matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr.ma

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  14
  15 include "basic_2/unfold/ltpss_sn.ma".
  16 include "basic_2/reducibility/ltpr.ma".
  17
  18 (* FOCALIZED PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ***********************)
  19
  20 definition lfpr: relation lenv ≝
  21    λL1,L2. ∃∃L. L1 ➡ L & L ⊢ ▶* [0, |L|] L2
  22 .
  23
  24 interpretation
  25   "focalized parallel reduction (environment)"
  26   'FocalizedPRed L1 L2 = (lfpr L1 L2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 (* Note: lemma 250 *)
  31 lemma lfpr_refl: ∀L. ⦃L⦄ ➡ ⦃L⦄.
  32 /2 width=3/ qed.
  33
  34 lemma ltpss_sn_lfpr: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 → ⦃L1⦄ ➡ ⦃L2⦄.
  35 /3 width=5/ qed.
  36
  37 (* Basic inversion lemmas ***************************************************)
  38
  39 lemma lfpr_inv_atom1: ∀L2. ⦃⋆⦄ ➡ ⦃L2⦄ → L2 = ⋆.
  40 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_sn_inv_atom1 … HL2) -HL2 //
  41 qed-.