--- a/src/HOL/Inequalities.thy Tue Nov 03 11:20:21 2015 +0100
+++ b/src/HOL/Inequalities.thy Tue Nov 10 14:18:41 2015 +0000
@@ -31,9 +31,10 @@
have "m*(m-1) \<le> n*(n + 1)"
using assms by (meson diff_le_self order_trans le_add1 mult_le_mono)
hence "int(\<Sum> {m..n}) = int((n*(n+1) - m*(m-1)) div 2)" using assms
- by (auto simp: Setsum_Icc_int[transferred, OF assms] zdiv_int int_mult
- split: zdiff_int_split)
- thus ?thesis by simp
+ by (auto simp: Setsum_Icc_int[transferred, OF assms] zdiv_int int_mult simp del: of_nat_setsum
+ split: zdiff_int_split)
+ thus ?thesis
+ by blast
qed
lemma Setsum_Ico_nat: assumes "(m::nat) \<le> n"
@@ -75,7 +76,6 @@
(\<And>i j. \<lbrakk> i\<le>j; j<n \<rbrakk> \<Longrightarrow> b i \<ge> b j) \<Longrightarrow>
n * (\<Sum>i=0..<n. a i * b i) \<le> (\<Sum>i=0..<n. a i) * (\<Sum>i=0..<n. b i)"
using Chebyshev_sum_upper[where 'a=real, of n a b]
-by (simp del: real_of_nat_mult real_of_nat_setsum
- add: real_of_nat_mult[symmetric] real_of_nat_setsum[symmetric] real_of_nat_def[symmetric])
+by (simp del: of_nat_mult of_nat_setsum add: of_nat_mult[symmetric] of_nat_setsum[symmetric])
end