helm/software/matita/contribs/formal_topology/overlap/basic_pairs_to_o-basic_pairs.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_pairs.ma".
  16 include "o-basic_pairs.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_pair_of_basic_pair: cic:/matita/formal_topology/basic_pairs/basic_pair.ind#xpointer(1/1) → basic_pair.
  21  intro;
  22  constructor 1;
  23   [ apply (SUBSETS (concr b));
  24   | apply (SUBSETS (form b));
  25   | apply (orelation_of_relation ?? (rel b)); ]
  26 qed.
  27
  28 definition o_relation_pair_of_relation_pair:
  29  ∀BP1,BP2.cic:/matita/formal_topology/basic_pairs/relation_pair.ind#xpointer(1/1) BP1 BP2 →
  30   relation_pair (o_basic_pair_of_basic_pair BP1) (o_basic_pair_of_basic_pair BP2).
  31  intros;
  32  constructor 1;
  33   [ apply (orelation_of_relation ?? (r \sub \c));
  34   | apply (orelation_of_relation ?? (r \sub \f));
  35   | lapply (commute ?? r);
  36     lapply (orelation_of_relation_preserves_equality ???? Hletin);
  37     apply (.= (orelation_of_relation_preserves_composition (concr BP1) ??? (rel BP2)) ^ -1);
  38     apply (.= (orelation_of_relation_preserves_equality ???? (commute ?? r)));
  39     apply (orelation_of_relation_preserves_composition ?? (form BP2)  (rel BP1) ?); ]
  40 qed.