src/HOL/Analysis/Harmonic_Numbers.thy

                      \<longlonglongrightarrow> euler_mascheroni - euler_mascheroni + ln 2"
     by (intro tendsto_intros euler_mascheroni_LIMSEQ filterlim_compose[OF euler_mascheroni_LIMSEQ]
               filterlim_subseq) (auto simp: strict_mono_def)
   hence "(\<lambda>n. ?em (2*n) - ?em n + ln (2::real)) \<longlonglongrightarrow> ln 2" by simp
   ultimately have "(\<lambda>n. (\<Sum>k<2*n. (-1)^k / real_of_nat (Suc k))) \<longlonglongrightarrow> ln 2"
-    by (rule Lim_transform_eventually)
+    by (blast intro: Lim_transform_eventually)
 
   moreover have "summable (\<lambda>k. (-1)^k * inverse (real_of_nat (Suc k)))"
     using LIMSEQ_inverse_real_of_nat
     by (intro summable_Leibniz(1) decseq_imp_monoseq decseq_SucI) simp_all
   hence A: "(\<lambda>n. \<Sum>k<n. (-1)^k / real_of_nat (Suc k)) \<longlonglongrightarrow> (\<Sum>k. (-1)^k / real_of_nat (Suc k))"