--- a/src/HOL/Hyperreal/Lim.thy Wed Nov 01 17:14:16 2006 +0100
+++ b/src/HOL/Hyperreal/Lim.thy Wed Nov 01 17:57:02 2006 +0100
@@ -766,6 +766,15 @@
apply (blast intro: LIM_unique)
done
+text{*Differentiation of finite sum*}
+
+lemma DERIV_sumr [rule_format (no_asm)]:
+ "(\<forall>r. m \<le> r & r < (m + n) --> DERIV (%x. f r x) x :> (f' r x))
+ --> DERIV (%x. \<Sum>n=m..<n::nat. f n x :: real) x :> (\<Sum>r=m..<n. f' r x)"
+apply (induct "n")
+apply (auto intro: DERIV_add)
+done
+
text{*Alternative definition for differentiability*}
lemma DERIV_LIM_iff: