author paulson Mon, 24 Sep 2018 14:33:17 +0100 changeset 69110 697789794af1 parent 69045 8c240fdeffcb (current diff) parent 69109 c9ea9290880f (diff) child 69111 a3efc22181a8
merged
```--- a/src/HOL/Deriv.thy	Sun Sep 23 21:49:31 2018 +0200
+++ b/src/HOL/Deriv.thy	Mon Sep 24 14:33:17 2018 +0100
@@ -1384,19 +1384,19 @@
assumes "a < b"
and contf: "continuous_on {a..b} f"
and derf: "\<And>x. \<lbrakk>a < x; x < b\<rbrakk> \<Longrightarrow> (f has_derivative f' x) (at x)"
-  obtains z where "a < z" "z < b" "f b - f a = (f' z) (b - a)"
+  obtains \<xi> where "a < \<xi>" "\<xi> < b" "f b - f a = (f' \<xi>) (b - a)"
proof -
have "\<exists>x. a < x \<and> x < b \<and> (\<lambda>y. f' x y - (f b - f a) / (b - a) * y) = (\<lambda>v. 0)"
proof (intro Rolle_deriv[OF \<open>a < b\<close>])
fix x
assume x: "a < x" "x < b"
-    show "((\<lambda>x. f x - (f b - f a) / (b - a) * x) has_derivative
-        (\<lambda>xa. f' x xa - (f b - f a) / (b - a) * xa)) (at x)"
+    show "((\<lambda>x. f x - (f b - f a) / (b - a) * x)
+          has_derivative (\<lambda>y. f' x y - (f b - f a) / (b - a) * y)) (at x)"
by (intro derivative_intros derf[OF x])
qed (use assms in \<open>auto intro!: continuous_intros simp: field_simps\<close>)
-  then obtain x where
-    "a < x" "x < b"
-    "(\<lambda>y. f' x y - (f b - f a) / (b - a) * y) = (\<lambda>v. 0)" by metis
+  then obtain \<xi> where
+    "a < \<xi>" "\<xi> < b" "(\<lambda>y. f' \<xi> y - (f b - f a) / (b - a) * y) = (\<lambda>v. 0)"
+    by metis
then show ?thesis