more lemmas to Vec1.thy
authorhuffman
Mon, 26 Apr 2010 16:28:58 -0700
changeset 36435 bbe2730e6db6
parent 36434 2a74926bd760
child 36436 1c0f42fb92f1
more lemmas to Vec1.thy
src/HOL/Multivariate_Analysis/Derivative.thy
src/HOL/Multivariate_Analysis/Vec1.thy
--- a/src/HOL/Multivariate_Analysis/Derivative.thy	Mon Apr 26 15:51:10 2010 -0700
+++ b/src/HOL/Multivariate_Analysis/Derivative.thy	Mon Apr 26 16:28:58 2010 -0700
@@ -634,11 +634,6 @@
 
 subsection {* The traditional Rolle theorem in one dimension. *}
 
-lemma vec1_le[simp]:fixes a::real shows "vec1 a \<le> vec1 b \<longleftrightarrow> a \<le> b"
-  unfolding vector_le_def by auto
-lemma vec1_less[simp]:fixes a::real shows "vec1 a < vec1 b \<longleftrightarrow> a < b"
-  unfolding vector_less_def by auto 
-
 lemma rolle: fixes f::"real\<Rightarrow>real"
   assumes "a < b" "f a = f b" "continuous_on {a..b} f"
   "\<forall>x\<in>{a<..<b}. (f has_derivative f'(x)) (at x)"
--- a/src/HOL/Multivariate_Analysis/Vec1.thy	Mon Apr 26 15:51:10 2010 -0700
+++ b/src/HOL/Multivariate_Analysis/Vec1.thy	Mon Apr 26 16:28:58 2010 -0700
@@ -394,6 +394,11 @@
     hence "\<exists>K. \<forall>x. \<bar>f x\<bar> \<le> \<bar>x\<bar> * K" apply(rule_tac x=K in exI)
       unfolding vec1_dest_vec1_simps by (auto simp add:field_simps) }
   thus ?thesis unfolding linear_def bounded_linear_def additive_def bounded_linear_axioms_def o_def
-    unfolding vec1_dest_vec1_simps by auto qed 
+    unfolding vec1_dest_vec1_simps by auto qed
+
+lemma vec1_le[simp]:fixes a::real shows "vec1 a \<le> vec1 b \<longleftrightarrow> a \<le> b"
+  unfolding vector_le_def by auto
+lemma vec1_less[simp]:fixes a::real shows "vec1 a < vec1 b \<longleftrightarrow> a < b"
+  unfolding vector_less_def by auto
 
 end