src/HOL/Probability/Borel_Space.thy
changeset 46884 154dc6ec0041
parent 46731 5302e932d1e5
child 46905 6b1c0a80a57a
     1.1 --- a/src/HOL/Probability/Borel_Space.thy	Mon Mar 12 15:12:22 2012 +0100
     1.2 +++ b/src/HOL/Probability/Borel_Space.thy	Mon Mar 12 21:41:11 2012 +0100
     1.3 @@ -1417,7 +1417,7 @@
     1.4  proof
     1.5    fix a
     1.6    have "?sup -` {a<..} \<inter> space M = (\<Union>i\<in>A. {x\<in>space M. a < f i x})"
     1.7 -    by (auto simp: less_SUP_iff SUP_apply)
     1.8 +    by (auto simp: less_SUP_iff)
     1.9    then show "?sup -` {a<..} \<inter> space M \<in> sets M"
    1.10      using assms by auto
    1.11  qed
    1.12 @@ -1430,7 +1430,7 @@
    1.13  proof
    1.14    fix a
    1.15    have "?inf -` {..<a} \<inter> space M = (\<Union>i\<in>A. {x\<in>space M. f i x < a})"
    1.16 -    by (auto simp: INF_less_iff INF_apply)
    1.17 +    by (auto simp: INF_less_iff)
    1.18    then show "?inf -` {..<a} \<inter> space M \<in> sets M"
    1.19      using assms by auto
    1.20  qed