1) Some reorganization.

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / saturations_to_o-saturations.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/saturations_to_o-saturations.ma
new file mode 100644 (file)
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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 "saturations.ma".
+include "o-saturations.ma".
+include "relations_to_o-algebra.ma".
+
+(* These are only conversions :-) *)
+
+definition o_operator_of_operator:
+ ∀C:REL. (Ω \sup C => Ω \sup C) → (SUBSETS C ⇒ SUBSETS C).
+ intros;apply t;
+qed.
+
+definition is_o_saturation_of_is_saturation:
+ ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
+  is_saturation ? R → is_o_saturation ? (o_operator_of_operator ? R).
+ intros; apply i;
+qed.
+
+definition is_o_reduction_of_is_reduction:
+ ∀C:REL.∀R: unary_morphism1 (Ω \sup C) (Ω \sup C).
+  is_reduction ? R → is_o_reduction ? (o_operator_of_operator ? R).
+ intros; apply i;
+qed.
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