matita/matita/contribs/lambda_delta/basic_2/computation/lcprs.ma

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  14
  15 include "basic_2/reducibility/lcpr.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
  18
  19 definition lcprs: relation lenv ≝ TC … lcpr.
  20
  21 interpretation
  22   "context-sensitive parallel computation (environment)"
  23   'CPRedStar L1 L2 = (lcprs L1 L2).
  24
  25 (* Basic eliminators ********************************************************)
  26
  27 lemma lcprs_ind: ∀L1. ∀R:predicate lenv. R L1 →
  28                  (∀L,L2. L1 ⊢ ➡* L → L ⊢ ➡ L2 → R L → R L2) →
  29                  ∀L2. L1 ⊢ ➡* L2 → R L2.
  30 #L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
  31 qed-.
  32
  33 (* Basic properties *********************************************************)
  34
  35 lemma lcprs_refl: ∀L. L ⊢ ➡* L.
  36 /2 width=1/ qed.
  37
  38 lemma lcprs_strap1: ∀L1,L,L2.
  39                     L1 ⊢ ➡* L → L ⊢ ➡ L2 → L1 ⊢ ➡* L2.
  40 /2 width=3/ qed.
  41
  42 lemma lcprs_strap2: ∀L1,L,L2.
  43                     L1 ⊢ ➡ L → L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
  44 /2 width=3/ qed.