remove more bounded_linear locale interpretations (cf. f0de18b62d63)
1.1 --- a/src/HOL/Complex.thy Thu Aug 18 19:53:03 2011 -0700
1.2 +++ b/src/HOL/Complex.thy Thu Aug 18 21:23:31 2011 -0700
1.3 @@ -339,12 +339,23 @@
1.4
1.5 subsection {* Completeness of the Complexes *}
1.6
1.7 -interpretation Re: bounded_linear "Re"
1.8 +lemma bounded_linear_Re: "bounded_linear Re"
1.9 by (rule bounded_linear_intro [where K=1], simp_all add: complex_norm_def)
1.10
1.11 -interpretation Im: bounded_linear "Im"
1.12 +lemma bounded_linear_Im: "bounded_linear Im"
1.13 by (rule bounded_linear_intro [where K=1], simp_all add: complex_norm_def)
1.14
1.15 +lemmas tendsto_Re [tendsto_intros] =
1.16 + bounded_linear.tendsto [OF bounded_linear_Re]
1.17 +
1.18 +lemmas tendsto_Im [tendsto_intros] =
1.19 + bounded_linear.tendsto [OF bounded_linear_Im]
1.20 +
1.21 +lemmas isCont_Re [simp] = bounded_linear.isCont [OF bounded_linear_Re]
1.22 +lemmas isCont_Im [simp] = bounded_linear.isCont [OF bounded_linear_Im]
1.23 +lemmas Cauchy_Re = bounded_linear.Cauchy [OF bounded_linear_Re]
1.24 +lemmas Cauchy_Im = bounded_linear.Cauchy [OF bounded_linear_Im]
1.25 +
1.26 lemma tendsto_Complex [tendsto_intros]:
1.27 assumes "(f ---> a) net" and "(g ---> b) net"
1.28 shows "((\<lambda>x. Complex (f x) (g x)) ---> Complex a b) net"
1.29 @@ -370,9 +381,9 @@
1.30 proof
1.31 fix X :: "nat \<Rightarrow> complex"
1.32 assume X: "Cauchy X"
1.33 - from Re.Cauchy [OF X] have 1: "(\<lambda>n. Re (X n)) ----> lim (\<lambda>n. Re (X n))"
1.34 + from Cauchy_Re [OF X] have 1: "(\<lambda>n. Re (X n)) ----> lim (\<lambda>n. Re (X n))"
1.35 by (simp add: Cauchy_convergent_iff convergent_LIMSEQ_iff)
1.36 - from Im.Cauchy [OF X] have 2: "(\<lambda>n. Im (X n)) ----> lim (\<lambda>n. Im (X n))"
1.37 + from Cauchy_Im [OF X] have 2: "(\<lambda>n. Im (X n)) ----> lim (\<lambda>n. Im (X n))"
1.38 by (simp add: Cauchy_convergent_iff convergent_LIMSEQ_iff)
1.39 have "X ----> Complex (lim (\<lambda>n. Re (X n))) (lim (\<lambda>n. Im (X n)))"
1.40 using LIMSEQ_Complex [OF 1 2] by simp
1.41 @@ -511,10 +522,16 @@
1.42 lemma complex_mod_mult_cnj: "cmod (z * cnj z) = (cmod z)\<twosuperior>"
1.43 by (simp add: norm_mult power2_eq_square)
1.44
1.45 -interpretation cnj: bounded_linear "cnj"
1.46 +lemma bounded_linear_cnj: "bounded_linear cnj"
1.47 using complex_cnj_add complex_cnj_scaleR
1.48 by (rule bounded_linear_intro [where K=1], simp)
1.49
1.50 +lemmas tendsto_cnj [tendsto_intros] =
1.51 + bounded_linear.tendsto [OF bounded_linear_cnj]
1.52 +
1.53 +lemmas isCont_cnj [simp] =
1.54 + bounded_linear.isCont [OF bounded_linear_cnj]
1.55 +
1.56
1.57 subsection{*The Functions @{term sgn} and @{term arg}*}
1.58