src/HOL/Library/Ring_and_Field_Example.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Ring_and_Field_Example.thy	Sat Jan 20 00:32:56 2001 +0100
@@ -0,0 +1,24 @@
+
+header {* \title{}\subsection{Example: The ordered ring of integers} *}
+
+theory Ring_and_Field_Example = Ring_and_Field:
+
+instance int :: ordered_ring
+proof
+  fix i j k :: int
+  show "(i + j) + k = i + (j + k)" by simp
+  show "i + j = j + i" by simp
+  show "0 + i = i" by simp
+  show "- i + i = 0" by simp
+  show "i - j = i + (-j)" by simp
+  show "(i * j) * k = i * (j * k)" by simp
+  show "i * j = j * i" by simp
+  show "#1 * i = i" by simp
+  show "0 = (#0::int)" by simp
+  show "(i + j) * k = i * k + j * k" by (simp add: int_distrib)
+  show "i \<le> j ==> k + i \<le> k + j" by simp
+  show "i < j ==> 0 < k ==> k * i < k * j" by (simp add: zmult_zless_mono2)
+  show "\<bar>i\<bar> = (if i < 0 then -i else i)" by (simp only: zabs_def)
+qed
+
+end