matita/matita/contribs/lambda_delta/basic_2/reducibility/xpr.ma

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  14
  15 include "basic_2/static/ssta.ma".
  16 include "basic_2/reducibility/cpr.ma".
  17
  18 (* EXTENDED PARALLEL REDUCTION ON TERMS *************************************)
  19
  20 definition xpr: ∀h. sd h → lenv → relation term ≝
  21    λh,g,L,T1,T2. L ⊢ T1 ➡ T2 ∨ ∃l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2.
  22
  23 interpretation
  24    "extended parallel reduction (term)"
  25    'XPRed h g L T1 T2 = (xpr h g L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma cpr_xpr: ∀h,g,L,T1,T2. L ⊢ T1 ➡ T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
  30 /2 width=1/ qed.
  31
  32 lemma ssta_xpr: ∀h,g,L,T1,T2,l. ⦃h, L⦄ ⊢ T1 •[g, l + 1] T2 → ⦃h, L⦄ ⊢ T1 ➸[g] T2.
  33 /3 width=2/ qed.
  34
  35 lemma xpr_refl: ∀h,g,L,T. ⦃h, L⦄ ⊢ T ➸[g] T.
  36 /2 width=1/ qed.