# HG changeset patch
# User nipkow
# Date 1244114792 -7200
# Node ID a1c4c1500abe3e88ab0093c5a480ee6b75fb9b2b
# Parent  b8bdef62bfa6e65d7256332f7e3207fad93688dd
A few finite lemmas

diff -r b8bdef62bfa6 -r a1c4c1500abe src/HOL/Finite_Set.thy
--- a/src/HOL/Finite_Set.thy	Wed Jun 03 12:24:09 2009 -0700
+++ b/src/HOL/Finite_Set.thy	Thu Jun 04 13:26:32 2009 +0200
@@ -1333,6 +1333,10 @@
 apply (auto simp add: insert_Diff_if add_ac)
 done
 
+lemma setsum_diff1_ring: assumes "finite A" "a \<in> A"
+  shows "setsum f (A - {a}) = setsum f A - (f a::'a::ring)"
+unfolding setsum_diff1'[OF assms] by auto
+
 (* By Jeremy Siek: *)
 
 lemma setsum_diff_nat: 
diff -r b8bdef62bfa6 -r a1c4c1500abe src/HOL/Fun.thy
--- 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)
diff -r b8bdef62bfa6 -r a1c4c1500abe src/HOL/SetInterval.thy
--- a/src/HOL/SetInterval.thy	Wed Jun 03 12:24:09 2009 -0700
+++ b/src/HOL/SetInterval.thy	Thu Jun 04 13:26:32 2009 +0200
@@ -468,7 +468,6 @@
 lemma card_greaterThanLessThan [simp]: "card {l<..<u} = u - Suc l"
   by (subst atLeastSucLessThan_greaterThanLessThan [THEN sym], simp)
 
-
 lemma ex_bij_betw_nat_finite:
   "finite M \<Longrightarrow> \<exists>h. bij_betw h {0..<card M} M"
 apply(drule finite_imp_nat_seg_image_inj_on)
@@ -479,6 +478,17 @@
   "finite M \<Longrightarrow> \<exists>h. bij_betw h M {0..<card M}"
 by (blast dest: ex_bij_betw_nat_finite bij_betw_inv)
 
+lemma finite_same_card_bij:
+  "finite A \<Longrightarrow> finite B \<Longrightarrow> card A = card B \<Longrightarrow> EX h. bij_betw h A B"
+apply(drule ex_bij_betw_finite_nat)
+apply(drule ex_bij_betw_nat_finite)
+apply(auto intro!:bij_betw_trans)
+done
+
+lemma ex_bij_betw_nat_finite_1:
+  "finite M \<Longrightarrow> \<exists>h. bij_betw h {1 .. card M} M"
+by (rule finite_same_card_bij) auto
+
 
 subsection {* Intervals of integers *}