helm/software/matita/contribs/dama/dama_duality/tend.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "sequence.ma".
  16 include "metric_space.ma".
  17 include "nat/orders.ma".
  18
  19 definition tends0 ≝
  20   λO:pogroup.λs:sequence O.∀e:O.0 < e → ∃N.∀n.N < n → -e < s n ∧ s n < e.
  21
  22 definition d2s ≝
  23   λR.λms:metric_space R.λs:sequence ms.λk.λn. δ (s n) k.
  24
  25 notation "s ⇝ x" non associative with precedence 50 for @{'tends $s $x}.
  26 interpretation "tends to" 'tends s x = (tends0 _ (d2s _ _ s x)).
  27