--- a/src/HOL/Finite_Set.thy Fri Nov 26 14:19:16 2010 +0100
+++ b/src/HOL/Finite_Set.thy Fri Nov 26 18:06:48 2010 +0100
@@ -2009,6 +2009,15 @@
by (simp add: card_Diff_subset AB)
qed
+lemma diff_card_le_card_Diff:
+assumes "finite B" shows "card A - card B \<le> card(A - B)"
+proof-
+ have "card A - card B \<le> card A - card (A \<inter> B)"
+ using card_mono[OF assms Int_lower2, of A] by arith
+ also have "\<dots> = card(A-B)" using assms by(simp add: card_Diff_subset_Int)
+ finally show ?thesis .
+qed
+
lemma card_Diff1_less: "finite A ==> x: A ==> card (A - {x}) < card A"
apply (rule Suc_less_SucD)
apply (simp add: card_Suc_Diff1 del:card_Diff_insert)