1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: MainLemma.v,v 1.3 2004/04/23 10:00:57 lcf Exp $ *)
21 (*#* printing two_n %\ensuremath{2n}% #2n# *)
23 (*#* printing Small %\ensuremath{\frac13^n}% *)
25 (*#* printing Smaller %\ensuremath{\frac13^{2n^2}}% *)
27 include "reals/CSumsReals.ma".
29 include "fta/KeyLemma.ma".
40 Let [a : nat->IR], [n : nat], [a_0 : IR] and [eps : IR] such that [0 < n],
41 [(Zero [<] eps)], [forall (k : nat)(Zero [<=] (a k))], [(a n) [=] One], and
46 alias id "a" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a.var".
48 alias id "n" = "cic:/CoRN/fta/MainLemma/Main_Lemma/n.var".
50 alias id "gt_n_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var".
52 alias id "eps" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var".
54 alias id "eps_pos" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var".
56 alias id "a_nonneg" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var".
58 alias id "a_n_1" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var".
60 alias id "a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var".
62 alias id "eps_le_a_0" = "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var".
64 inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con".
67 %\begin{convention}% We define the following local abbreviations:
70 - [Smaller := p3m (two_n * n)]
77 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__".
79 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__".
81 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__".
85 inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con".
89 inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con".
93 inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con".
97 inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con".
101 inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con".
105 inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con".
107 inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con".
111 inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con".
115 inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con".
119 inline procedural "cic:/CoRN/fta/MainLemma/Main.con".