--- a/src/HOL/Complete_Lattice.thy Wed Jul 13 19:40:18 2011 +0200
+++ b/src/HOL/Complete_Lattice.thy Wed Jul 13 19:43:12 2011 +0200
@@ -392,15 +392,6 @@
lemma Inter_Un_distrib: "\<Inter>(A \<union> B) = \<Inter>A \<inter> \<Inter>B"
by (fact Inf_union_distrib)
-lemma (in bounded_lattice_bot) bot_less:
- -- {* FIXME: tighten classes bot, top to partial orders (uniqueness!), move lemmas there *}
- "a \<noteq> bot \<longleftrightarrow> bot < a"
- by (auto simp add: less_le_not_le intro!: antisym)
-
-lemma (in bounded_lattice_top) less_top:
- "a \<noteq> top \<longleftrightarrow> a < top"
- by (auto simp add: less_le_not_le intro!: antisym)
-
lemma (in complete_lattice) Inf_top_conv [no_atp]:
"\<Sqinter>A = \<top> \<longleftrightarrow> (\<forall>x\<in>A. x = \<top>)"
"\<top> = \<Sqinter>A \<longleftrightarrow> (\<forall>x\<in>A. x = \<top>)"
--- a/src/HOL/Orderings.thy Wed Jul 13 19:40:18 2011 +0200
+++ b/src/HOL/Orderings.thy Wed Jul 13 19:43:12 2011 +0200
@@ -1086,10 +1086,24 @@
class bot = order +
fixes bot :: 'a
assumes bot_least [simp]: "bot \<le> x"
+begin
+
+lemma bot_less:
+ "a \<noteq> bot \<longleftrightarrow> bot < a"
+ by (auto simp add: less_le_not_le intro!: antisym)
+
+end
class top = order +
fixes top :: 'a
assumes top_greatest [simp]: "x \<le> top"
+begin
+
+lemma less_top:
+ "a \<noteq> top \<longleftrightarrow> a < top"
+ by (auto simp add: less_le_not_le intro!: antisym)
+
+end
subsection {* Dense orders *}