src/HOL/Library/Extended_Real.thy
changeset 63040 eb4ddd18d635
parent 62975 1d066f6ab25d
child 63060 293ede07b775
--- a/src/HOL/Library/Extended_Real.thy	Sun Apr 24 21:31:14 2016 +0200
+++ b/src/HOL/Library/Extended_Real.thy	Mon Apr 25 16:09:26 2016 +0200
@@ -3900,7 +3900,7 @@
   shows   Liminf_inverse_ereal: "Liminf F (\<lambda>x. inverse (f x)) = inverse (Limsup F f)"
   and     Limsup_inverse_ereal: "Limsup F (\<lambda>x. inverse (f x)) = inverse (Liminf F f)"
 proof -
-  def inv \<equiv> "\<lambda>x. if x \<le> 0 then \<infinity> else inverse x :: ereal"
+  define inv where [abs_def]: "inv x = (if x \<le> 0 then \<infinity> else inverse x)" for x :: ereal
   have "continuous_on ({..0} \<union> {0..}) inv" unfolding inv_def
     by (intro continuous_on_If) (auto intro!: continuous_intros)
   also have "{..0} \<union> {0..} = (UNIV :: ereal set)" by auto