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".
19 (* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
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 inline cic:/CoRN/fta/CC_Props/re_is_Cauchy.con.
46 inline cic:/CoRN/fta/CC_Props/im_is_Cauchy.con.
48 inline cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con.
50 inline cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con.
52 inline cic:/CoRN/fta/CC_Props/LimCC.con.
54 inline cic:/CoRN/fta/CC_Props/CC_SeqLimit.con.
56 inline cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con.
58 inline cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con.
60 inline cic:/CoRN/fta/CC_Props/LimCC_is_lim.con.
62 inline cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con.
64 inline cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con.
66 (*#* ** Continuity for [CC]
70 Section Continuity_for_CC.
74 %\begin{convention}% Let [f : CC->CC].
78 inline cic:/CoRN/fta/CC_Props/f.var.
80 (* (CSetoid_un_op CC). *)
82 inline cic:/CoRN/fta/CC_Props/CCfunLim.con.
84 inline cic:/CoRN/fta/CC_Props/CCcontinAt.con.
86 inline cic:/CoRN/fta/CC_Props/CCcontin.con.
88 inline cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con.
90 inline cic:/CoRN/fta/CC_Props/f_seq.con.
92 inline cic:/CoRN/fta/CC_Props/poly_pres_lim.con.
95 End Continuity_for_CC.
98 inline cic:/CoRN/fta/CC_Props/seq_yields_zero.con.