helm/software/matita/contribs/procedural/CoRN/fta/KneserLemma.mma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  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