# HG changeset patch
# User nipkow
# Date 861779696 -7200
# Node ID a3b73ba44a11a99b134bfeff1cb631eb1bf148ac
# Parent  4be22c30096663edb35f2966fb92ca2e7c17e72f
Tidied up.

diff -r 4be22c300966 -r a3b73ba44a11 src/HOL/List.ML
--- a/src/HOL/List.ML	Tue Apr 22 18:05:42 1997 +0200
+++ b/src/HOL/List.ML	Wed Apr 23 09:14:56 1997 +0200
@@ -6,20 +6,13 @@
 List lemmas
 *)
 
-open List;
-
-AddIffs list.distinct;
-AddIffs list.inject;
-
-bind_thm("Cons_inject", (hd list.inject) RS iffD1 RS conjE);
-
-goal List.thy "!x. xs ~= x#xs";
+goal thy "!x. xs ~= x#xs";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed_spec_mp "not_Cons_self";
 Addsimps [not_Cons_self];
 
-goal List.thy "(xs ~= []) = (? y ys. xs = y#ys)";
+goal thy "(xs ~= []) = (? y ys. xs = y#ys)";
 by (list.induct_tac "xs" 1);
 by (Simp_tac 1);
 by (Asm_simp_tac 1);
@@ -28,7 +21,7 @@
 
 (** list_case **)
 
-goal List.thy
+goal thy
  "P(list_case a f xs) = ((xs=[] --> P(a)) & \
 \                        (!y ys. xs=y#ys --> P(f y ys)))";
 by (list.induct_tac "xs" 1);
@@ -36,12 +29,12 @@
 by (Blast_tac 1);
 qed "expand_list_case";
 
-val prems = goal List.thy "[| P([]); !!x xs. P(x#xs) |] ==> P(xs)";
+val prems = goal thy "[| P([]); !!x xs. P(x#xs) |] ==> P(xs)";
 by(list.induct_tac "xs" 1);
 by(REPEAT(resolve_tac prems 1));
 qed "list_cases";
 
-goal List.thy  "(xs=[] --> P([])) & (!y ys. xs=y#ys --> P(y#ys)) --> P(xs)";
+goal thy  "(xs=[] --> P([])) & (!y ys. xs=y#ys --> P(y#ys)) --> P(xs)";
 by (list.induct_tac "xs" 1);
 by (Blast_tac 1);
 by (Blast_tac 1);
@@ -51,38 +44,38 @@
 
 (** @ - append **)
 
-goal List.thy "(xs@ys)@zs = xs@(ys@zs)";
+goal thy "(xs@ys)@zs = xs@(ys@zs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "append_assoc";
 Addsimps [append_assoc];
 
-goal List.thy "xs @ [] = xs";
+goal thy "xs @ [] = xs";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "append_Nil2";
 Addsimps [append_Nil2];
 
-goal List.thy "(xs@ys = []) = (xs=[] & ys=[])";
+goal thy "(xs@ys = []) = (xs=[] & ys=[])";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "append_is_Nil_conv";
 AddIffs [append_is_Nil_conv];
 
-goal List.thy "([] = xs@ys) = (xs=[] & ys=[])";
+goal thy "([] = xs@ys) = (xs=[] & ys=[])";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 by(Blast_tac 1);
 qed "Nil_is_append_conv";
 AddIffs [Nil_is_append_conv];
 
-goal List.thy "(xs @ ys = xs @ zs) = (ys=zs)";
+goal thy "(xs @ ys = xs @ zs) = (ys=zs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "same_append_eq";
 AddIffs [same_append_eq];
 
-goal List.thy "!ys. (xs @ [x] = ys @ [y]) = (xs = ys & x = y)"; 
+goal thy "!ys. (xs @ [x] = ys @ [y]) = (xs = ys & x = y)"; 
 by(list.induct_tac "xs" 1);
  br allI 1;
  by(list.induct_tac "ys" 1);
@@ -93,62 +86,62 @@
 qed_spec_mp "append1_eq_conv";
 AddIffs [append1_eq_conv];
 
-goal List.thy "xs ~= [] --> hd xs # tl xs = xs";
+goal thy "xs ~= [] --> hd xs # tl xs = xs";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "hd_Cons_tl";
 Addsimps [hd_Cons_tl];
 
-goal List.thy "hd(xs@ys) = (if xs=[] then hd ys else hd xs)";
+goal thy "hd(xs@ys) = (if xs=[] then hd ys else hd xs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "hd_append";
 
