* NULL case *)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1032	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1033	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1034	apply(simp_all)[8]
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1035	(* EMPTY case *)
72 9128b9440e93 updated R1 and notes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 71 diff changeset	1036	apply(simp)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1037	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1038	apply(simp_all)[8]
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1039	(* CHAR case *)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1040	apply(case_tac "c = c'")
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1041	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1042	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1043	apply(simp_all)[8]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1044	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1045	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1046	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1047	apply(simp_all)[8]
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1048	(* ALT case *)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1049	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1050	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1051	apply(simp_all)[8]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1052	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1053	apply(subst v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1054	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1055	apply(rotate_tac 3)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1056	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1057	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1058	apply(subst v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1059	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1060	apply(rotate_tac 2)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1061	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1062	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1063	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1064	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1065	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1066	apply(rotate_tac 3)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1067	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1068	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1069	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1070	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1071	apply(simp_all)[5]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1072	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1073	apply(subst v4)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1074	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1075	apply(subst v4)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1076	apply(simp)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1077	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1078	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1079	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1080	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1081	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1082	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1083	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1084	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1085	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1086	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1087	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1088	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1089	apply(simp_all)[5]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1090	(* SEQ case*)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1091	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1092	apply(case_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1093	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1094	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1095	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1096	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1097	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1098	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1099	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1100	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1101	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1102	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1103	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1104	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1105	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1106	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1107	apply(rule ValOrd.intros(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1108	apply metis
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1109	using injval_inj
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1110	apply(simp add: inj_on_def)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1111	apply metis
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1112	(* SEQ nullable case *)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1113	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1114	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1115	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1116	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1117	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1118	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1119	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1120	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1121	apply(clarify)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1122	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1123	apply(simp_all)[5]
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1124	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1125	apply(erule ValOrd.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1126	apply(simp_all)[8]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1127	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1128	apply(erule ValOrd.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1129	apply(simp_all)[8]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1130	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1131	apply(rule ValOrd.intros(1))
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1132	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1133	apply(rule ValOrd.intros(2))
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1134	apply metis
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1135	using injval_inj
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1136	apply(simp add: inj_on_def)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1137	apply metis
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1138	apply(clarify)
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1139	apply(simp)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1140	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1141	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1142	apply(clarify)
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1143	apply(erule ValOrd.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1144	apply(simp_all)[8]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1145	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1146	apply(simp)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1147	apply(rule ValOrd.intros(2))
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1148	apply (metis h)
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1149	apply (metis list.distinct(1) mkeps_flat v4)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1150	(* last case *)
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1151	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1152	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1153	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1154	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1155	apply(rotate_tac 6)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1156	apply(erule Prf.cases)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1157	apply(simp_all)[5]
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1158	apply(clarify)
498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1159	prefer 2
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1160	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1161	apply(erule ValOrd.cases)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1162	apply(simp_all)[8]
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1163	apply(clarify)
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1164	apply(rule ValOrd.intros(1))
6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1165	apply(metis)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1166	apply(rule ValOrd.intros(2))
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1167	prefer 2
73 6e035162345a solved one case Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 72 diff changeset	1168	thm mkeps_flat v4
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1169	apply (metis list.distinct(1) mkeps_flat v4)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1170	oops
63 498171d2379a updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 62 diff changeset	1171
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1172
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1173	lemma POSIX_der:
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1174	assumes "POSIX v (der c r)" "\<turnstile> v : der c r"
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1175	shows "POSIX (injval r c v) r"
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1176	using assms
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1177	unfolding POSIX_def
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1178	apply(auto)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1179	thm v3
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1180	apply (erule v3)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1181	thm v4
