--- a/src/HOL/Library/Countable_Complete_Lattices.thy Sun Nov 18 09:51:41 2018 +0100
+++ b/src/HOL/Library/Countable_Complete_Lattices.thy Sun Nov 18 18:07:51 2018 +0000
@@ -66,13 +66,13 @@
lemma ccInf_insert [simp]: "countable A \<Longrightarrow> Inf (insert a A) = inf a (Inf A)"
by (force intro: le_infI le_infI1 le_infI2 antisym ccInf_greatest ccInf_lower)
-lemma ccINF_insert [simp]: "countable A \<Longrightarrow> (INF x\<in>insert a A. f x) = inf (f a) (INFIMUM A f)"
+lemma ccINF_insert [simp]: "countable A \<Longrightarrow> (INF x\<in>insert a A. f x) = inf (f a) (Inf (f ` A))"
unfolding image_insert by simp
lemma ccSup_insert [simp]: "countable A \<Longrightarrow> Sup (insert a A) = sup a (Sup A)"
by (force intro: le_supI le_supI1 le_supI2 antisym ccSup_least ccSup_upper)
-lemma ccSUP_insert [simp]: "countable A \<Longrightarrow> (SUP x\<in>insert a A. f x) = sup (f a) (SUPREMUM A f)"
+lemma ccSUP_insert [simp]: "countable A \<Longrightarrow> (SUP x\<in>insert a A. f x) = sup (f a) (Sup (f ` A))"
unfolding image_insert by simp
lemma ccINF_empty [simp]: "(INF x\<in>{}. f x) = top"