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src/HOL/Analysis/Continuum_Not_Denumerable.thy
changeset 77200 8f2e6186408f
parent 75078 ec86cb2418e1 
--- a/src/HOL/Analysis/Continuum_Not_Denumerable.thy	Sun Feb 05 20:09:39 2023 +0100
+++ b/src/HOL/Analysis/Continuum_Not_Denumerable.thy	Mon Feb 06 15:41:23 2023 +0000
@@ -176,9 +176,7 @@
 qed
 
 lemma uncountable_closed_interval: "uncountable {a..b} \<longleftrightarrow> a < b" for a b :: real
-  apply (rule iffI)
-   apply (metis atLeastAtMost_singleton atLeastatMost_empty countable_finite finite.emptyI finite_insert linorder_neqE_linordered_idom)
-  using real_interval_avoid_countable_set by fastforce
+  using infinite_Icc_iff by (fastforce dest: countable_finite real_interval_avoid_countable_set)
 
 lemma open_minus_countable:
   fixes S A :: "real set"
isabelle