# HG changeset patch # User huffman # Date 1272732220 25200 # Node ID de62713aec6e9b1dc777891c5cb070f141bcc3e0 # Parent 1a251f69e96b75139100b634aa6566612c360ffa swap ordering on nets, so x <= y means 'x is finer than y' diff -r 1a251f69e96b -r de62713aec6e src/HOL/Limits.thy --- a/src/HOL/Limits.thy Sat May 01 07:53:42 2010 -0700 +++ b/src/HOL/Limits.thy Sat May 01 09:43:40 2010 -0700 @@ -101,26 +101,26 @@ subsection {* Finer-than relation *} -text {* @{term "net \ net'"} means that @{term net'} is finer than -@{term net}. *} +text {* @{term "net \ net'"} means that @{term net} is finer than +@{term net'}. *} -instantiation net :: (type) "{order,top}" +instantiation net :: (type) "{order,bot}" begin definition le_net_def [code del]: - "net \ net' \ (\P. eventually P net \ eventually P net')" + "net \ net' \ (\P. eventually P net' \ eventually P net)" definition less_net_def [code del]: "(net :: 'a net) < net' \ net \ net' \ \ net' \ net" definition - top_net_def [code del]: - "top = Abs_net (\P. True)" + bot_net_def [code del]: + "bot = Abs_net (\P. True)" -lemma eventually_top [simp]: "eventually P top" -unfolding top_net_def +lemma eventually_bot [simp]: "eventually P bot" +unfolding bot_net_def by (subst eventually_Abs_net, rule is_filter.intro, auto) instance proof @@ -136,22 +136,22 @@ fix x y :: "'a net" assume "x \ y" and "y \ x" thus "x = y" unfolding le_net_def expand_net_eq by fast next - fix x :: "'a net" show "x \ top" + fix x :: "'a net" show "bot \ x" unfolding le_net_def by simp qed end lemma net_leD: - "net \ net' \ eventually P net \ eventually P net'" + "net \ net' \ eventually P net' \ eventually P net" unfolding le_net_def by simp lemma net_leI: - "(\P. eventually P net \ eventually P net') \ net \ net'" + "(\P. eventually P net' \ eventually P net) \ net \ net'" unfolding le_net_def by simp lemma eventually_False: - "eventually (\x. False) net \ net = top" + "eventually (\x. False) net \ net = bot" unfolding expand_net_eq by (auto elim: eventually_rev_mp)