src/HOL/Analysis/Continuum_Not_Denumerable.thy
changeset 75078 ec86cb2418e1
parent 70136 f03a01a18c6e
child 77200 8f2e6186408f
--- a/src/HOL/Analysis/Continuum_Not_Denumerable.thy	Mon Feb 14 16:41:48 2022 +0100
+++ b/src/HOL/Analysis/Continuum_Not_Denumerable.thy	Tue Feb 15 13:00:05 2022 +0000
@@ -97,6 +97,12 @@
 lemma uncountable_UNIV_real: "uncountable (UNIV :: real set)"
   using real_non_denum unfolding uncountable_def by auto
 
+corollary complex_non_denum: "\<nexists>f :: nat \<Rightarrow> complex. surj f"
+  by (metis (full_types) Re_complex_of_real comp_surj real_non_denum surj_def)
+
+lemma uncountable_UNIV_complex: "uncountable (UNIV :: complex set)"
+  using complex_non_denum unfolding uncountable_def by auto
+
 lemma bij_betw_open_intervals:
   fixes a b c d :: real
   assumes "a < b" "c < d"