-goal List.thy "tl(xs@ys) = (case xs of [] => tl(ys) | z#zs => zs@ys)";
+goal thy "tl(xs@ys) = (case xs of [] => tl(ys) | z#zs => zs@ys)";
 by(simp_tac (!simpset setloop(split_tac[expand_list_case])) 1);
 qed "tl_append";
 
 (** map **)
 
-goal List.thy
+goal thy
   "(!x. x : set_of_list xs --> f x = g x) --> map f xs = map g xs";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 bind_thm("map_ext", impI RS (allI RS (result() RS mp)));
 
-goal List.thy "map (%x.x) = (%xs.xs)";
+goal thy "map (%x.x) = (%xs.xs)";
 by (rtac ext 1);
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "map_ident";
 Addsimps[map_ident];
 
-goal List.thy "map f (xs@ys) = map f xs @ map f ys";
+goal thy "map f (xs@ys) = map f xs @ map f ys";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "map_append";
 Addsimps[map_append];
 
-goalw List.thy [o_def] "map (f o g) xs = map f (map g xs)";
+goalw thy [o_def] "map (f o g) xs = map f (map g xs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "map_compose";
 Addsimps[map_compose];
 
-goal List.thy "rev(map f xs) = map f (rev xs)";
+goal thy "rev(map f xs) = map f (rev xs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "rev_map";
 
 (** rev **)
 
-goal List.thy "rev(xs@ys) = rev(ys) @ rev(xs)";
+goal thy "rev(xs@ys) = rev(ys) @ rev(xs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "rev_append";
 Addsimps[rev_append];
 
-goal List.thy "rev(rev l) = l";
+goal thy "rev(rev l) = l";
 by (list.induct_tac "l" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "rev_rev_ident";
@@ -157,13 +150,13 @@
 
 (** mem **)
 
-goal List.thy "x mem (xs@ys) = (x mem xs | x mem ys)";
+goal thy "x mem (xs@ys) = (x mem xs | x mem ys)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS (asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
 qed "mem_append";
 Addsimps[mem_append];
 
-goal List.thy "x mem [x:xs.P(x)] = (x mem xs & P(x))";
+goal thy "x mem [x:xs.P(x)] = (x mem xs & P(x))";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS (asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
 qed "mem_filter";
@@ -184,25 +177,25 @@
 by (Blast_tac 1);
 qed "set_of_list_mem_eq";
 
-goal List.thy "set_of_list l <= set_of_list (x#l)";
+goal thy "set_of_list l <= set_of_list (x#l)";
 by (Simp_tac 1);
 by (Blast_tac 1);
 qed "set_of_list_subset_Cons";
 
-goal List.thy "(set_of_list xs = {}) = (xs = [])";
+goal thy "(set_of_list xs = {}) = (xs = [])";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 qed "set_of_list_empty";
 Addsimps [set_of_list_empty];
 
-goal List.thy "set_of_list(rev xs) = set_of_list(xs)";
+goal thy "set_of_list(rev xs) = set_of_list(xs)";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 by(Blast_tac 1);
 qed "set_of_list_rev";
 Addsimps [set_of_list_rev];
 
-goal List.thy "set_of_list(map f xs) = f``(set_of_list xs)";
+goal thy "set_of_list(map f xs) = f``(set_of_list xs)";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 qed "set_of_list_map";
@@ -211,19 +204,19 @@
 
 (** list_all **)
 
-goal List.thy "list_all (%x.True) xs = True";
+goal thy "list_all (%x.True) xs = True";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "list_all_True";
 Addsimps [list_all_True];
 
-goal List.thy "list_all p (xs@ys) = (list_all p xs & list_all p ys)";
+goal thy "list_all p (xs@ys) = (list_all p xs & list_all p ys)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "list_all_append";
 Addsimps [list_all_append];
 
-goal List.thy "list_all P xs = (!x. x mem xs --> P(x))";
+goal thy "list_all P xs = (!x. x mem xs --> P(x))";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS (asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
 by (Blast_tac 1);
@@ -232,7 +225,7 @@
 
 (** filter **)
 
-goal List.thy "[x:xs@ys . P] = [x:xs . P] @ [y:ys . P]";
+goal thy "[x:xs@ys . P] = [x:xs . P] @ [y:ys . P]";
 by(list.induct_tac "xs" 1);
  by(ALLGOALS (asm_simp_tac (!simpset setloop (split_tac [expand_if]))));
 qed "filter_append";
@@ -241,44 +234,44 @@
 