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1182	apply(subst (asm) v4)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1183	apply(assumption)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1184	apply(drule_tac x="projval r c v'" in spec)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1185	apply(drule mp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1186	apply(rule conjI)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1187	thm v3_proj
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1188	apply(rule v3_proj)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1189	apply(simp)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1190	apply(rule_tac x="flat v" in exI)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1191	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1192	thm t
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1193	apply(rule_tac c="c" in t)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1194	apply(simp)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1195	thm v4_proj
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1196	apply(subst v4_proj)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1197	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1198	apply(rule_tac x="flat v" in exI)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1199	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1200	apply(simp)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1201	oops
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1202
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1203	lemma POSIX_der:
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1204	assumes "POSIX v (der c r)" "\<turnstile> v : der c r"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1205	shows "POSIX (injval r c v) r"
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1206	using assms
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1207	apply(induct c r arbitrary: v rule: der.induct)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1208	(* null case*)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1209	apply(simp add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1210	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1211	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1212	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1213	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1214	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1215	(* empty case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1216	apply(simp add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1217	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1218	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1219	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1220	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1221	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1222	(* char case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1223	apply(simp add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1224	apply(case_tac "c = c'")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1225	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1226	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1227	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1228	apply (metis Prf.intros(5))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1229	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1230	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1231	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1232	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1233	apply (metis ValOrd.intros(8))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1234	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1235	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1236	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1237	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1238	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1239	(* alt case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1240	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1241	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1242	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1243	apply(simp (no_asm) add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1244	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1245	apply (metis Prf.intros(2) v3)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1246	apply(rotate_tac 4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1247	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1248	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1249	apply (metis POSIX_ALT2 POSIX_def ValOrd.intros(6))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1250	apply (metis ValOrd.intros(3) order_refl)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1251	apply(simp (no_asm) add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1252	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1253	apply (metis Prf.intros(3) v3)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1254	apply(rotate_tac 4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1255	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1256	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1257	defer
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1258	apply (metis POSIX_ALT1a POSIX_def ValOrd.intros(5))
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1259	prefer 2
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1260	apply(subst (asm) (5) POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1261	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1262	apply(rotate_tac 5)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1263	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1264	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1265	apply(rule ValOrd.intros)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1266	apply(subst (asm) v4)
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1267	apply(simp)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1268	apply(drule_tac x="Left (projval r1a c v1)" in spec)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1269	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1270	apply(drule mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1271	apply(rule conjI)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1272	apply (metis Prf.intros(2) v3_proj)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1273	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1274	apply (metis v4_proj2)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1275	apply(erule ValOrd.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1276	apply(simp_all)[8]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1277	apply (metis less_not_refl v4_proj2)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1278	(* seq case *)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1279	apply(case_tac "nullable r1")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1280	defer
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1281	apply(simp add: POSIX_def)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1282	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1283	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1284	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1285	apply (metis Prf.intros(1) v3)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1286	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1287	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1288	apply(erule Prf.cases)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1289	apply(simp_all)[5]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1290	apply(clarify)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1291	apply(subst (asm) (3) v4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1292	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1293	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1294	apply(subgoal_tac "flat v1a \<noteq> []")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1295	prefer 2
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1296	apply (metis Prf_flat_L nullable_correctness)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1297	apply(subgoal_tac "\<exists>s. flat v1a = c # s")
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1298	prefer 2
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1299	apply (metis append_eq_Cons_conv)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1300	apply(auto)[1]
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1301
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1302
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1303	apply(auto)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1304	thm v3
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1305	apply (erule v3)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1306	thm v4
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1307	apply(subst (asm) v4)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1308	apply(assumption)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1309	apply(drule_tac x="projval r c v'" in spec)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1310	apply(drule mp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1311	apply(rule conjI)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1312	thm v3_proj
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1313	apply(rule v3_proj)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1314	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1315	apply(rule_tac x="flat v" in exI)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1316	apply(simp)
f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1317	thm t
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1318	apply(rule_tac c="c" in t)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1319	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1320	thm v4_proj
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1321	apply(subst v4_proj)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1322	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1323	apply(rule_tac x="flat v" in exI)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1324	apply(simp)
dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1325	apply(simp)
75 f95a405c3180 updated Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 74 diff changeset	1326	oops
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1327
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1328
