update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / subset_ext.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma b/matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma
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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 "ground/lib/subset.ma".
+
+(* EXTENSIONS FOR SUBSETS ***************************************************)
+
+definition subset_ext_f1 (A1) (A0) (f:A1→A0): 𝒫❨A1❩ → 𝒫❨A0❩ ≝
+           λu1,a0. ∃∃a1. a1 ϵ u1 & f a1 = a0.
+
+definition subset_ext_p1 (A1) (Q:predicate A1): predicate (𝒫❨A1❩) ≝
+           λu1. ∀a1. a1 ϵ u1 → Q a1.
+
+(* Basic constructions ******************************************************)
+
+lemma subset_in_ext_f1_dx (A1) (A0) (f) (u1) (a1):
+      a1 ϵ u1 → f a1 ϵ subset_ext_f1 A1 A0 f u1.
+/2 width=3 by ex2_intro/ qed.
+
+(* Basic inversions *********************************************************)
+
+lemma subset_in_inv_ext_p1_dx (A1) (Q) (u1) (a1):
+      a1 ϵ u1 → subset_ext_p1 A1 Q u1 → Q a1.
+/2 width=1 by/ qed-.