--- a/src/HOL/Conditionally_Complete_Lattices.thy Mon Jan 22 16:08:50 2018 +0100
+++ b/src/HOL/Conditionally_Complete_Lattices.thy Mon Jan 22 22:45:45 2018 +0100
@@ -10,19 +10,6 @@
imports Finite_Set Lattices_Big Set_Interval
begin
-context linorder
-begin
-
-lemma Sup_fin_eq_Max:
- "finite X \<Longrightarrow> X \<noteq> {} \<Longrightarrow> Sup_fin X = Max X"
- by (induct X rule: finite_ne_induct) (simp_all add: sup_max)
-
-lemma Inf_fin_eq_Min:
- "finite X \<Longrightarrow> X \<noteq> {} \<Longrightarrow> Inf_fin X = Min X"
- by (induct X rule: finite_ne_induct) (simp_all add: inf_min)
-
-end
-
context preorder
begin
@@ -471,10 +458,10 @@
..
lemma cSup_eq_Max: "finite (X::'a::conditionally_complete_linorder set) \<Longrightarrow> X \<noteq> {} \<Longrightarrow> Sup X = Max X"
- using cSup_eq_Sup_fin[of X] Sup_fin_eq_Max[of X] by simp
+ using cSup_eq_Sup_fin[of X] by (simp add: Sup_fin_Max)
lemma cInf_eq_Min: "finite (X::'a::conditionally_complete_linorder set) \<Longrightarrow> X \<noteq> {} \<Longrightarrow> Inf X = Min X"
- using cInf_eq_Inf_fin[of X] Inf_fin_eq_Min[of X] by simp
+ using cInf_eq_Inf_fin[of X] by (simp add: Inf_fin_Min)
lemma cSup_lessThan[simp]: "Sup {..<x::'a::{conditionally_complete_linorder, no_bot, dense_linorder}} = x"
by (auto intro!: cSup_eq_non_empty intro: dense_le)