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1329	lemma POSIX_ex: "\<turnstile> v : r \<Longrightarrow> \<exists>v. POSIX v r"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1330	apply(induct r arbitrary: v)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1331	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1332	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1333	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1334	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1335	apply(rule_tac x="Void" in exI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1336	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1337	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1338	apply (metis Prf.intros(4))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1339	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1340	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1341	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1342	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1343	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1344	apply(rule_tac x="Char c" in exI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1345	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1346	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1347	apply (metis Prf.intros(5))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1348	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1349	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1350	apply (metis ValOrd.intros(8))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1351	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1352	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1353	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1354	apply(drule_tac x="v1" in meta_spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1355	apply(drule_tac x="v2" in meta_spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1356	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1357	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1358	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1359	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1360	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1361	apply (metis POSIX_ALT_I1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1362	apply (metis POSIX_ALT_I1 POSIX_ALT_I2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1363	apply(case_tac "nullable r1a")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1364	apply(rule_tac x="Seq (mkeps r1a) va" in exI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1365	apply(auto simp add: POSIX_def)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1366	apply (metis Prf.intros(1) mkeps_nullable)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1367	apply(simp add: mkeps_flat)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1368	apply(rotate_tac 7)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1369	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1370	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1371	apply(case_tac "mkeps r1 = v1a")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1372	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1373	apply (rule ValOrd.intros(1))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1374	apply (metis append_Nil mkeps_flat)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1375	apply (rule ValOrd.intros(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1376	apply(drule mkeps_POSIX)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1377	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1378
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1379	apply metis
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1380	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1381	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1382	apply(erule disjE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1383	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1384
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1385	apply(drule_tac x="v2" in spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1386
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1387	lemma POSIX_ex2: "\<turnstile> v : r \<Longrightarrow> \<exists>v. POSIX v r \<and> \<turnstile> v : r"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1388	apply(induct r arbitrary: v)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1389	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1390	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1391	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1392	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1393	apply(rule_tac x="Void" in exI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1394	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1395	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1396	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1397	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1398	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1399	apply (metis Prf.intros(4))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1400	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1401	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1402	apply(rule_tac x="Char c" in exI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1403	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1404	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1405	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1406	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1407	apply (metis ValOrd.intros(8))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1408	apply (metis Prf.intros(5))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1409	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1410	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1411	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1412	apply(drule_tac x="v1" in meta_spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1413	apply(drule_tac x="v2" in meta_spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1414	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1415	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1416	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1417	apply(rule ccontr)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1418	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1419	apply(drule_tac x="Seq v va" in spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1420	apply(drule mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1421	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1422	apply (metis Prf.intros(1))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1423
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1424
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1425	oops
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1426
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1427	lemma POSIX_ALT_cases:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1428	assumes "\<turnstile> v : (ALT r1 r2)" "POSIX v (ALT r1 r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1429	shows "(\<exists>v1. v = Left v1 \<and> POSIX v1 r1) \<or> (\<exists>v2. v = Right v2 \<and> POSIX v2 r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1430	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1431	apply(erule_tac Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1432	apply(simp_all)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1433	unfolding POSIX_def
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1434	apply(auto)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1435	apply (metis POSIX_ALT2 POSIX_def assms(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1436	by (metis POSIX_ALT1b assms(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1437
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1438	lemma POSIX_ALT_cases2:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1439	assumes "POSIX v (ALT r1 r2)" "\<turnstile> v : (ALT r1 r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1440	shows "(\<exists>v1. v = Left v1 \<and> POSIX v1 r1) \<or> (\<exists>v2. v = Right v2 \<and> POSIX v2 r2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1441	using assms POSIX_ALT_cases by auto
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1442
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1443	lemma Prf_flat_empty:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1444	assumes "\<turnstile> v : r" "flat v = []"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1445	shows "nullable r"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1446	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1447	apply(induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1448	apply(auto)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1449	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1450
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1451	lemma POSIX_proj:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1452	assumes "POSIX v r" "\<turnstile> v : r" "\<exists>s. flat v = c#s"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1453	shows "POSIX (projval r c v) (der c r)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1454	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1455	apply(induct r c v arbitrary: rule: projval.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1456	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1457	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1458	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1459	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1460	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1461	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1462	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1463	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1464	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1465	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1466	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1467	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1468	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1469	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1470	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1471	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1472	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1473	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1474	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1475	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1476	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1477	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1478	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1479	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1480	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1481	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1482	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1483	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1484	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1485	apply(erule_tac [!] exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1486	prefer 3
