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

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  14
  15 include "basic_2/unfold/ltpss.ma".
  16 include "basic_2/reducibility/ltpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
  19
  20 definition lcpr: relation lenv ≝
  21    λL1,L2. ∃∃L. L1 ➡ L & L ▶* [0, |L|] L2
  22 .
  23
  24 interpretation
  25   "context-sensitive parallel reduction (environment)"
  26   'CPRed L1 L2 = (lcpr L1 L2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma lcpr_refl: ∀L. L ⊢ ➡ L.
  31 /2 width=3/ qed.
  32
  33 (* Basic inversion lemmas ***************************************************)
  34
  35 lemma lcpr_inv_atom1: ∀L2. ⋆ ⊢ ➡ L2 → L2 = ⋆.
  36 #L2 * #L #HL >(ltpr_inv_atom1 … HL) -HL #HL2 >(ltpss_inv_atom1 … HL2) -HL2 //
  37 qed-.