matita/matita/contribs/lambdadelta/basic_2A/reduction/fpb.ma

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  14
  15 include "basic_2A/notation/relations/btpredproper_8.ma".
  16 include "basic_2A/substitution/fqu.ma".
  17 include "basic_2A/multiple/lleq.ma".
  18 include "basic_2A/reduction/lpx.ma".
  19
  20 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
  21
  22 inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpb_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
  24 | fpb_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → fpb h g G1 L1 T1 G1 L1 T2
  25 | fpb_lpx: ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → (L1 ≡[T1, 0] L2 → ⊥) → fpb h g G1 L1 T1 G1 L2 T1
  26 .
  27
  28 interpretation
  29    "'rst' proper parallel reduction (closure)"
  30    'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpb h g G1 L1 T1 G2 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) →
  35                ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
  36 /3 width=1 by fpb_cpx, cpr_cpx/ qed.
  37
  38 lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → (L1 ≡[T, 0] L2 → ⊥) →
  39                ⦃G, L1, T⦄ ≻[h, g] ⦃G, L2, T⦄.
  40 /3 width=1 by fpb_lpx, lpr_lpx/ qed.