--- a/src/HOL/Limits.thy Mon Jan 14 14:33:53 2013 +0100
+++ b/src/HOL/Limits.thy Mon Jan 14 17:16:59 2013 +0100
@@ -68,6 +68,17 @@
using assms unfolding eventually_def
by (rule is_filter.conj [OF is_filter_Rep_filter])
+lemma eventually_Ball_finite:
+ assumes "finite A" and "\<forall>y\<in>A. eventually (\<lambda>x. P x y) net"
+ shows "eventually (\<lambda>x. \<forall>y\<in>A. P x y) net"
+using assms by (induct set: finite, simp, simp add: eventually_conj)
+
+lemma eventually_all_finite:
+ fixes P :: "'a \<Rightarrow> 'b::finite \<Rightarrow> bool"
+ assumes "\<And>y. eventually (\<lambda>x. P x y) net"
+ shows "eventually (\<lambda>x. \<forall>y. P x y) net"
+using eventually_Ball_finite [of UNIV P] assms by simp
+
lemma eventually_mp:
assumes "eventually (\<lambda>x. P x \<longrightarrow> Q x) F"
assumes "eventually (\<lambda>x. P x) F"
--- a/src/HOL/Multivariate_Analysis/Finite_Cartesian_Product.thy Mon Jan 14 14:33:53 2013 +0100
+++ b/src/HOL/Multivariate_Analysis/Finite_Cartesian_Product.thy Mon Jan 14 17:16:59 2013 +0100
@@ -210,17 +210,6 @@
lemma isCont_vec_nth [simp]: "isCont f a \<Longrightarrow> isCont (\<lambda>x. f x $ i) a"
unfolding isCont_def by (rule tendsto_vec_nth)
-lemma eventually_Ball_finite: (* TODO: move *)
- assumes "finite A" and "\<forall>y\<in>A. eventually (\<lambda>x. P x y) net"
- shows "eventually (\<lambda>x. \<forall>y\<in>A. P x y) net"
-using assms by (induct set: finite, simp, simp add: eventually_conj)
-
-lemma eventually_all_finite: (* TODO: move *)
- fixes P :: "'a \<Rightarrow> 'b::finite \<Rightarrow> bool"
- assumes "\<And>y. eventually (\<lambda>x. P x y) net"
- shows "eventually (\<lambda>x. \<forall>y. P x y) net"
-using eventually_Ball_finite [of UNIV P] assms by simp
-
lemma vec_tendstoI:
assumes "\<And>i. ((\<lambda>x. f x $ i) ---> a $ i) net"
shows "((\<lambda>x. f x) ---> a) net"