moved formal_topology into library"

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/saturations.ma
deleted file mode 100644 (file)
index cc0db52..0000000
--- a/helm/software/matita/contribs/formal_topology/overlap/saturations.ma
+++ /dev/null
@@ -1,38 +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 "relations.ma".
-
-definition is_saturation: ∀C:REL. Ω^C ⇒_1 Ω^C → CProp1 ≝
- λC:REL.λA:Ω^C ⇒_1 Ω^C. ∀U,V. (U ⊆ A V) =_1 (A U ⊆ A V).
-
-definition is_reduction: ∀C:REL. Ω^C ⇒_1 Ω^C → CProp1 ≝
- λC:REL.λJ: Ω^C ⇒_1 Ω^C. ∀U,V. (J U ⊆ V) =_1 (J U ⊆ J V).
-
-theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ⊆ A U.
- intros; apply (fi ?? (i ??)); apply subseteq_refl.
-qed.
-
-theorem saturation_monotone:
- ∀C,A. is_saturation C A →
-  ∀U,V. U ⊆ V → A U ⊆ A V.
- intros; apply (if ?? (i ??)); apply subseteq_trans; [apply V|3: apply saturation_expansive ]
- assumption.
-qed.
-
-theorem saturation_idempotent: ∀C,A. is_saturation C A → ∀U. A (A U) = A U.
- intros; split;
-  [ apply (if ?? (i ??)); apply subseteq_refl
-  | apply saturation_expansive; assumption]
-qed.