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1487	apply(frule POSIX_SEQ1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1488	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1489	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1490	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1491	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1492	apply(case_tac "flat v1 = []")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1493	apply(subgoal_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1494	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1495	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1496	apply(rule_tac v="v1" in Prf_flat_empty)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1497	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1498	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1499	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1500	apply(frule POSIX_SEQ2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1501	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1502	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1503	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1504	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1505	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1506	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1507	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1508	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1509	apply(rule ccontr)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1510	apply(subgoal_tac "\<turnstile> val.Right (projval r2 c v2) : (ALT (SEQ (der c r1) r2) (der c r2))")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1511	apply(rotate_tac 11)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1512	apply(frule POSIX_ex)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1513	apply(erule exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1514	apply(drule POSIX_ALT_cases2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1515	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1516	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1517	apply(drule v3_proj)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1518	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1519	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1520	apply(drule POSIX_ex)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1521	apply(erule exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1522	apply(frule POSIX_ALT_cases2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1523	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1524	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1525	apply(erule
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1526	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1527	apply(case_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1528	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1529	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1530	apply(rotate_tac 1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1531	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1532	apply(rule POSIX_SEQ1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1533	apply(assumption)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1534	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1535	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1536	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1537	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1538	apply(rotate_tac 7)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1539	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1540	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1541	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1542	apply(rotate_tac 7)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1543	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1544	apply (metis Cons_eq_append_conv)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1545
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1546
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1547	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1548	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1549	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1550	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1551	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1552	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1553	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1554
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1555
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1556	lemma POSIX_proj:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1557	assumes "POSIX v r" "\<turnstile> v : r" "\<exists>s. flat v = c#s"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1558	shows "POSIX (projval r c v) (der c r)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1559	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1560	apply(induct r arbitrary: c v rule: rexp.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1561	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1562	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1563	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1564	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1565	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1566	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1567	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1568	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1569	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1570	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1571	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1572
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1573	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1574	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1575	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1576	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1577	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1578	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1579	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1580	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1581	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1582	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1583	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1584	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1585	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1586	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1587	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1588	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1589	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1590	apply(erule_tac [!] exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1591	prefer 3
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1592	apply(frule POSIX_SEQ1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1593	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1594	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1595	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1596	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1597	apply(case_tac "flat v1 = []")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1598	apply(subgoal_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1599	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1600	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1601	apply(rule_tac v="v1" in Prf_flat_empty)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1602	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1603	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1604
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1605
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1606	lemma POSIX_proj:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1607	assumes "POSIX v r" "\<turnstile> v : r" "\<exists>s. flat v = c#s"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1608	shows "POSIX (projval r c v) (der c r)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1609	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1610	apply(induct r c v arbitrary: rule: projval.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1611	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1612	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1613	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1614	defer
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1615	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1616	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1617	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1618	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1619	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1620	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1621	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1622	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1623	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1624	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1625	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1626	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1627	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1628	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1629	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1630	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1631	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1632	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1633	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1634	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1635	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1636	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1637	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1638	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1639	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1640	apply(erule_tac [!] exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1641	prefer 3
