helm/software/matita/library/formal_topology/saturations_to_o-saturations.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 "formal_topology/saturations.ma".
  16 include "formal_topology/o-saturations.ma".
  17 include "formal_topology/relations_to_o-algebra.ma".
  18
  19 (* These are only conversions :-) *)
  20
  21 definition o_operator_of_operator: ∀C:REL. (Ω^C ⇒_1 Ω^C) → ((POW C) ⇒_1 (POW C)) ≝ λC,t.t.
  22
  23 definition is_o_saturation_of_is_saturation:
  24   ∀C:REL.∀R: Ω^C ⇒_1 Ω^C. is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
  25 intros (C R i); apply i; qed.
  26
  27 definition is_o_reduction_of_is_reduction:
  28   ∀C:REL.∀R: Ω^C ⇒_1 Ω^C.is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
  29 intros (C R i); apply i; qed.