--- a/src/HOL/MacLaurin.thy Tue Jun 30 18:16:22 2009 +0200
+++ b/src/HOL/MacLaurin.thy Tue Jun 30 18:21:55 2009 +0200
@@ -91,7 +91,7 @@
apply (simp (no_asm) add: divide_inverse mult_assoc del: fact_Suc power_Suc)
apply (rule DERIV_cmult)
apply (rule lemma_DERIV_subst)
- apply (best intro: DERIV_chain2 intro!: DERIV_intros)
+ apply (best intro!: DERIV_intros)
apply (subst fact_Suc)
apply (subst real_of_nat_mult)
apply (simp add: mult_ac)
@@ -565,9 +565,7 @@
apply (clarify)
apply (subst (1 2 3) mod_Suc_eq_Suc_mod)
apply (cut_tac m=m in mod_exhaust_less_4)
- apply (safe, simp_all)
- apply (rule DERIV_minus, simp)
- apply (rule lemma_DERIV_subst, rule DERIV_minus, rule DERIV_cos, simp)
+ apply (safe, auto intro!: DERIV_intros)
done
from Maclaurin_all_le [OF diff_0 DERIV_diff]
obtain t where t1: "\<bar>t\<bar> \<le> \<bar>x\<bar>" and