helm/software/matita/contribs/formal_topology/overlap/basic_topologies_to_o-basic_topologies.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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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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  13 (**************************************************************************)
  14
  15 include "basic_topologies.ma".
  16 include "o-basic_topologies.ma".
  17 include "relations_to_o-algebra.ma".
  18
  19 (* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
  20 definition o_basic_topology_of_basic_topology: cic:/matita/formal_topology/basic_topologies/basic_topology.ind#xpointer(1/1) → basic_topology.
  21  intro;
  22  constructor 1;
  23   [ apply (SUBSETS (carrbt b));
  24   | apply (A b);
  25   | apply (J b);
  26   | apply (A_is_saturation b);
  27   | apply (J_is_reduction b);
  28   | apply (compatibility b); ]
  29 qed.
  30
  31 definition o_relation_pair_of_relation_pair:
  32  ∀S,T.cic:/matita/formal_topology/basic_topologies/continuous_relation.ind#xpointer(1/1) S T →
  33   continuous_relation (o_basic_topology_of_basic_topology S) (o_basic_topology_of_basic_topology T).
  34  intros;
  35  constructor 1;
  36   [ apply (orelation_of_relation ?? (cont_rel ?? c));
  37   | apply (reduced ?? c);
  38   | apply (saturated ?? c); ]
  39 qed.