src/HOL/Finite_Set.thy
changeset 70723 4e39d87c9737
parent 70178 4900351361b0
child 71258 d67924987c34
--- a/src/HOL/Finite_Set.thy	Tue Sep 17 16:21:31 2019 +0100
+++ b/src/HOL/Finite_Set.thy	Wed Sep 18 14:41:37 2019 +0100
@@ -1493,12 +1493,11 @@
   using card_Un_Int [of A B] by simp
 
 lemma card_Un_le: "card (A \<union> B) \<le> card A + card B"
-  apply (cases "finite A")
-   apply (cases "finite B")
-    apply (use le_iff_add card_Un_Int in blast)
-   apply simp
-  apply simp
-  done
+proof (cases "finite A \<and> finite B")
+  case True
+  then show ?thesis
+    using le_iff_add card_Un_Int [of A B] by auto
+qed auto
 
 lemma card_Diff_subset:
   assumes "finite B"