equal
deleted
inserted
replaced
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}"] |