 (** concat **)
 
-goal List.thy  "concat(xs@ys) = concat(xs)@concat(ys)";
+goal thy  "concat(xs@ys) = concat(xs)@concat(ys)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed"concat_append";
 Addsimps [concat_append];
 
-goal List.thy "rev(concat ls) = concat (map rev (rev ls))";
+goal thy "rev(concat ls) = concat (map rev (rev ls))";
 by (list.induct_tac "ls" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "rev_concat";
 
 (** length **)
 
-goal List.thy "length(xs@ys) = length(xs)+length(ys)";
+goal thy "length(xs@ys) = length(xs)+length(ys)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed"length_append";
 Addsimps [length_append];
 
-goal List.thy "length (map f l) = length l";
+goal thy "length (map f l) = length l";
 by (list.induct_tac "l" 1);
 by (ALLGOALS Simp_tac);
 qed "length_map";
 Addsimps [length_map];
 
-goal List.thy "length(rev xs) = length(xs)";
+goal thy "length(rev xs) = length(xs)";
 by (list.induct_tac "xs" 1);
 by (ALLGOALS Asm_simp_tac);
 qed "length_rev";
 Addsimps [length_rev];
 
-goal List.thy "(length xs = 0) = (xs = [])";
+goal thy "(length xs = 0) = (xs = [])";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 qed "length_0_conv";
 AddIffs [length_0_conv];
 
-goal List.thy "(0 < length xs) = (xs ~= [])";
+goal thy "(0 < length xs) = (xs ~= [])";
 by(list.induct_tac "xs" 1);
 by(ALLGOALS Asm_simp_tac);
 qed "length_greater_0_conv";
@@ -287,7 +280,7 @@
 
 (** nth **)
 
-goal List.thy
+goal thy
   "!xs. nth n (xs@ys) = \
 \          (if n < length xs then nth n xs else nth (n - length xs) ys)";
 by(nat_ind_tac "n" 1);
@@ -300,7 +293,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "nth_append";
 
-goal List.thy "!n. n < length xs --> nth n (map f xs) = f (nth n xs)";
+goal thy "!n. n < length xs --> nth n (map f xs) = f (nth n xs)";
 by (list.induct_tac "xs" 1);
 (* case [] *)
 by (Asm_full_simp_tac 1);
@@ -311,7 +304,7 @@
 qed_spec_mp "nth_map";
 Addsimps [nth_map];
 
-goal List.thy "!n. n < length xs --> list_all P xs --> P(nth n xs)";
+goal thy "!n. n < length xs --> list_all P xs --> P(nth n xs)";
 by (list.induct_tac "xs" 1);
 (* case [] *)
 by (Simp_tac 1);
@@ -321,7 +314,7 @@
 by (ALLGOALS Asm_full_simp_tac);
 qed_spec_mp "list_all_nth";
 
-goal List.thy "!n. n < length xs --> (nth n xs) mem xs";
+goal thy "!n. n < length xs --> (nth n xs) mem xs";
 by (list.induct_tac "xs" 1);
 (* case [] *)
 by (Simp_tac 1);
@@ -360,7 +353,7 @@
 Delsimps [take_Cons,drop_Cons];
 Addsimps [take_0,take_Suc_Cons,drop_0,drop_Suc_Cons];
 
-goal List.thy "!xs. length(take n xs) = min (length xs) n";
+goal thy "!xs. length(take n xs) = min (length xs) n";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -369,7 +362,7 @@
 qed_spec_mp "length_take";
 Addsimps [length_take];
 
-goal List.thy "!xs. length(drop n xs) = (length xs - n)";
+goal thy "!xs. length(drop n xs) = (length xs - n)";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -378,7 +371,7 @@
 qed_spec_mp "length_drop";
 Addsimps [length_drop];
 
-goal List.thy "!xs. length xs <= n --> take n xs = xs";
+goal thy "!xs. length xs <= n --> take n xs = xs";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -386,7 +379,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "take_all";
 
-goal List.thy "!xs. length xs <= n --> drop n xs = []";
+goal thy "!xs. length xs <= n --> drop n xs = []";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -394,7 +387,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "drop_all";
 
-goal List.thy 
+goal thy 
   "!xs. take n (xs @ ys) = (take n xs @ take (n - length xs) ys)";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
@@ -404,7 +397,7 @@
 qed_spec_mp "take_append";
 Addsimps [take_append];
 
