remove duplicate copy of lemma sqrt_add_le_add_sqrt
authorhuffman
Tue, 06 Sep 2011 08:00:28 -0700
changeset 44750 5b11f36fcacb
parent 44749 5b1e1432c320
child 44752 eaf394237ba7
child 44755 257ac9da021f
remove duplicate copy of lemma sqrt_add_le_add_sqrt
src/HOL/Multivariate_Analysis/Linear_Algebra.thy
--- a/src/HOL/Multivariate_Analysis/Linear_Algebra.thy	Tue Sep 06 07:48:59 2011 -0700
+++ b/src/HOL/Multivariate_Analysis/Linear_Algebra.thy	Tue Sep 06 08:00:28 2011 -0700
@@ -415,16 +415,6 @@
   from power2_le_imp_le[OF th yz] show ?thesis .
 qed
 
-text {* TODO: move to NthRoot *}
-lemma sqrt_add_le_add_sqrt:
-  assumes x: "0 \<le> x" and y: "0 \<le> y"
-  shows "sqrt (x + y) \<le> sqrt x + sqrt y"
-apply (rule power2_le_imp_le)
-apply (simp add: power2_sum x y)
-apply (simp add: mult_nonneg_nonneg x y)
-apply (simp add: x y)
-done
-
 subsection {* A generic notion of "hull" (convex, affine, conic hull and closure). *}
 
 definition hull :: "('a set \<Rightarrow> bool) \<Rightarrow> 'a set \<Rightarrow> 'a set" (infixl "hull" 75) where