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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
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9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 (* This file was automatically generated: do not edit *********************)
16
17 include "CoRN.ma".
18
19 (* $Id: KneserLemma.v,v 1.7 2004/04/23 10:00:57 lcf Exp $ *)
20
21 (*#* printing Smallest %\ensuremath{\frac13^{2n^2+n}}% *)
22
23 (*#* printing eta_0 %\ensuremath{\eta_0}% #&eta;<SUB>0</SUB># *)
24
25 include "complex/NRootCC.ma".
26
27 include "complex/AbsCC.ma".
28
29 include "fta/MainLemma.ma".
30
31 (*#* ** Kneser Lemma *)
32
33 (* UNEXPORTED
34 Section Kneser_Lemma
35 *)
36
37 (*#*
38 %\begin{convention}% Let [b : nat->CC], [n : nat] and [c : IR]
39 such that [0 < n], [b_0 := b 0], [b_n := (b n) [=] One] and
40 [(AbsCC b_0) [<] c].
41 %\end{convention}%
42 *)
43
44 (* UNEXPORTED
45 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var
46 *)
47
48 (* UNEXPORTED
49 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var
50 *)
51
52 (* UNEXPORTED
53 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var
54 *)
55
56 (* begin hide *)
57
58 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__" as definition.
59
60 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__" as definition.
61
62 (* end hide *)
63
64 (* UNEXPORTED
65 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var
66 *)
67
68 (* UNEXPORTED
69 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var
70 *)
71
72 (* UNEXPORTED
73 cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var
74 *)
75
76 (*#* 
77 %\begin{convention}% We define the following local abbreviations:
78  - [two_n := 2 * n]
79  - [Small := p3m n]
80  - [Smaller := p3m (two_n * n)]
81  - [Smallest := Small[*]Smaller]
82  - [q := One[-]Smallest]
83  - [a i := AbsCC (b i)]
84
85 %\end{convention}%
86 *)
87
88 (* begin hide *)
89
90 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__" as definition.
91
92 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__" as definition.
93
94 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__" as definition.
95
96 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__" as definition.
97
98 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__" as definition.
99
100 (* end hide *)
101
102 inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con" as lemma.
103
104 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__" as definition.
105
106 inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con" as lemma.
107
108 inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con" as lemma.
109
110 inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con" as lemma.
111
112 (* less_cotransitive_unfolded on 
113   {Zero  [<]  y[/]x[//]H3[-]Half[*]eps} + 
114   {y[/]x[//]H3[-]Half[*]eps  [<]  Half[*]eps}. *)
115
116 inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con" as lemma.
117
118 (* begin hide *)
119
120 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__" as definition.
121
122 (* end hide *)
123
124 inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con" as lemma.
125
126 (* end hide *)
127
128 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con" as lemma.
129
130 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con" as lemma.
131
132 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con" as lemma.
133
134 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con" as lemma.
135
136 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con" as lemma.
137
138 (* end hide *)
139
140 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con" as lemma.
141
142 (* end hide *)
143
144 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con" as lemma.
145
146 (* end hide *)
147
148 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con" as lemma.
149
150 (* UNEXPORTED
151 End Kneser_Lemma
152 *)
153
154 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con" as lemma.
155