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13 (**************************************************************************)
14
15 (* This file was automatically generated: do not edit *********************)
16
17 include "CoRN.ma".
18
19 (* $Id: CC_Props.v,v 1.3 2004/04/23 10:00:56 lcf Exp $ *)
20
21 include "complex/AbsCC.ma".
22
23 (*#* * More properties of complex numbers
24 ** Sequences and limits *)
25
26 (* UNEXPORTED
27 Hint Resolve AbsIR_sqrt_sqr: algebra.
28 *)
29
30 inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_re.con" as lemma.
31
32 inline procedural "cic:/CoRN/fta/CC_Props/absCC_absIR_im.con" as lemma.
33
34 inline procedural "cic:/CoRN/fta/CC_Props/seq_re.con" as definition.
35
36 inline procedural "cic:/CoRN/fta/CC_Props/seq_im.con" as definition.
37
38 inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy_prop.con" as definition.
39
40 inline procedural "cic:/CoRN/fta/CC_Props/CC_CauchySeq.ind".
41
42 (* COERCION
43 cic:/matita/CoRN-Procedural/fta/CC_Props/CC_seq.con
44 *)
45
46 inline procedural "cic:/CoRN/fta/CC_Props/re_is_Cauchy.con" as lemma.
47
48 inline procedural "cic:/CoRN/fta/CC_Props/im_is_Cauchy.con" as lemma.
49
50 inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2re.con" as definition.
51
52 inline procedural "cic:/CoRN/fta/CC_Props/CC_Cauchy2im.con" as definition.
53
54 inline procedural "cic:/CoRN/fta/CC_Props/LimCC.con" as definition.
55
56 inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit.con" as definition.
57
58 inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_sqr.con" as lemma.
59
60 inline procedural "cic:/CoRN/fta/CC_Props/AbsSmall_AbsCC.con" as lemma.
61
62 inline procedural "cic:/CoRN/fta/CC_Props/LimCC_is_lim.con" as lemma.
63
64 inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_uniq.con" as lemma.
65
66 inline procedural "cic:/CoRN/fta/CC_Props/CC_SeqLimit_unq.con" as lemma.
67
68 (*#* ** Continuity for [CC]
69 *)
70
71 (* UNEXPORTED
72 Section Continuity_for_CC
73 *)
74
75 (*#*
76 %\begin{convention}% Let [f : CC->CC].
77 %\end{convention}%
78 *)
79
80 (* UNEXPORTED
81 cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var
82 *)
83
84 (* (CSetoid_un_op CC). *)
85
86 inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim.con" as definition.
87
88 inline procedural "cic:/CoRN/fta/CC_Props/CCcontinAt.con" as definition.
89
90 inline procedural "cic:/CoRN/fta/CC_Props/CCcontin.con" as definition.
91
92 inline procedural "cic:/CoRN/fta/CC_Props/CCfunLim_SeqLimit.con" as lemma.
93
94 inline procedural "cic:/CoRN/fta/CC_Props/f_seq.con" as definition.
95
96 inline procedural "cic:/CoRN/fta/CC_Props/poly_pres_lim.con" as lemma.
97
98 (* UNEXPORTED
99 End Continuity_for_CC
100 *)
101
102 inline procedural "cic:/CoRN/fta/CC_Props/seq_yields_zero.con" as lemma.
103