--- a/src/HOL/List.ML Mon Dec 29 21:39:22 1997 +0100
+++ b/src/HOL/List.ML Tue Dec 30 11:14:09 1997 +0100
@@ -438,8 +438,7 @@
section "nth";
goal thy
- "!xs. nth n (xs@ys) = \
-\ (if n < length xs then nth n xs else nth (n - length xs) ys)";
+ "!xs. (xs@ys)!n = (if n < length xs then xs!n else ys!(n - length xs))";
by (nat_ind_tac "n" 1);
by (Asm_simp_tac 1);
by (rtac allI 1);
@@ -450,7 +449,7 @@
by (ALLGOALS Asm_simp_tac);
qed_spec_mp "nth_append";
-goal thy "!n. n < length xs --> nth n (map f xs) = f (nth n xs)";
+goal thy "!n. n < length xs --> (map f xs)!n = f(xs!n)";
by (induct_tac "xs" 1);
(* case [] *)
by (Asm_full_simp_tac 1);
@@ -461,7 +460,7 @@
qed_spec_mp "nth_map";
Addsimps [nth_map];
-goal thy "!n. n < length xs --> list_all P xs --> P(nth n xs)";
+goal thy "!n. n < length xs --> list_all P xs --> P(xs!n)";
by (induct_tac "xs" 1);
(* case [] *)
by (Simp_tac 1);
@@ -471,7 +470,7 @@
by (ALLGOALS Asm_full_simp_tac);
qed_spec_mp "list_all_nth";
-goal thy "!n. n < length xs --> (nth n xs) mem xs";
+goal thy "!n. n < length xs --> xs!n mem xs";
by (induct_tac "xs" 1);
(* case [] *)
by (Simp_tac 1);
@@ -643,7 +642,7 @@
by (ALLGOALS Asm_simp_tac);
qed_spec_mp "drop_map";
-goal thy "!n i. i < n --> nth i (take n xs) = nth i xs";
+goal thy "!n i. i < n --> (take n xs)!i = xs!i";
by (induct_tac "xs" 1);
by (ALLGOALS Asm_simp_tac);
by (Clarify_tac 1);
@@ -654,7 +653,7 @@
qed_spec_mp "nth_take";
Addsimps [nth_take];
-goal thy "!xs i. n + i <= length xs --> nth i (drop n xs) = nth (n + i) xs";
+goal thy "!xs i. n + i <= length xs --> (drop n xs)!i = xs!(n+i)";
by (nat_ind_tac "n" 1);
by (ALLGOALS Asm_simp_tac);
by (rtac allI 1);