--- a/src/HOL/Fact.thy Fri Jun 27 22:08:55 2014 +0200
+++ b/src/HOL/Fact.thy Sat Jun 28 09:16:42 2014 +0200
@@ -202,7 +202,7 @@
also from Suc.hyps have "... = Suc (n + d') * \<Prod>{n + 1..n + d'}"
unfolding div_mult1_eq[of _ "fact (n + d')"] by (simp add: fact_mod)
also have "... = \<Prod>{n + 1..n + Suc d'}"
- by (simp add: atLeastAtMostSuc_conv setprod_insert)
+ by (simp add: atLeastAtMostSuc_conv setprod.insert)
finally show ?case .
qed
from this `m = n + d` show ?thesis by simp
@@ -314,7 +314,7 @@
assumes "r \<le> n" shows "fact n div fact (n - r) \<le> n ^ r"
proof -
have "\<And>r. r \<le> n \<Longrightarrow> \<Prod>{n - r..n} = (n - r) * \<Prod>{Suc (n - r)..n}"
- by (subst setprod_insert[symmetric]) (auto simp: atLeastAtMost_insertL)
+ by (subst setprod.insert[symmetric]) (auto simp: atLeastAtMost_insertL)
with assms show ?thesis
by (induct r rule: nat.induct) (auto simp add: fact_div_fact Suc_diff_Suc mult_le_mono)
qed