matita/matita/contribs/lambdadelta/ground/lib/subset_ext.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground/lib/subset.ma".
  16
  17 (* EXTENSIONS FOR SUBSETS ***************************************************)
  18
  19 definition subset_ext_f1 (A1) (A0) (f:A1→A0): 𝒫❨A1❩ → 𝒫❨A0❩ ≝
  20            λu1,a0. ∃∃a1. a1 ϵ u1 & f a1 = a0.
  21
  22 definition subset_ext_p1 (A1) (Q:predicate A1): predicate (𝒫❨A1❩) ≝
  23            λu1. ∀a1. a1 ϵ u1 → Q a1.
  24
  25 (* Basic constructions ******************************************************)
  26
  27 lemma subset_in_ext_f1_dx (A1) (A0) (f) (u1) (a1):
  28       a1 ϵ u1 → f a1 ϵ subset_ext_f1 A1 A0 f u1.
  29 /2 width=3 by ex2_intro/ qed.
  30
  31 (* Basic inversions *********************************************************)
  32
  33 lemma subset_in_inv_ext_p1_dx (A1) (Q) (u1) (a1):
  34       a1 ϵ u1 → subset_ext_p1 A1 Q u1 → Q a1.
  35 /2 width=1 by/ qed-.