src/HOL/OrderedGroup.thy
 changeset 31034 736f521ad036 parent 31016 e1309df633c6 child 31902 862ae16a799d
1.1 --- a/src/HOL/OrderedGroup.thy	Mon May 04 14:49:48 2009 +0200
1.2 +++ b/src/HOL/OrderedGroup.thy	Mon May 04 14:49:49 2009 +0200
1.3 @@ -637,27 +637,6 @@
1.4  lemma le_iff_diff_le_0: "a \<le> b \<longleftrightarrow> a - b \<le> 0"
1.5  by (simp add: algebra_simps)
1.7 -lemma sum_nonneg_eq_zero_iff:
1.8 -  assumes x: "0 \<le> x" and y: "0 \<le> y"
1.9 -  shows "(x + y = 0) = (x = 0 \<and> y = 0)"
1.10 -proof -
1.11 -  have "x + y = 0 \<Longrightarrow> x = 0"
1.12 -  proof -
1.13 -    from y have "x + 0 \<le> x + y" by (rule add_left_mono)
1.14 -    also assume "x + y = 0"
1.15 -    finally have "x \<le> 0" by simp
1.16 -    then show "x = 0" using x by (rule antisym)
1.17 -  qed
1.18 -  moreover have "x + y = 0 \<Longrightarrow> y = 0"
1.19 -  proof -
1.20 -    from x have "0 + y \<le> x + y" by (rule add_right_mono)
1.21 -    also assume "x + y = 0"
1.22 -    finally have "y \<le> 0" by simp
1.23 -    then show "y = 0" using y by (rule antisym)
1.24 -  qed
1.25 -  ultimately show ?thesis by auto
1.26 -qed
1.27 -
1.28  text{*Legacy - use @{text algebra_simps} *}
1.29  lemmas group_simps[noatp] = algebra_simps