--- a/src/HOL/Rings.thy Tue Mar 31 15:01:06 2015 +0100
+++ b/src/HOL/Rings.thy Tue Mar 31 16:48:48 2015 +0100
@@ -1260,6 +1260,10 @@
"\<bar>x - a\<bar> < r \<longleftrightarrow> a - r < x \<and> x < a + r"
by (auto simp add: diff_less_eq ac_simps abs_less_iff)
+lemma abs_diff_le_iff:
+ "\<bar>x - a\<bar> \<le> r \<longleftrightarrow> a - r \<le> x \<and> x \<le> a + r"
+ by (auto simp add: diff_le_eq ac_simps abs_le_iff)
+
end
hide_fact (open) comm_mult_left_mono comm_mult_strict_left_mono distrib