helm/software/matita/contribs/CoRN-Procedural/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 alias id "b" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var".
  45
  46 alias id "n" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var".
  47
  48 alias id "gt_n_0" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var".
  49
  50 (* begin hide *)
  51
  52 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__".
  53
  54 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__".
  55
  56 (* end hide *)
  57
  58 alias id "b_n_1" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var".
  59
  60 alias id "c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var".
  61
  62 alias id "b_0_lt_c" = "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var".
  63
  64 (*#*
  65 %\begin{convention}% We define the following local abbreviations:
  66  - [two_n := 2 * n]
  67  - [Small := p3m n]
  68  - [Smaller := p3m (two_n * n)]
  69  - [Smallest := Small[*]Smaller]
  70  - [q := One[-]Smallest]
  71  - [a i := AbsCC (b i)]
  72
  73 %\end{convention}%
  74 *)
  75
  76 (* begin hide *)
  77
  78 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__".
  79
  80 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__".
  81
  82 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__".
  83
  84 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__".
  85
  86 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__".
  87
  88 (* end hide *)
  89
  90 inline procedural "cic:/CoRN/fta/KneserLemma/b_0'_exists.con".
  91
  92 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__".
  93
  94 inline procedural "cic:/CoRN/fta/KneserLemma/eta_0_pos.con".
  95
  96 inline procedural "cic:/CoRN/fta/KneserLemma/eta_exists.con".
  97
  98 inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists_1.con".
  99
 100 (* less_cotransitive_unfolded on
 101   {Zero  [<]  y[/]x[//]H3[-]Half[*]eps} +
 102   {y[/]x[//]H3[-]Half[*]eps  [<]  Half[*]eps}. *)
 103
 104 inline procedural "cic:/CoRN/fta/KneserLemma/eps_exists.con".
 105
 106 (* begin hide *)
 107
 108 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__".
 109
 110 (* end hide *)
 111
 112 inline procedural "cic:/CoRN/fta/KneserLemma/z_exists.con".
 113
 114 (* end hide *)
 115
 116 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1'.con".
 117
 118 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1''.con".
 119
 120 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_1.con".
 121
 122 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2a.con".
 123
 124 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2b.con".
 125
 126 (* end hide *)
 127
 128 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2c.con".
 129
 130 (* end hide *)
 131
 132 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_2.con".
 133
 134 (* end hide *)
 135
 136 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser_3.con".
 137
 138 (* UNEXPORTED
 139 End Kneser_Lemma
 140 *)
 141
 142 inline procedural "cic:/CoRN/fta/KneserLemma/Kneser.con".
 143