--- a/src/HOL/Library/Formal_Power_Series.thy Fri Jul 17 10:07:15 2009 +0200
+++ b/src/HOL/Library/Formal_Power_Series.thy Fri Jul 17 13:12:18 2009 -0400
@@ -2514,7 +2514,7 @@
proof-
{fix n
have "?l$n = ?r $ n"
- apply (auto simp add: E_def field_simps power_Suc[symmetric]simp del: fact_Suc_nat of_nat_Suc power_Suc)
+ apply (auto simp add: E_def field_simps power_Suc[symmetric]simp del: fact_Suc of_nat_Suc power_Suc)
by (simp add: of_nat_mult ring_simps)}
then show ?thesis by (simp add: fps_eq_iff)
qed
@@ -2531,7 +2531,7 @@
apply simp
unfolding th
using fact_gt_zero_nat
- apply (simp add: field_simps del: of_nat_Suc fact_Suc_nat)
+ apply (simp add: field_simps del: of_nat_Suc fact_Suc)
apply (drule sym)
by (simp add: ring_simps of_nat_mult power_Suc)}
note th' = this
@@ -2697,7 +2697,7 @@
also have "\<dots> = of_nat (n+1) * ((- 1)^(n div 2) * c^Suc n / of_nat (fact (Suc n)))"
using en by (simp add: fps_sin_def)
also have "\<dots> = (- 1)^(n div 2) * c^Suc n * (of_nat (n+1) / (of_nat (Suc n) * of_nat (fact n)))"
- unfolding fact_Suc_nat of_nat_mult
+ unfolding fact_Suc of_nat_mult
by (simp add: field_simps del: of_nat_add of_nat_Suc)
also have "\<dots> = (- 1)^(n div 2) *c^Suc n / of_nat (fact n)"
by (simp add: field_simps del: of_nat_add of_nat_Suc)
@@ -2721,7 +2721,7 @@
also have "\<dots> = of_nat (n+1) * ((- 1)^((n + 1) div 2) * c^Suc n / of_nat (fact (Suc n)))"
using en by (simp add: fps_cos_def)
also have "\<dots> = (- 1)^((n + 1) div 2)*c^Suc n * (of_nat (n+1) / (of_nat (Suc n) * of_nat (fact n)))"
- unfolding fact_Suc_nat of_nat_mult
+ unfolding fact_Suc of_nat_mult
by (simp add: field_simps del: of_nat_add of_nat_Suc)
also have "\<dots> = (- 1)^((n + 1) div 2) * c^Suc n / of_nat (fact n)"
by (simp add: field_simps del: of_nat_add of_nat_Suc)
@@ -2763,7 +2763,7 @@
"fps_sin c $ (n + 2) = - (c * c * fps_sin c $ n / (of_nat(n+1) * of_nat(n+2)))"
unfolding fps_sin_def
apply (cases n, simp)
-apply (simp add: divide_eq_iff eq_divide_iff del: of_nat_Suc fact_Suc_nat)
+apply (simp add: divide_eq_iff eq_divide_iff del: of_nat_Suc fact_Suc)
apply (simp add: of_nat_mult del: of_nat_Suc mult_Suc)
done
@@ -2776,7 +2776,7 @@
lemma fps_cos_nth_add_2:
"fps_cos c $ (n + 2) = - (c * c * fps_cos c $ n / (of_nat(n+1) * of_nat(n+2)))"
unfolding fps_cos_def
-apply (simp add: divide_eq_iff eq_divide_iff del: of_nat_Suc fact_Suc_nat)
+apply (simp add: divide_eq_iff eq_divide_iff del: of_nat_Suc fact_Suc)
apply (simp add: of_nat_mult del: of_nat_Suc mult_Suc)
done