src/HOL/Int.thy
 changeset 64272 f76b6dda2e56 parent 64267 b9a1486e79be child 64714 53bab28983f1
```--- a/src/HOL/Int.thy	Mon Oct 17 14:37:32 2016 +0200
+++ b/src/HOL/Int.thy	Mon Oct 17 17:33:07 2016 +0200
@@ -866,7 +866,7 @@
qed

-subsection \<open>@{term sum} and @{term setprod}\<close>
+subsection \<open>@{term sum} and @{term prod}\<close>

lemma of_nat_sum [simp]: "of_nat (sum f A) = (\<Sum>x\<in>A. of_nat(f x))"
by (induct A rule: infinite_finite_induct) auto
@@ -874,14 +874,14 @@
lemma of_int_sum [simp]: "of_int (sum f A) = (\<Sum>x\<in>A. of_int(f x))"
by (induct A rule: infinite_finite_induct) auto

-lemma of_nat_setprod [simp]: "of_nat (setprod f A) = (\<Prod>x\<in>A. of_nat(f x))"
+lemma of_nat_prod [simp]: "of_nat (prod f A) = (\<Prod>x\<in>A. of_nat(f x))"
by (induct A rule: infinite_finite_induct) auto

-lemma of_int_setprod [simp]: "of_int (setprod f A) = (\<Prod>x\<in>A. of_int(f x))"
+lemma of_int_prod [simp]: "of_int (prod f A) = (\<Prod>x\<in>A. of_int(f x))"
by (induct A rule: infinite_finite_induct) auto

lemmas int_sum = of_nat_sum [where 'a=int]
-lemmas int_setprod = of_nat_setprod [where 'a=int]
+lemmas int_prod = of_nat_prod [where 'a=int]

text \<open>Legacy theorems\<close>```