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1642	apply(frule POSIX_SEQ1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1643	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1644	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1645	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1646	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1647	apply(case_tac "flat v1 = []")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1648	apply(subgoal_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1649	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1650	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1651	apply(rule_tac v="v1" in Prf_flat_empty)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1652	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1653	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1654	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1655	apply(rule ccontr)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1656	apply(drule v3_proj)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1657	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1658	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1659	apply(drule POSIX_ex)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1660	apply(erule exE)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1661	apply(frule POSIX_ALT_cases2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1662	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1663	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1664	apply(erule
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1665	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1666	apply(case_tac "nullable r1")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1667	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1668	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1669	apply(rotate_tac 1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1670	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1671	apply(rule POSIX_SEQ1)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1672	apply(assumption)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1673	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1674	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1675	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1676	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1677	apply(rotate_tac 7)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1678	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1679	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1680	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1681	apply(rotate_tac 7)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1682	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1683	apply (metis Cons_eq_append_conv)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1684
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1685
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1686	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1687	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1688	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1689	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1690	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1691	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1692	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1693
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1694	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1695	(* NULL case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1696	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1697	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1698	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1699	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1700	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1701	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1702	apply (metis ValOrd.intros(7))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1703	apply(rotate_tac 4)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1704	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1705	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1706	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1707	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1708	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1709	apply(frule POSIX_ALT1a)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1710	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1711	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1712	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1713	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1714	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1715	apply(rule POSIX_ALT_I2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1716	apply(assumption)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1717	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1718
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1719	thm v4_proj2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1720	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1721	apply(subst (asm) (13) POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1722
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1723	apply(drule_tac x="projval v2" in spec)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1724	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1725	apply(drule mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1726	apply(rule conjI)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1727	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1728	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1729
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1730	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1731	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1732	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1733	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1734	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1735	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1736	apply(subst (asm) (2) POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1737
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1738	apply (metis ValOrd.intros(5))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1739	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1740	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1741	apply(rotate_tac 3)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1742	apply(drule_tac c="c" in t2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1743	apply(subst (asm) v4_proj)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1744	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1745	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1746	thm contrapos_np contrapos_nn
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1747	apply(erule contrapos_np)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1748	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1749	apply(subst v4_proj2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1750	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1751	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1752	apply(subgoal_tac "\<not>(length (flat v1) < length (flat (projval r2a c v2a)))")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1753	prefer 2
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1754	apply(erule contrapos_nn)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1755	apply (metis nat_less_le v4_proj2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1756	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1757
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1758	apply(blast)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1759	thm contrapos_nn
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1760
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1761	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1762	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1763	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1764	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1765	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1766	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1767	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1768	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1769	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1770	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1771	apply (metis POSIX_ALT2 POSIX_def flat.simps(3))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1772	apply metis
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1773	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1774	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1775	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1776	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1777	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1778	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1779	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1780	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1781	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1782	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1783	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1784	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1785
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1786	apply(drule meta_mp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1787	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1788	apply (metis POSIX_ALT2 POSIX_def flat.simps(3))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1789	apply metis
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1790	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1791	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1792	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1793
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1794
