moved formal_topology into library"

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
deleted file mode 100644 (file)
index bb19350..0000000
--- a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
+++ /dev/null
@@ -1,37 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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 "o-algebra.ma".
-
-definition is_o_saturation: ∀C:OA. C ⇒_1 C → CProp1 ≝
- λC:OA.λA:C ⇒_1 C.∀U,V. (U ≤ A V) =_1 (A U ≤ A V).
-
-definition is_o_reduction: ∀C:OA. C ⇒_1 C → CProp1 ≝
- λC:OA.λJ:C ⇒_1 C.∀U,V. (J U ≤ V) =_1 (J U ≤ J V).
-
-theorem o_saturation_expansive: ∀C,A. is_o_saturation C A → ∀U. U ≤ A U.
- intros; apply (fi ?? (i ??)); apply (oa_leq_refl C).
-qed.
-
-theorem o_saturation_monotone: ∀C:OA.∀A:C ⇒_1 C. is_o_saturation C A → ∀U,V. U ≤ V → A U ≤ A V.
- intros; apply (if ?? (i ??)); apply (oa_leq_trans C);
-  [apply V|3: apply o_saturation_expansive ]
- assumption.
-qed.
-
-theorem o_saturation_idempotent: ∀C:OA.∀A:C ⇒_1 C. is_o_saturation C A → ∀U. A (A U) =_1 A U.
- intros; apply (oa_leq_antisym C);
-  [ apply (if ?? (i (A U) U)); apply (oa_leq_refl C).
-  | apply o_saturation_expansive; assumption]
-qed.