add lema about card and vimage
authorAndreas Lochbihler
Wed, 11 Feb 2015 14:15:59 +0100
changeset 59520 76d7c593c6e8
parent 59519 2fb0c0fc62a3
child 59521 ef8ac8d2315e
add lema about card and vimage
src/HOL/Finite_Set.thy
--- a/src/HOL/Finite_Set.thy	Wed Feb 11 14:12:30 2015 +0100
+++ b/src/HOL/Finite_Set.thy	Wed Feb 11 14:15:59 2015 +0100
@@ -1638,6 +1638,8 @@
 shows "finite A"
 using assms finite_imageD finite_subset by blast
 
+lemma card_vimage_inj: "\<lbrakk> inj f; A \<subseteq> range f \<rbrakk> \<Longrightarrow> card (f -` A) = card A"
+by(auto 4 3 simp add: subset_image_iff inj_vimage_image_eq intro: card_image[symmetric, OF subset_inj_on])
 
 subsubsection {* Pigeonhole Principles *}