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
47 cic:/CoRN/fta/MainLemma/Main_Lemma/a.var
51 cic:/CoRN/fta/MainLemma/Main_Lemma/n.var
55 cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var
59 cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var
63 cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var
67 cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var
71 cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var
75 cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var
79 cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var
82 inline procedural "cic:/CoRN/fta/MainLemma/a_0_pos.con" as lemma.
85 %\begin{convention}% We define the following local abbreviations:
88 - [Smaller := p3m (two_n * n)]
95 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__" as definition.
97 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__" as definition.
99 inline procedural "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__" as definition.
103 inline procedural "cic:/CoRN/fta/MainLemma/Main_1a'.con" as lemma.
107 inline procedural "cic:/CoRN/fta/MainLemma/Main_1b'.con" as lemma.
111 inline procedural "cic:/CoRN/fta/MainLemma/Main_1a.con" as lemma.
115 inline procedural "cic:/CoRN/fta/MainLemma/Main_1b.con" as lemma.
119 inline procedural "cic:/CoRN/fta/MainLemma/Main_1.con" as lemma.
123 inline procedural "cic:/CoRN/fta/MainLemma/Main_2'.con" as lemma.
125 inline procedural "cic:/CoRN/fta/MainLemma/Main_2.con" as lemma.
129 inline procedural "cic:/CoRN/fta/MainLemma/Main_3a.con" as lemma.
133 inline procedural "cic:/CoRN/fta/MainLemma/Main_3.con" as lemma.
137 inline procedural "cic:/CoRN/fta/MainLemma/Main.con" as lemma.