# HG changeset patch # User hoelzl # Date 1358425294 -3600 # Node ID 1aa1a7991fd924f07dd7eaa6f866ba205bf1888f # Parent 3690724028b182daf3667b69c61446c2633ec17e move auxiliary lemma to top diff -r 3690724028b1 -r 1aa1a7991fd9 src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy --- a/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Jan 17 13:20:17 2013 +0100 +++ b/src/HOL/Multivariate_Analysis/Topology_Euclidean_Space.thy Thu Jan 17 13:21:34 2013 +0100 @@ -17,6 +17,13 @@ Norm_Arith begin +(* TODO: Move this to RComplete.thy -- would need to include Glb into RComplete *) +lemma real_isGlb_unique: "[| isGlb R S x; isGlb R S y |] ==> x = (y::real)" + apply (frule isGlb_isLb) + apply (frule_tac x = y in isGlb_isLb) + apply (blast intro!: order_antisym dest!: isGlb_le_isLb) + done + lemma countable_PiE: "finite I \ (\i. i \ I \ countable (F i)) \ countable (PiE I F)" by (induct I arbitrary: F rule: finite_induct) (auto simp: PiE_insert_eq) @@ -2321,13 +2328,6 @@ shows "finite S ==> Inf(insert x S) = (if S = {} then x else min x (Inf S))" by (rule Inf_insert, rule finite_imp_bounded, simp) -(* TODO: Move this to RComplete.thy -- would need to include Glb into RComplete *) -lemma real_isGlb_unique: "[| isGlb R S x; isGlb R S y |] ==> x = (y::real)" - apply (frule isGlb_isLb) - apply (frule_tac x = y in isGlb_isLb) - apply (blast intro!: order_antisym dest!: isGlb_le_isLb) - done - subsection {* Compactness *} subsubsection{* Open-cover compactness *}