matita/matita/contribs/lambdadelta/basic_2/reduction/fpbc.ma

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  14
  15 include "basic_2/notation/relations/btpredproper_8.ma".
  16 include "basic_2/reduction/fpb.ma".
  17
  18 (* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
  19
  20 inductive fpbc (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
  21 | fpbc_fqu: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → fpbc h g G1 L1 T1 G2 L2 T2
  22 | fpbc_cpx: ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → fpbc h g G1 L1 T1 G1 L1 T2
  23 .
  24
  25 interpretation
  26    "'big tree' proper parallel reduction (closure)"
  27    'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (fpbc h g G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma cpr_fpbc: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) →
  32                 ⦃G, L, T1⦄ ≻[h, g] ⦃G, L, T2⦄.
  33 /3 width=1 by fpbc_cpx, cpr_cpx/ qed.
  34
  35 (* Basic forward lemmas *****************************************************)
  36
  37 lemma fpbc_fwd_fpb: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  38                     ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
  39 #h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  40 /3 width=1 by fpb_fquq, fpb_cpx, fqu_fquq/
  41 qed-.