1.1 --- a/src/HOL/Complete_Lattice.thy Sat Jul 16 21:53:50 2011 +0200
1.2 +++ b/src/HOL/Complete_Lattice.thy Sat Jul 16 22:04:02 2011 +0200
1.3 @@ -108,20 +108,6 @@
1.4 with `a \<sqsubseteq> b` show "a \<sqsubseteq> \<Squnion>B" by auto
1.5 qed
1.6
1.7 -lemma top_le:
1.8 - "\<top> \<sqsubseteq> x \<Longrightarrow> x = \<top>"
1.9 - by (rule antisym) auto
1.10 -
1.11 -lemma le_bot:
1.12 - "x \<sqsubseteq> \<bottom> \<Longrightarrow> x = \<bottom>"
1.13 - by (rule antisym) auto
1.14 -
1.15 -lemma not_less_bot [simp]: "\<not> (x \<sqsubset> \<bottom>)"
1.16 - using bot_least [of x] by (auto simp: le_less)
1.17 -
1.18 -lemma not_top_less [simp]: "\<not> (\<top> \<sqsubset> x)"
1.19 - using top_greatest [of x] by (auto simp: le_less)
1.20 -
1.21 lemma Sup_upper2: "u \<in> A \<Longrightarrow> v \<sqsubseteq> u \<Longrightarrow> v \<sqsubseteq> \<Squnion>A"
1.22 using Sup_upper[of u A] by auto
1.23