--- a/src/HOL/Library/List_lexord.thy Wed Nov 22 10:20:17 2006 +0100
+++ b/src/HOL/Library/List_lexord.thy Wed Nov 22 10:20:18 2006 +0100
@@ -9,10 +9,9 @@
imports Main
begin
-instance list :: (ord) ord ..
-defs (overloaded)
+instance list :: (ord) ord
list_le_def: "(xs::('a::ord) list) \<le> ys \<equiv> (xs < ys \<or> xs = ys)"
- list_less_def: "(xs::('a::ord) list) < ys \<equiv> (xs, ys) \<in> lexord {(u,v). u < v}"
+ list_less_def: "(xs::('a::ord) list) < ys \<equiv> (xs, ys) \<in> lexord {(u,v). u < v}" ..
lemmas list_ord_defs = list_less_def list_le_def
@@ -28,29 +27,29 @@
apply assumption
done
-instance list::(linorder)linorder
+instance list :: (linorder) linorder
apply (intro_classes, unfold list_le_def list_less_def, safe)
apply (cut_tac x = x and y = y and r = "{(a,b). a < b}" in lexord_linear)
apply force
apply simp
done
-lemma not_less_Nil[simp]: "~(x < [])"
+lemma not_less_Nil [simp, code func]: "~(x < [])"
by (unfold list_less_def) simp
-lemma Nil_less_Cons[simp]: "[] < a # x"
+lemma Nil_less_Cons [simp, code func]: "[] < a # x"
by (unfold list_less_def) simp
-lemma Cons_less_Cons[simp]: "(a # x < b # y) = (a < b | a = b & x < y)"
+lemma Cons_less_Cons [simp, code func]: "(a # x < b # y) = (a < b | a = b & x < y)"
by (unfold list_less_def) simp
-lemma le_Nil[simp]: "(x <= []) = (x = [])"
+lemma le_Nil [simp, code func]: "(x <= []) = (x = [])"
by (unfold list_ord_defs, cases x) auto
-lemma Nil_le_Cons [simp]: "([] <= x)"
+lemma Nil_le_Cons [simp, code func]: "([] <= x)"
by (unfold list_ord_defs, cases x) auto
-lemma Cons_le_Cons[simp]: "(a # x <= b # y) = (a < b | a = b & x <= y)"
+lemma Cons_le_Cons [simp, code func]: "(a # x <= b # y) = (a < b | a = b & x <= y)"
by (unfold list_ord_defs) auto
end