matita/matita/contribs/lambdadelta/basic_2/dynamic/ypr.ma

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  14
  15 include "basic_2/notation/relations/btpred_6.ma".
  16 include "basic_2/relocation/fsup.ma".
  17 include "basic_2/reduction/lpr.ma".
  18 include "basic_2/dynamic/lsubsv.ma".
  19
  20 (* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
  21
  22 inductive ypr (h) (g) (L1) (T1): relation2 lenv term ≝
  23 | ypr_fsup  : ∀L2,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ypr h g L1 T1 L2 T2
  24 | ypr_lpr   : ∀L2. L1 ⊢ ➡ L2 → ypr h g L1 T1 L2 T1
  25 | ypr_cpr   : ∀T2. L1 ⊢ T1 ➡ T2 → ypr h g L1 T1 L1 T2
  26 | ypr_ssta  : ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[h, g] ⦃l+1, T2⦄ → ypr h g L1 T1 L1 T2
  27 | ypr_lsubsv: ∀L2. h ⊢ L2 ¡⊑[h, g] L1 → ypr h g L1 T1 L2 T1
  28 .
  29
  30 interpretation
  31    "'big tree' parallel reduction (closure)"
  32    'BTPRed 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.