--- a/src/HOL/Int.thy Wed Apr 01 11:34:21 2009 -0700
+++ b/src/HOL/Int.thy Wed Apr 01 22:29:27 2009 +0200
@@ -1382,8 +1382,6 @@
subsection {* @{term setsum} and @{term setprod} *}
-text {*By Jeremy Avigad*}
-
lemma of_nat_setsum: "of_nat (setsum f A) = (\<Sum>x\<in>A. of_nat(f x))"
apply (cases "finite A")
apply (erule finite_induct, auto)
@@ -1404,26 +1402,6 @@
apply (erule finite_induct, auto)
done
-lemma setprod_nonzero_nat:
- "finite A ==> (\<forall>x \<in> A. f x \<noteq> (0::nat)) ==> setprod f A \<noteq> 0"
- by (rule setprod_nonzero, auto)
-
-lemma setprod_pos_nat:
- "finite S ==> (ALL x : S. f x > (0::nat)) ==> setprod f S > 0"
-using setprod_nonzero_nat by simp
-
-lemma setprod_zero_eq_nat:
- "finite A ==> (setprod f A = (0::nat)) = (\<exists>x \<in> A. f x = 0)"
- by (rule setprod_zero_eq, auto)
-
-lemma setprod_nonzero_int:
- "finite A ==> (\<forall>x \<in> A. f x \<noteq> (0::int)) ==> setprod f A \<noteq> 0"
- by (rule setprod_nonzero, auto)
-
-lemma setprod_zero_eq_int:
- "finite A ==> (setprod f A = (0::int)) = (\<exists>x \<in> A. f x = 0)"
- by (rule setprod_zero_eq, auto)
-
lemmas int_setsum = of_nat_setsum [where 'a=int]
lemmas int_setprod = of_nat_setprod [where 'a=int]