--- a/src/HOL/Library/Continuity.thy Fri Mar 16 21:32:07 2007 +0100
+++ b/src/HOL/Library/Continuity.thy Fri Mar 16 21:32:08 2007 +0100
@@ -12,15 +12,15 @@
subsection {* Continuity for complete lattices *}
definition
- chain :: "(nat \<Rightarrow> 'a::order) \<Rightarrow> bool" where
+ chain :: "(nat \<Rightarrow> 'a::complete_lattice) \<Rightarrow> bool" where
"chain M \<longleftrightarrow> (\<forall>i. M i \<le> M (Suc i))"
definition
- continuous :: "('a::comp_lat \<Rightarrow> 'a::comp_lat) \<Rightarrow> bool" where
+ continuous :: "('a::complete_lattice \<Rightarrow> 'a::complete_lattice) \<Rightarrow> bool" where
"continuous F \<longleftrightarrow> (\<forall>M. chain M \<longrightarrow> F (SUP i. M i) = (SUP i. F (M i)))"
abbreviation
- bot :: "'a::order" where
+ bot :: "'a::complete_lattice" where
"bot \<equiv> Sup {}"
lemma SUP_nat_conv:
@@ -34,7 +34,7 @@
apply (blast intro:SUP_leI le_SUPI)
done
-lemma continuous_mono: fixes F :: "'a::comp_lat \<Rightarrow> 'a::comp_lat"
+lemma continuous_mono: fixes F :: "'a::complete_lattice \<Rightarrow> 'a::complete_lattice"
assumes "continuous F" shows "mono F"
proof
fix A B :: "'a" assume "A <= B"