1.1 --- a/src/HOL/SEQ.thy Sun Sep 04 07:15:13 2011 -0700
1.2 +++ b/src/HOL/SEQ.thy Sun Sep 04 09:49:45 2011 -0700
1.3 @@ -380,22 +380,6 @@
1.4 shows "\<lbrakk>X ----> a; a \<noteq> 0\<rbrakk> \<Longrightarrow> Bseq (\<lambda>n. inverse (X n))"
1.5 unfolding Bseq_conv_Bfun by (rule Bfun_inverse)
1.6
1.7 -lemma LIMSEQ_add_const: (* FIXME: delete *)
1.8 - fixes a :: "'a::real_normed_vector"
1.9 - shows "f ----> a ==> (%n.(f n + b)) ----> a + b"
1.10 -by (intro tendsto_intros)
1.11 -
1.12 -(* FIXME: delete *)
1.13 -lemma LIMSEQ_add_minus:
1.14 - fixes a b :: "'a::real_normed_vector"
1.15 - shows "[| X ----> a; Y ----> b |] ==> (%n. X n + -Y n) ----> a + -b"
1.16 -by (intro tendsto_intros)
1.17 -
1.18 -lemma LIMSEQ_diff_const: (* FIXME: delete *)
1.19 - fixes a b :: "'a::real_normed_vector"
1.20 - shows "f ----> a ==> (%n.(f n - b)) ----> a - b"
1.21 -by (intro tendsto_intros)
1.22 -
1.23 lemma LIMSEQ_diff_approach_zero:
1.24 fixes L :: "'a::real_normed_vector"
1.25 shows "g ----> L ==> (%x. f x - g x) ----> 0 ==> f ----> L"
1.26 @@ -438,7 +422,8 @@
1.27
1.28 lemma LIMSEQ_inverse_real_of_nat_add_minus:
1.29 "(%n. r + -inverse(real(Suc n))) ----> r"
1.30 - using LIMSEQ_add_minus [OF tendsto_const LIMSEQ_inverse_real_of_nat] by auto
1.31 + using tendsto_add [OF tendsto_const
1.32 + tendsto_minus [OF LIMSEQ_inverse_real_of_nat]] by auto
1.33
1.34 lemma LIMSEQ_inverse_real_of_nat_add_minus_mult:
1.35 "(%n. r*( 1 + -inverse(real(Suc n)))) ----> r"