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

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  14
  15 include "basic_2/substitution/csup.ma".
  16 include "basic_2/reducibility/xpr.ma".
  17
  18 (* HYPER PARALLEL REDUCTION ON CLOSURES *************************************)
  19
  20 inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝
  21 | ypr_cpr : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2
  22 | ypr_ssta: ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] T2 → ypr h g L1 T1 L1 T2
  23 | ypr_csup: ∀L2,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ypr h g L1 T1 L2 T2
  24 .
  25
  26 interpretation
  27    "hyper parallel reduction (closure)"
  28    'YPRed h g L1 T1 L2 T2 = (ypr h g L1 T1 L2 T2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma ypr_refl: ∀h,g. bi_reflexive … (ypr h g).
  33 /2 width=1/ qed.
  34
  35 lemma xpr_ypr: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •➡[g] T2 → h ⊢ ⦃L, T1⦄ •⥸[g] ⦃L, T2⦄.
  36 #h #g #L #T1 #T2 * /2 width=1/ /2 width=2/
  37 qed.