--- a/src/HOLCF/FOCUS/Stream_adm.thy Tue Jul 01 01:28:44 2008 +0200
+++ b/src/HOLCF/FOCUS/Stream_adm.thy Tue Jul 01 02:19:53 2008 +0200
@@ -34,8 +34,8 @@
assumes 1: "Porder.chain Y"
assumes 2: "!i. P (Y i)"
assumes 3: "(!!Y. [| Porder.chain Y; !i. P (Y i); !k. ? j. Fin k < #((Y j)::'a::flat stream)|]
- ==> P(lub (range Y)))"
- shows "P(lub (range Y))"
+ ==> P(LUB i. Y i))"
+ shows "P(LUB i. Y i)"
apply (rule increasing_chain_adm_lemma [of _ P, OF 1 2])
apply (erule 3, assumption)
apply (erule thin_rl)
@@ -59,7 +59,7 @@
(* should be without reference to stream length? *)
lemma flatstream_admI: "[|(!!Y. [| Porder.chain Y; !i. P (Y i);
- !k. ? j. Fin k < #((Y j)::'a::flat stream)|] ==> P(lub (range Y)))|]==> adm P"
+ !k. ? j. Fin k < #((Y j)::'a::flat stream)|] ==> P(LUB i. Y i))|]==> adm P"
apply (unfold adm_def)
apply (intro strip)
apply (erule (1) flatstream_adm_lemma)
@@ -190,13 +190,13 @@
done
lemma adm_set:
-"{lub (range Y) |Y. Porder.chain Y & (\<forall>i. Y i \<in> P)} \<subseteq> P \<Longrightarrow> adm (\<lambda>x. x\<in>P)"
+"{\<Squnion>i. Y i |Y. Porder.chain Y & (\<forall>i. Y i \<in> P)} \<subseteq> P \<Longrightarrow> adm (\<lambda>x. x\<in>P)"
apply (unfold adm_def)
apply (fast)
done
-lemma def_gfp_admI: "P \<equiv> gfp F \<Longrightarrow> {lub (range Y) |Y. Porder.chain Y \<and> (\<forall>i. Y i \<in> P)} \<subseteq>
- F {lub (range Y) |Y. Porder.chain Y \<and> (\<forall>i. Y i \<in> P)} \<Longrightarrow> adm (\<lambda>x. x\<in>P)"
+lemma def_gfp_admI: "P \<equiv> gfp F \<Longrightarrow> {\<Squnion>i. Y i |Y. Porder.chain Y \<and> (\<forall>i. Y i \<in> P)} \<subseteq>
+ F {\<Squnion>i. Y i |Y. Porder.chain Y \<and> (\<forall>i. Y i \<in> P)} \<Longrightarrow> adm (\<lambda>x. x\<in>P)"
apply (simp)
apply (rule adm_set)
apply (erule gfp_upperbound)