matita/matita/contribs/lambdadelta/basic_2/substitution/cofrees.ma

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  14
  15 include "basic_2/notation/relations/cofreestar_3.ma".
  16 include "basic_2/substitution/cpys.ma".
  17
  18 (* CONTEXT-SENSITIVE EXCLUSION FROM FREE VARIABLES **************************)
  19
  20 definition cofrees: relation3 nat lenv term ≝
  21                     λd,L,U1. ∀U2. ⦃⋆, L⦄ ⊢ U1 ▶*[d, ∞] U2 → ∃T2. ⇧[d, 1] T2 ≡ U2.
  22
  23 interpretation
  24    "context-sensitive exclusion from free variables (term)"
  25    'CoFreeStar d L T = (cofrees d L T).
  26
  27 (* Basic forward lemmas *****************************************************)
  28
  29 lemma cofrees_fwd_lift: ∀L,U,d. d ~ϵ 𝐅*⦃L, U⦄ → ∃T. ⇧[d, 1] T ≡ U.
  30 /2 width=1 by/ qed-.
  31
  32 lemma nlift_frees: ∀L,U,d. (∀T. ⇧[d, 1] T ≡ U → ⊥) → (d ~ϵ 𝐅*⦃L, U⦄ → ⊥).
  33 #L #U #d #HnTU #H elim (cofrees_fwd_lift … H) -H /2 width=2 by/
  34 qed-.