helm/software/matita/contribs/CoRN-Decl/ftc/StrongIVT.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/ftc/StrongIVT".
  18
  19 (* $Id: StrongIVT.v,v 1.5 2004/04/23 10:01:01 lcf Exp $ *)
  20
  21 (* INCLUDE
  22 WeakIVT
  23 *)
  24
  25 (* INCLUDE
  26 CalculusTheorems
  27 *)
  28
  29 (* UNEXPORTED
  30 Section IVT'.
  31 *)
  32
  33 (*#* ** Strong IVT for partial functions
  34
  35 The IVT can be generalized to arbitrary partial functions; in the first
  36 part, we will simply do that, repeating the previous construction.
  37
  38 The same notations and conventions apply as before.
  39 *)
  40
  41 inline cic:/CoRN/ftc/StrongIVT/a.var.
  42
  43 inline cic:/CoRN/ftc/StrongIVT/b.var.
  44
  45 inline cic:/CoRN/ftc/StrongIVT/Hab'.var.
  46
  47 inline cic:/CoRN/ftc/StrongIVT/Hab.var.
  48
  49 (* begin hide *)
  50
  51 inline cic:/CoRN/ftc/StrongIVT/I.con.
  52
  53 inline cic:/CoRN/ftc/StrongIVT/I'.con.
  54
  55 (* end hide *)
  56
  57 inline cic:/CoRN/ftc/StrongIVT/F.var.
  58
  59 inline cic:/CoRN/ftc/StrongIVT/contF.var.
  60
  61 (* begin hide *)
  62
  63 inline cic:/CoRN/ftc/StrongIVT/incF.con.
  64
  65 (* end hide *)
  66
  67 (* begin show *)
  68
  69 inline cic:/CoRN/ftc/StrongIVT/incrF.var.
  70
  71 (* end show *)
  72
  73 (* begin hide *)
  74
  75 inline cic:/CoRN/ftc/StrongIVT/Ha.con.
  76
  77 inline cic:/CoRN/ftc/StrongIVT/Hb.con.
  78
  79 inline cic:/CoRN/ftc/StrongIVT/HFab'.con.
  80
  81 (* end hide *)
  82
  83 (* begin show *)
  84
  85 inline cic:/CoRN/ftc/StrongIVT/z.var.
  86
  87 inline cic:/CoRN/ftc/StrongIVT/Haz.var.
  88
  89 inline cic:/CoRN/ftc/StrongIVT/Hzb.var.
  90
  91 (* end show *)
  92
  93 inline cic:/CoRN/ftc/StrongIVT/IVT'_seq_lemma.con.
  94
  95 (* end hide *)
  96
  97 inline cic:/CoRN/ftc/StrongIVT/IVT'_aux_seq_type.ind.
  98
  99 inline cic:/CoRN/ftc/StrongIVT/IVT'_iter.con.
 100
 101 inline cic:/CoRN/ftc/StrongIVT/IVT'_seq.con.
 102
 103 inline cic:/CoRN/ftc/StrongIVT/a'_seq.con.
 104
 105 inline cic:/CoRN/ftc/StrongIVT/b'_seq.con.
 106
 107 inline cic:/CoRN/ftc/StrongIVT/a'_seq_I.con.
 108
 109 inline cic:/CoRN/ftc/StrongIVT/b'_seq_I.con.
 110
 111 inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_b'_seq.con.
 112
 113 inline cic:/CoRN/ftc/StrongIVT/a'_seq_less_z.con.
 114
 115 inline cic:/CoRN/ftc/StrongIVT/z_less_b'_seq.con.
 116
 117 inline cic:/CoRN/ftc/StrongIVT/a'_seq_mon.con.
 118
 119 inline cic:/CoRN/ftc/StrongIVT/b'_seq_mon.con.
 120
 121 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist_n.con.
 122
 123 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_dist.con.
 124
 125 inline cic:/CoRN/ftc/StrongIVT/a'_seq_Cauchy.con.
 126
 127 inline cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con.
 128
 129 inline cic:/CoRN/ftc/StrongIVT/xa.con.
 130
 131 inline cic:/CoRN/ftc/StrongIVT/xb.con.
 132
 133 inline cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con.
 134
 135 inline cic:/CoRN/ftc/StrongIVT/xa'_in_interval.con.
 136
 137 inline cic:/CoRN/ftc/StrongIVT/IVT'_I.con.
 138
 139 (* UNEXPORTED
 140 End IVT'.
 141 *)
 142
 143 (*#* **Other formulations
 144
 145 We now generalize the various statements of the intermediate value
 146 theorem to more widely applicable forms.
 147 *)
 148
 149 inline cic:/CoRN/ftc/StrongIVT/Weak_IVT.con.
 150
 151 inline cic:/CoRN/ftc/StrongIVT/IVT_inc.con.
 152
 153 (* UNEXPORTED
 154 Transparent Min.
 155 *)
 156
 157 inline cic:/CoRN/ftc/StrongIVT/IVT_dec.con.
 158
 159 inline cic:/CoRN/ftc/StrongIVT/IVT'_inc.con.
 160
 161 (* UNEXPORTED
 162 Transparent Min.
 163 *)
 164
 165 inline cic:/CoRN/ftc/StrongIVT/IVT'_dec.con.
 166