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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  14
  15 include "ground_2/relocation/rtmap_id.ma".
  16 include "static_2/notation/relations/subseteq_4.ma".
  17 include "static_2/syntax/lveq.ma".
  18 include "static_2/static/frees.ma".
  19
  20 (* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
  21
  22 definition fsle: bi_relation lenv term ≝ λL1,T1,L2,T2.
  23                  ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≘ f2 &
  24                                 L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
  25
  26 interpretation "free variables inclusion (restricted closure)"
  27    'SubSetEq L1 T1 L2 T2 = (fsle L1 T1 L2 T2).
  28
  29 interpretation "free variables inclusion (term)"
  30    'subseteq T1 T2 = (fsle LAtom T1 LAtom T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma fsle_sort: ∀L,s1,s2. ⦃L, ⋆s1⦄ ⊆ ⦃L, ⋆s2⦄.
  35 /3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
  36
  37 lemma fsle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
  38 /3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.