src/HOL/Probability/Lebesgue_Measure.thy
changeset 63040 eb4ddd18d635
parent 62975 1d066f6ab25d
child 63262 e497387de7af
equal deleted inserted replaced
63039:1a20fd9cf281 63040:eb4ddd18d635
   193       apply (drule_tac x = "epsilon / 2" in spec)
   193       apply (drule_tac x = "epsilon / 2" in spec)
   194       using egt0 unfolding mult.commute [of 2] by force
   194       using egt0 unfolding mult.commute [of 2] by force
   195     then obtain a' where a'lea [arith]: "a' > a" and
   195     then obtain a' where a'lea [arith]: "a' > a" and
   196       a_prop: "F a' - F a < epsilon / 2"
   196       a_prop: "F a' - F a < epsilon / 2"
   197       by auto
   197       by auto
   198     def S' \<equiv> "{i. l i < r i}"
   198     define S' where "S' = {i. l i < r i}"
   199     obtain S :: "nat set" where
   199     obtain S :: "nat set" where
   200       "S \<subseteq> S'" and finS: "finite S" and
   200       "S \<subseteq> S'" and finS: "finite S" and
   201       Sprop: "{a'..b} \<subseteq> (\<Union>i \<in> S. {l i<..<r i + delta i})"
   201       Sprop: "{a'..b} \<subseteq> (\<Union>i \<in> S. {l i<..<r i + delta i})"
   202     proof (rule compactE_image)
   202     proof (rule compactE_image)
   203       show "compact {a'..b}"
   203       show "compact {a'..b}"