--- a/src/HOL/Transcendental.thy Fri Aug 19 17:59:19 2011 -0700
+++ b/src/HOL/Transcendental.thy Fri Aug 19 18:06:27 2011 -0700
@@ -1166,7 +1166,7 @@
lemma DERIV_ln: "0 < x \<Longrightarrow> DERIV ln x :> inverse x"
apply (rule DERIV_inverse_function [where f=exp and a=0 and b="x+1"])
- apply (erule lemma_DERIV_subst [OF DERIV_exp exp_ln])
+ apply (erule DERIV_cong [OF DERIV_exp exp_ln])
apply (simp_all add: abs_if isCont_ln)
done
@@ -1309,9 +1309,6 @@
lemma cos_zero [simp]: "cos 0 = 1"
unfolding cos_def cos_coeff_def by (simp add: powser_zero)
-lemma lemma_DERIV_subst: "[| DERIV f x :> D; D = E |] ==> DERIV f x :> E"
- by (rule DERIV_cong) (* TODO: delete *)
-
lemma sin_cos_squared_add [simp]: "(sin x)\<twosuperior> + (cos x)\<twosuperior> = 1"
proof -
have "\<forall>x. DERIV (\<lambda>x. (sin x)\<twosuperior> + (cos x)\<twosuperior>) x :> 0"