--- a/src/HOL/Fun.thy Wed Jun 03 12:24:09 2009 -0700
+++ b/src/HOL/Fun.thy Thu Jun 04 13:26:32 2009 +0200
@@ -250,6 +250,10 @@
lemma bij_betw_imp_inj_on: "bij_betw f A B \<Longrightarrow> inj_on f A"
by (simp add: bij_betw_def)
+lemma bij_betw_trans:
+ "bij_betw f A B \<Longrightarrow> bij_betw g B C \<Longrightarrow> bij_betw (g o f) A C"
+by(auto simp add:bij_betw_def comp_inj_on)
+
lemma bij_betw_inv: assumes "bij_betw f A B" shows "EX g. bij_betw g B A"
proof -
have i: "inj_on f A" and s: "f ` A = B"
@@ -300,6 +304,9 @@
apply (blast del: subsetI intro: vimage_subsetI vimage_subsetD)
done
+lemma inj_on_Un_image_eq_iff: "inj_on f (A \<union> B) \<Longrightarrow> f ` A = f ` B \<longleftrightarrow> A = B"
+by(blast dest: inj_onD)
+
lemma inj_on_image_Int:
"[| inj_on f C; A<=C; B<=C |] ==> f`(A Int B) = f`A Int f`B"
apply (simp add: inj_on_def, blast)