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
  31 @(TC_star_ind … HL1 IHL1 … HL12) //
  32 qed-.
  33
  34 lemma lcprs_ind_dx: ∀L2. ∀R:predicate lenv. R L2 →
  35                     (∀L1,L. L1 ⊢ ➡ L → L ⊢ ➡* L2 → R L → R L1) →
  36                     ∀L1. L1 ⊢ ➡* L2 → R L1.
  37 #L2 #R #HL2 #IHL2 #L1 #HL12
  38 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
  39 qed-.
  40
  41 (* Basic properties *********************************************************)
  42
  43 lemma lcprs_refl: ∀L. L ⊢ ➡* L.
  44 /2 width=1/ qed.
  45
  46 lemma lcprs_strap1: ∀L1,L,L2.
  47                     L1 ⊢ ➡* L → L ⊢ ➡ L2 → L1 ⊢ ➡* L2.
  48 /2 width=3/ qed.
  49
  50 lemma lcprs_strap2: ∀L1,L,L2.
  51                     L1 ⊢ ➡ L → L ⊢ ➡* L2 → L1 ⊢ ➡* L2.
  52 /2 width=3/ qed.