1.1 --- a/src/HOL/Fun.thy Fri May 20 21:38:32 2011 +0200
1.2 +++ b/src/HOL/Fun.thy Fri May 20 21:38:32 2011 +0200
1.3 @@ -478,6 +478,11 @@
1.4 lemma surj_image_vimage_eq: "surj f ==> f ` (f -` A) = A"
1.5 by simp
1.6
1.7 +lemma surj_vimage_empty:
1.8 + assumes "surj f" shows "f -` A = {} \<longleftrightarrow> A = {}"
1.9 + using surj_image_vimage_eq[OF `surj f`, of A]
1.10 + by (intro iffI) fastsimp+
1.11 +
1.12 lemma inj_vimage_image_eq: "inj f ==> f -` (f ` A) = A"
1.13 by (simp add: inj_on_def, blast)
1.14