helm/software/matita/contribs/formal_topology/overlap/concrete_spaces_to_o-concrete_spaces.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 "concrete_spaces.ma".
  16 include "o-concrete_spaces.ma".
  17 include "basic_pairs_to_o-basic_pairs.ma".
  18
  19 (* Qui, per fare le cose per bene, ci serve la nozione di funtore categorico *)
  20 definition o_concrete_space_of_concrete_space: cic:/matita/formal_topology/concrete_spaces/concrete_space.ind#xpointer(1/1) → concrete_space.
  21  intro;
  22  constructor 1;
  23   [ apply (o_basic_pair_of_basic_pair (bp c));
  24   | lapply depth=0 (downarrow c);
  25     constructor 1;
  26      [ apply
  27      |
  28     apply (o_operator_of_operator);fintersectsS);
  29   |
  30   |
  31   |
  32   |
  33   |
  34   ]
  35 qed.
  36
  37 definition o_convergent_relation_pair_of_convergent_relation_pair:
  38  ∀BP1,BP2.cic:/matita/formal_topology/concrete_spaces/convergent_relation_pair.ind#xpointer(1/1) BP1 BP2 →
  39   convergent_relation_pair (o_concrete_space_of_concrete_space BP1) (o_concrete_space_of_concrete_space BP2).
  40  intros;
  41  constructor 1;
  42   [ apply (orelation_of_relation ?? (r \sub \c));
  43   | apply (orelation_of_relation ?? (r \sub \f));
  44   | lapply (commute ?? r);
  45     lapply (orelation_of_relation_preserves_equality ???? Hletin);
  46     apply (.= (orelation_of_relation_preserves_composition (concr BP1) ??? (rel BP2)) ^ -1);
  47     apply (.= (orelation_of_relation_preserves_equality ???? (commute ?? r)));
  48     apply (orelation_of_relation_preserves_composition ?? (form BP2)  (rel BP1) ?); ]
  49 qed.