src/HOL/Probability/Measure_Space.thy
changeset 63040 eb4ddd18d635
parent 62975 1d066f6ab25d
child 63333 158ab2239496
equal deleted inserted replaced
63039:1a20fd9cf281 63040:eb4ddd18d635
   565     using I \<open>finite I\<close> by (intro antisym INF_lower INF_greatest F emeasure_mono) auto
   565     using I \<open>finite I\<close> by (intro antisym INF_lower INF_greatest F emeasure_mono) auto
   566   ultimately show ?thesis
   566   ultimately show ?thesis
   567     by simp
   567     by simp
   568 next
   568 next
   569   assume "infinite I"
   569   assume "infinite I"
   570   def L \<equiv> "\<lambda>n. LEAST i. i \<in> I \<and> i \<ge> n"
   570   define L where "L n = (LEAST i. i \<in> I \<and> i \<ge> n)" for n
   571   have L: "L n \<in> I \<and> n \<le> L n" for n
   571   have L: "L n \<in> I \<and> n \<le> L n" for n
   572     unfolding L_def
   572     unfolding L_def
   573   proof (rule LeastI_ex)
   573   proof (rule LeastI_ex)
   574     show "\<exists>x. x \<in> I \<and> n \<le> x"
   574     show "\<exists>x. x \<in> I \<and> n \<le> x"
   575       using \<open>infinite I\<close> finite_subset[of I "{..< n}"]
   575       using \<open>infinite I\<close> finite_subset[of I "{..< n}"]