-goal List.thy "!xs. drop n (xs@ys) = drop n xs @ drop (n - length xs) ys"; 
+goal thy "!xs. drop n (xs@ys) = drop n xs @ drop (n - length xs) ys"; 
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -413,7 +406,7 @@
 qed_spec_mp "drop_append";
 Addsimps [drop_append];
 
-goal List.thy "!xs n. take n (take m xs) = take (min n m) xs"; 
+goal thy "!xs n. take n (take m xs) = take (min n m) xs"; 
 by(nat_ind_tac "m" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -424,7 +417,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "take_take";
 
-goal List.thy "!xs. drop n (drop m xs) = drop (n + m) xs"; 
+goal thy "!xs. drop n (drop m xs) = drop (n + m) xs"; 
 by(nat_ind_tac "m" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -432,7 +425,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "drop_drop";
 
-goal List.thy "!xs n. take n (drop m xs) = drop m (take (n + m) xs)"; 
+goal thy "!xs n. take n (drop m xs) = drop m (take (n + m) xs)"; 
 by(nat_ind_tac "m" 1);
  by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -440,7 +433,7 @@
  by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "take_drop";
 
-goal List.thy "!xs. take n (map f xs) = map f (take n xs)"; 
+goal thy "!xs. take n (map f xs) = map f (take n xs)"; 
 by(nat_ind_tac "n" 1);
 by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -448,7 +441,7 @@
 by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "take_map"; 
 
-goal List.thy "!xs. drop n (map f xs) = map f (drop n xs)"; 
+goal thy "!xs. drop n (map f xs) = map f (drop n xs)"; 
 by(nat_ind_tac "n" 1);
 by(ALLGOALS Asm_simp_tac);
 br allI 1;
@@ -456,7 +449,7 @@
 by(ALLGOALS Asm_simp_tac);
 qed_spec_mp "drop_map";
 
-goal List.thy
+goal thy
   "!n i. i < n --> nth i (take n xs) = nth i xs";
 by(list.induct_tac "xs" 1);
  by(ALLGOALS Asm_simp_tac);
@@ -468,7 +461,7 @@
 qed_spec_mp "nth_take";
 Addsimps [nth_take];
 
-goal List.thy
+goal thy
   "!xs i. n + i < length xs --> nth i (drop n xs) = nth (n + i) xs";
 by(nat_ind_tac "n" 1);
  by(ALLGOALS Asm_simp_tac);
@@ -480,7 +473,7 @@
 
 (** takeWhile & dropWhile **)
 
-goal List.thy
+goal thy
   "x:set_of_list xs & ~P(x) --> takeWhile P (xs @ ys) = takeWhile P xs";
 by(list.induct_tac "xs" 1);
  by(Simp_tac 1);
@@ -489,7 +482,7 @@
 bind_thm("takeWhile_append1", conjI RS (result() RS mp));
 Addsimps [takeWhile_append1];
 
-goal List.thy
+goal thy
   "(!x:set_of_list xs.P(x)) --> takeWhile P (xs @ ys) = xs @ takeWhile P ys";
 by(list.induct_tac "xs" 1);
  by(Simp_tac 1);
@@ -497,7 +490,7 @@
 bind_thm("takeWhile_append2", ballI RS (result() RS mp));
 Addsimps [takeWhile_append2];
 
-goal List.thy
+goal thy
   "x:set_of_list xs & ~P(x) --> dropWhile P (xs @ ys) = (dropWhile P xs)@ys";
 by(list.induct_tac "xs" 1);
  by(Simp_tac 1);
@@ -506,7 +499,7 @@
 bind_thm("dropWhile_append1", conjI RS (result() RS mp));
 Addsimps [dropWhile_append1];
 
-goal List.thy
+goal thy
   "(!x:set_of_list xs.P(x)) --> dropWhile P (xs @ ys) = dropWhile P ys";
 by(list.induct_tac "xs" 1);
  by(Simp_tac 1);
@@ -514,7 +507,7 @@
 bind_thm("dropWhile_append2", ballI RS (result() RS mp));
 Addsimps [dropWhile_append2];
 
-goal List.thy "x:set_of_list(takeWhile P xs) --> x:set_of_list xs & P x";
+goal thy "x:set_of_list(takeWhile P xs) --> x:set_of_list xs & P x";
 by(list.induct_tac "xs" 1);
  by(Simp_tac 1);
 by(asm_full_simp_tac (!simpset setloop (split_tac[expand_if])) 1);