author huffman Wed, 01 Nov 2006 17:57:02 +0100 changeset 21141 f0b5e6254a1f parent 21140 1c0805003c4f child 21142 a56a839e9feb
move DERIV_sumr from Series.thy to Lim.thy
 src/HOL/Hyperreal/Lim.thy file | annotate | diff | comparison | revisions src/HOL/Hyperreal/Series.thy file | annotate | diff | comparison | revisions
```--- 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:```
```--- a/src/HOL/Hyperreal/Series.thy	Wed Nov 01 17:14:16 2006 +0100
+++ b/src/HOL/Hyperreal/Series.thy	Wed Nov 01 17:57:02 2006 +0100
@@ -10,7 +10,7 @@
header{*Finite Summation and Infinite Series*}

theory Series
-imports SEQ Lim
+imports SEQ
begin

definition
@@ -560,14 +560,4 @@
apply (auto intro!: geometric_sums)
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
-
end```