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1795	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1796	(* EMPTY case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1797	apply(simp add: POSIX_def)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1798	apply(auto)[1]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1799	apply(rotate_tac 3)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1800	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1801	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1802	apply(drule_tac c="c" in t2)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1803	apply(subst (asm) v4_proj)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1804	apply(auto)[2]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1805
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1806	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1807	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1808	(* CHAR case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1809	apply(case_tac "c = c'")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1810	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1811	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1812	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1813	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1814	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1815	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1816	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1817	(* ALT case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1818
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1819
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1820	unfolding POSIX_def
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1821	apply(auto)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1822	thm v4
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1823
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1824	lemma Prf_inj:
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1825	assumes "v1 \<succ>(der c r) v2" "\<turnstile> v1 : der c r" "\<turnstile> v2 : der c r" "flat v1 = flat v2"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1826	shows "(injval r c v1) \<succ>r (injval r c v2)"
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1827	using assms
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1828	apply(induct arbitrary: v1 v2 rule: der.induct)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1829	(* NULL case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1830	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1831	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1832	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1833	(* EMPTY case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1834	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1835	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1836	(* CHAR case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1837	apply(case_tac "c = c'")
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1838	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1839	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1840	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1841	apply(rule ValOrd.intros)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1842	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1843	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1844	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1845	(* ALT case *)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1846	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1847	apply(erule ValOrd.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1848	apply(simp_all)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1849	apply(rule ValOrd.intros)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1850	apply(subst v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1851	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1852	apply(rotate_tac 3)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1853	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1854	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1855	apply(subst v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1856	apply(clarify)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1857	apply(rotate_tac 2)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1858	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1859	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1860	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1861	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1862	apply(clarify)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1863	apply(rotate_tac 3)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1864	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1865	apply(simp_all)[5]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1866	apply(clarify)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1867	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1868	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1869	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1870	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1871	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1872	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1873	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1874	apply(simp_all)[5]
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1875	(* SEQ case*)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1876	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1877	apply(case_tac "nullable r1")
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1878	defer
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1879	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1880	apply(erule ValOrd.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1881	apply(simp_all)[8]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1882	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1883	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1884	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1885	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1886	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1887	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1888	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1889	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1890	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1891	apply(rule ValOrd.intros(2))
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1892	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1893	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1894	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1895	apply(simp_all)[5]
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1896	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1897	defer
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1898	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1899	apply(erule ValOrd.cases)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1900	apply(simp_all del: injval.simps)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1901	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1902	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1903	apply(simp)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1904	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1905	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1906	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1907	apply(simp_all)[5]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1908	apply(clarify)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1909	apply(erule Prf.cases)
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1910	apply(simp_all)[5]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1911	apply(clarify)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1912	apply(rule ValOrd.intros(2))
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1913
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1914
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1915
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1916
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1917	done
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1918
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1919
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1920	txt {*
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1921	done
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1922	(* nullable case - unfinished *)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1923	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1924	apply(erule ValOrd.cases)
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1925	apply(simp_all del: injval.simps)[8]
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1926	apply(simp)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1927	apply(clarify)
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1928	apply(simp)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1929	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1930	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1931	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1932	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1933	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1934	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1935	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1936	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1937	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1938	apply(rule ValOrd.intros(2))
62 a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1939	oops
a6bb0152ccc2 updated some rules Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 56 diff changeset	1940	*}
55 c33cfa1e813a added some notes (still incomplete) Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 53 diff changeset	1941	oops
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1942
74 dfa9dbb8f8e6 updated from the session today Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 73 diff changeset	1943
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	1944
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1945	text {*
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1946	Injection followed by projection is the identity.
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1947	*}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1948
