1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/fta/CC_Props".
21 (* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
23 include "complex/AbsCC.ma".
25 (*#* * More properties of complex numbers
26 ** Sequences and limits *)
29 Hint Resolve AbsIR_sqrt_sqr: algebra.
32 inline "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con".
34 inline "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con".
36 inline "cic:/CoRN/fta/CC_Props/seq_re.con".
38 inline "cic:/CoRN/fta/CC_Props/seq_im.con".
40 inline "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con".
42 inline "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind".
44 coercion "cic:/matita/CoRN-Decl/fta/CC_Props/CC_seq.con" 0 (* compounds *).
46 inline "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con".
48 inline "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con".
50 inline "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con".
52 inline "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con".
54 inline "cic:/CoRN/fta/CC_Props/LimCC.con".
56 inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con".
58 inline "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con".
60 inline "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con".
62 inline "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con".
64 inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con".
66 inline "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con".
68 (*#* ** Continuity for [CC]
72 Section Continuity_for_CC.
76 %\begin{convention}% Let [f : CC->CC].
80 inline "cic:/CoRN/fta/CC_Props/f.var".
82 (* (CSetoid_un_op CC). *)
84 inline "cic:/CoRN/fta/CC_Props/CCfunLim.con".
86 inline "cic:/CoRN/fta/CC_Props/CCcontinAt.con".
88 inline "cic:/CoRN/fta/CC_Props/CCcontin.con".
90 inline "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con".
92 inline "cic:/CoRN/fta/CC_Props/f_seq.con".
94 inline "cic:/CoRN/fta/CC_Props/poly_pres_lim.con".
97 End Continuity_for_CC.
100 inline "cic:/CoRN/fta/CC_Props/seq_yields_zero.con".