src/HOL/Import/HOLLightReal.thy
changeset 44633 8a2fd7418435
parent 44282 f0de18b62d63
child 45051 c478d1876371
--- a/src/HOL/Import/HOLLightReal.thy	Wed Aug 31 13:28:29 2011 -0700
+++ b/src/HOL/Import/HOLLightReal.thy	Thu Sep 01 16:16:25 2011 +0900
@@ -301,10 +301,7 @@
   "(\<exists>(x :: real). P x) \<and> (\<exists>(M :: real). \<forall>x. P x \<longrightarrow> x \<le> M) \<longrightarrow>
    (\<exists>M. (\<forall>x. P x \<longrightarrow> x \<le> M) \<and>
           (\<forall>M'. (\<forall>x. P x \<longrightarrow> x \<le> M') \<longrightarrow> M \<le> M'))"
-  apply (intro allI impI, elim conjE)
-  apply (drule complete_real[unfolded Ball_def mem_def])
-  apply simp_all
-  done
+  using complete_real[unfolded Ball_def, of "Collect P"] by auto
 
 lemma REAL_COMPLETE_SOMEPOS:
   "(\<exists>(x :: real). P x \<and> 0 \<le> x) \<and> (\<exists>M. \<forall>x. P x \<longrightarrow> x \<le> M) \<longrightarrow>