removing lemma bij_betw_Disj_Un, as it is a special case of bij_between_combine (was added in d1fc454d6735, and has not been used since)
--- a/src/HOL/Fun.thy Sun Feb 05 08:36:41 2012 +0100
+++ b/src/HOL/Fun.thy Sun Feb 05 08:47:13 2012 +0100
@@ -427,28 +427,6 @@
using * by blast
qed
-(* FIXME: bij_betw_Disj_Un is special case of bij_betw_combine -- should be removed *)
-lemma bij_betw_Disj_Un:
- assumes DISJ: "A \<inter> B = {}" and DISJ': "A' \<inter> B' = {}" and
- B1: "bij_betw f A A'" and B2: "bij_betw f B B'"
- shows "bij_betw f (A \<union> B) (A' \<union> B')"
-proof-
- have 1: "inj_on f A \<and> inj_on f B"
- using B1 B2 by (auto simp add: bij_betw_def)
- have 2: "f`A = A' \<and> f`B = B'"
- using B1 B2 by (auto simp add: bij_betw_def)
- hence "f`(A - B) \<inter> f`(B - A) = {}"
- using DISJ DISJ' by blast
- hence "inj_on f (A \<union> B)"
- using 1 by (auto simp add: inj_on_Un)
- (* *)
- moreover
- have "f`(A \<union> B) = A' \<union> B'"
- using 2 by auto
- ultimately show ?thesis
- unfolding bij_betw_def by auto
-qed
-
lemma bij_betw_subset:
assumes BIJ: "bij_betw f A A'" and
SUB: "B \<le> A" and IM: "f ` B = B'"