matita/matita/contribs/lambdadelta/static_2/static/fsle.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/xoa/ex_4_4.ma".
  16 include "ground/relocation/rtmap_id.ma".
  17 include "static_2/notation/relations/subseteq_4.ma".
  18 include "static_2/syntax/lveq.ma".
  19 include "static_2/static/frees.ma".
  20
  21 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  22
  23 definition fsle: bi_relation lenv term ≝ λL1,T1,L2,T2.
  24                  ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅+❪T1❫ ≘ f1 & L2 ⊢ 𝐅+❪T2❫ ≘ f2 &
  25                                 L1 ≋ⓧ*[n1,n2] L2 & ⫰*[n1]f1 ⊆ ⫰*[n2]f2.
  26
  27 interpretation "free variables inclusion (restricted closure)"
  28    'SubSetEq L1 T1 L2 T2 = (fsle L1 T1 L2 T2).
  29
  30 interpretation "free variables inclusion (term)"
  31    'subseteq T1 T2 = (fsle LAtom T1 LAtom T2).
  32
  33 (* Basic properties *********************************************************)
  34
  35 lemma fsle_sort: ∀L,s1,s2. ❪L,⋆s1❫ ⊆ ❪L,⋆s2❫.
  36 /3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
  37
  38 lemma fsle_gref: ∀L,l1,l2. ❪L,§l1❫ ⊆ ❪L,§l2❫.
  39 /3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.