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1949	lemma proj_inj_id:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1950	assumes "\<turnstile> v : der c r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1951	shows "projval r c (injval r c v) = v"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1952	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1953	apply(induct r arbitrary: c v rule: rexp.induct)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1954	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1955	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1956	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1957	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1958	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1959	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1960	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1961	apply(case_tac "c = char")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1962	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1963	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1964	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1965	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1966	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1967	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1968	defer
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1969	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1970	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1971	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1972	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1973	apply(case_tac "nullable rexp1")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1974	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1975	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1976	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1977	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1978	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1979	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1980	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1981	apply (metis list.distinct(1) v4)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1982	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1983	apply (metis mkeps_flat)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1984	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1985	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1986	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1987	apply(auto)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1988	apply(simp add: v4)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1989	done
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	1990
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1991	lemma "L r \<noteq> {} \<Longrightarrow> \<exists>v. POSIX3 v r"
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1992	apply(induct r)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1993	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1994	apply(simp add: POSIX3_def)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1995	apply(rule_tac x="Void" in exI)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1996	apply(auto)[1]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1997	apply (metis Prf.intros(4))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1998	apply (metis POSIX3_def flat.simps(1) mkeps.simps(1) mkeps_POSIX3 nullable.simps(2) order_refl)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	1999	apply(simp add: POSIX3_def)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2000	apply(rule_tac x="Char char" in exI)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2001	apply(auto)[1]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2002	apply (metis Prf.intros(5))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2003	apply(erule Prf.cases)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2004	apply(simp_all)[5]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2005	apply (metis ValOrd.intros(8))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2006	apply(simp add: Sequ_def)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2007	apply(auto)[1]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2008	apply(drule meta_mp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2009	apply(auto)[2]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2010	apply(drule meta_mp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2011	apply(auto)[2]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2012	apply(rule_tac x="Seq v va" in exI)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2013	apply(simp (no_asm) add: POSIX3_def)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2014	apply(auto)[1]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2015	apply (metis POSIX3_def Prf.intros(1))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2016	apply(erule Prf.cases)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2017	apply(simp_all)[5]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2018	apply(clarify)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2019	apply(case_tac "v \<succ>r1a v1")
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2020	apply(rule ValOrd.intros(2))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2021	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2022	apply(case_tac "v = v1")
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2023	apply(rule ValOrd.intros(1))
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2024	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2025	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2026	apply (metis ValOrd_refl)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2027	apply(simp add: POSIX3_def)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2028	oops
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2029
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2030	lemma "\<exists>v. POSIX v r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2031	apply(induct r)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2032	apply(rule exI)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2033	apply(simp add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2034	apply (metis (full_types) Prf_flat_L der.simps(1) der.simps(2) der.simps(3) flat.simps(1) nullable.simps(1) nullable_correctness proj_inj_id projval.simps(1) v3 v4)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2035	apply(rule_tac x = "Void" in exI)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2036	apply(simp add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2037	apply (metis POSIX_def flat.simps(1) mkeps.simps(1) mkeps_POSIX nullable.simps(2))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2038	apply(rule_tac x = "Char char" in exI)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2039	apply(simp add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2040	apply(auto) [1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2041	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2042	apply(simp_all) [5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2043	apply (metis ValOrd.intros(8))
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2044	defer
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2045	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2046	apply (metis POSIX_ALT_I1)
11 26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	2047	(* maybe it is too early to instantiate this existential quantifier *)
26b8a5213355 changed theory name Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 10 diff changeset	2048	(* potentially this is the wrong POSIX value *)
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2049	apply(case_tac "r1 = NULL")
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2050	apply(simp add: POSIX_def)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2051	apply(auto)[1]
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2052	apply (metis L.simps(1) L.simps(4) Prf_flat_L mkeps_flat nullable.simps(1) nullable.simps(2) nullable_correctness seq_null(2))
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2053	apply(case_tac "r1 = EMPTY")
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2054	apply(rule_tac x = "Seq Void va" in exI )
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2055	apply(simp (no_asm) add: POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2056	apply(auto)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2057	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2058	apply(simp_all)
20 c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2059	apply(auto)[1]
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2060	apply(erule Prf.cases)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2061	apply(simp_all)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2062	apply(rule ValOrd.intros(2))
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2063	apply(rule ValOrd.intros)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2064	apply(case_tac "\<exists>c. r1 = CHAR c")
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2065	apply(auto)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2066	apply(rule_tac x = "Seq (Char c) va" in exI )
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2067	apply(simp (no_asm) add: POSIX_def)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2068	apply(auto)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2069	apply(erule Prf.cases)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2070	apply(simp_all)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2071	apply(auto)[1]
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2072	apply(erule Prf.cases)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2073	apply(simp_all)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2074	apply(auto)[1]
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2075	apply(rule ValOrd.intros(2))
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2076	apply(rule ValOrd.intros)
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2077	apply(case_tac "\<exists>r1a r1b. r1 = ALT r1a r1b")
c11651bbebf5 some small changes Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 12 diff changeset	2078	apply(auto)
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2079	oops (* not sure if this can be proved by induction *)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2080
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2081	text {*
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2082
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2083	HERE: Crucial lemma that does not go through in the sequence case.
