--- a/src/HOL/Deriv.thy Mon Jul 19 20:23:52 2010 +0200
+++ b/src/HOL/Deriv.thy Tue Jul 20 06:35:29 2010 +0200
@@ -1255,8 +1255,9 @@
assume "~ f a \<le> f b"
assume "a = b"
with prems show False by auto
- next assume "~ f a \<le> f b"
- assume "a ~= b"
+next
+ assume A: "~ f a \<le> f b"
+ assume B: "a ~= b"
with assms have "EX l z. a < z & z < b & DERIV f z :> l
& f b - f a = (b - a) * l"
apply -
@@ -1266,11 +1267,11 @@
apply (metis differentiableI less_le)
done
then obtain l z where "a < z" and "z < b" and "DERIV f z :> l"
- and "f b - f a = (b - a) * l"
+ and C: "f b - f a = (b - a) * l"
by auto
- from prems have "~(l >= 0)"
- by (metis diff_self diff_eq_diff_less_eq le_iff_diff_le_0 order_antisym linear
- split_mult_pos_le)
+ with A have "a < b" "f b < f a" by auto
+ with C have "\<not> l \<ge> 0" by (auto simp add: not_le algebra_simps)
+ (metis A add_le_cancel_right assms(1) less_eq_real_def mult_right_mono real_add_left_mono real_le_linear real_le_refl)
with prems show False
by (metis DERIV_unique order_less_imp_le)
qed