matita/matita/contribs/lambdadelta/basic_2/etc/csup/ypr.etc

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  14
  15 notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⥸ break [ g ] break ⦃ L2 , break T2 ⦄ )"
  16    non associative with precedence 45
  17    for @{ 'YPRed $h $g $L1 $T1 $L2 $T2 }.
  18
  19 include "basic_2/substitution/csup.ma".
  20 include "basic_2/reducibility/xpr.ma".
  21
  22 (* HYPER PARALLEL REDUCTION ON CLOSURES *************************************)
  23
  24 inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝
  25 | ypr_cpr : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2
  26 | ypr_ssta: ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] T2 → ypr h g L1 T1 L1 T2
  27 | ypr_csup: ∀L2,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ → ypr h g L1 T1 L2 T2
  28 .
  29
  30 interpretation
  31    "hyper parallel reduction (closure)"
  32    'YPRed h g L1 T1 L2 T2 = (ypr h g L1 T1 L2 T2).
  33
  34 (* Basic properties *********************************************************)
  35
  36 lemma ypr_refl: ∀h,g. bi_reflexive … (ypr h g).
  37 /2 width=1/ qed.
  38
  39 lemma xpr_ypr: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •➡[g] T2 → h ⊢ ⦃L, T1⦄ •⥸[g] ⦃L, T2⦄.
  40 #h #g #L #T1 #T2 * /2 width=1/ /2 width=2/
  41 qed.