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2084
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2085	*}
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2086	lemma v5:
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2087	assumes "\<turnstile> v : der c r" "POSIX v (der c r)"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2088	shows "POSIX (injval r c v) r"
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2089	using assms
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2090	apply(induct arbitrary: v rule: der.induct)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2091	(* NULL case *)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2092	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2093	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2094	apply(simp_all)[5]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2095	(* EMPTY case *)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2096	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2097	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2098	apply(simp_all)[5]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2099	(* CHAR case *)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2100	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2101	apply(case_tac "c = c'")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2102	apply(auto simp add: POSIX_def)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2103	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2104	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2105	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2106	apply(simp_all)[5]
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2107	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2108	apply(auto)[1]
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2109	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2110	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2111	(* base cases done *)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2112	(* ALT case *)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2113	apply(erule Prf.cases)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2114	apply(simp_all)[5]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2115	using POSIX_ALT POSIX_ALT_I1 apply blast
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2116	apply(clarify)
53 38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2117	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2118	apply(rule POSIX_ALT_I2)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2119	apply(drule POSIX_ALT1a)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2120	apply metis
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2121	apply(auto)[1]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2122	apply(subst v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2123	apply(assumption)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2124	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2125	apply(drule POSIX_ALT1a)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2126	apply(rotate_tac 1)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2127	apply(drule_tac x="v2" in meta_spec)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2128	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2129
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2130	apply(rotate_tac 4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2131	apply(erule Prf.cases)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2132	apply(simp_all)[5]
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2133	apply(rule ValOrd.intros)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2134	apply(simp)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2135	apply(subst (asm) v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2136	apply(assumption)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2137	apply(clarify)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2138	thm POSIX_ALT1a POSIX_ALT1b POSIX_ALT_I2
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2139	apply(subst (asm) v4)
38cde0214ad5 added some lemmas, attempted others Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 49 diff changeset	2140	apply(auto simp add: POSIX_def)[1]
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2141	apply(subgoal_tac "POSIX v2 (der c r2)")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2142	prefer 2
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2143	apply(auto simp add: POSIX_def)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2144	apply (metis POSIX_ALT1a POSIX_def flat.simps(4))
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2145	apply(frule POSIX_ALT1a)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2146	apply(drule POSIX_ALT1b)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2147	apply(rule POSIX_ALT_I2)
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2148	apply(rotate_tac 1)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2149	apply(drule_tac x="v2" in meta_spec)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2150	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2151	apply(subgoal_tac "\<turnstile> Right (injval r2 c v2) : (ALT r1 r2)")
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2152	prefer 2
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2153	apply (metis Prf.intros(3) v3)
48 652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2154	apply auto[1]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2155	apply(subst v4)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2156	apply(auto)[2]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2157	apply(subst (asm) (4) POSIX_def)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2158	apply(subst (asm) v4)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2159	apply(drule_tac x="v2" in meta_spec)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2160	apply(simp)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2161
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2162	apply(auto)[2]
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2163
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2164	thm POSIX_ALT_I2
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2165	apply(rule POSIX_ALT_I2)
652861c9473f added a function for calculating values Christian Urban <christian dot urban at kcl dot ac dot uk> parents: 20 diff changeset	2166
10 14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2167	apply(rule ccontr)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2168	apply(auto simp add: POSIX_def)[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2169
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2170	apply(rule allI)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2171	apply(rule impI)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2172	apply(erule conjE)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2173	thm POSIX_ALT_I2
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2174	apply(frule POSIX_ALT1a)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2175	apply(drule POSIX_ALT1b)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2176	apply(rule POSIX_ALT_I2)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2177	apply auto[1]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2178	apply(subst v4)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2179	apply(auto)[2]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2180	apply(rotate_tac 1)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2181	apply(drule_tac x="v2" in meta_spec)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2182	apply(simp)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2183	apply(subst (asm) (4) POSIX_def)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2184	apply(subst (asm) v4)
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2185	apply(auto)[2]
14d41b5b57b3 added test version Christian Urban <christian dot urban at kcl dot ac dot uk> parents: diff changeset	2186	(* stuck in the ALT case *)

author	Christian Urban <urbanc@in.tum.de>
	Sat, 25 Apr 2015 10:58:48 +0100
changeset 76	39cef7b9212a
parent 75	f95a405c3180
child 77	4b4c677501e7
permissions	-rw-r--r--