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[helm.git] / matita / contribs / dama / dama / tend.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "sequence.ma".
+include "metric_space.ma".
+include "nat/orders.ma".
+
+definition tends0 ≝ 
+  λO:pogroup.λs:sequence O.∀e:O.0 < e → ∃N.∀n.N < n → -e < s n ∧ s n < e.
+
+definition d2s ≝ 
+  λR.λms:metric_space R.λs:sequence ms.λk.λn. δ (s n) k.
+
+notation "s ⇝ x" non associative with precedence 50 for @{'tends $s $x}.
+interpretation "tends to" 'tends s x = 
+  (cic:/matita/tend/tends0.con _ (cic:/matita/tend/d2s.con _ _ s x)).
+