matita/matita/contribs/lambdadelta/basic_2/reducibility/ysc.ma

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  14
  15 include "basic_2/reducibility/ypr.ma".
  16
  17 (* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
  18
  19 inductive ysc (h) (g) (L1) (T1): relation2 lenv term ≝
  20 | ysc_fw  : ∀L2,T2. ♯{L2, T2} < ♯{L1, T1} → ysc h g L1 T1 L2 T2
  21 | ysc_cpr : ∀T2. L1 ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → ysc h g L1 T1 L1 T2
  22 | ysc_ssta: ∀T2,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] T2 → ysc h g L1 T1 L1 T2
  23 .
  24
  25 interpretation
  26    "'big tree' proper parallel reduction (closure)"
  27    'BTPRedProper h g L1 T1 L2 T2 = (ysc h g L1 T1 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma ysc_ypr: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ →
  32                h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄.
  33 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /2 width=1/ /2 width=2/
  34 qed.
  35
  36 (* Inversion lemmas on "big tree" parallel reduction for closures ***********)
  37
  38 lemma ypr_inv_ysc: ∀h,g,L1,L2,T1,T2. h ⊢ ⦃L1, T1⦄ ≽[g] ⦃L2, T2⦄ →
  39                    h ⊢ ⦃L1, T1⦄ ≻[g] ⦃L2, T2⦄ ∨ (L1 ➡ L2 ∧ T1 = T2).
  40 #h #g #L1 #L2 #T1 #T2 * -L2 -T2 /3 width=1/ /3 width=2/
  41 #T2 #HT12 elim (term_eq_dec T1 T2) #H destruct /3 width=1/ /4 width=1/
  42 qed-.