matita/matita/contribs/lambda_delta/Basic_2/computation/cprs.ma

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  14
  15 include "Basic_2/reducibility/cpr.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  18
  19 (* Basic_1: includes: pr3_pr2 *)
  20 definition cprs: lenv → relation term ≝
  21                  λL. TC … (cpr L).
  22
  23 interpretation "context-sensitive parallel computation (term)"
  24    'PRedStar L T1 T2 = (cprs L T1 T2).
  25
  26 (* Basic eliminators ********************************************************)
  27
  28 lemma cprs_ind: ∀L,T1. ∀R:predicate term. R T1 →
  29                 (∀T,T2. L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → R T → R T2) →
  30                 ∀T2. L ⊢ T1 ➡* T2 → R T2.
  31 #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
  32 qed-.
  33
  34 (* Basic properties *********************************************************)
  35
  36 (* Basic_1: was: pr3_refl *)
  37 lemma cprs_refl: ∀L,T. L ⊢ T ➡* T.
  38 /2 width=1/ qed.
  39
  40 lemma cprs_strap1: ∀L,T1,T,T2.
  41                    L ⊢ T1 ➡* T → L ⊢ T ➡ T2 → L ⊢ T1 ➡* T2.
  42 /2 width=3/ qed.
  43
  44 (* Basic_1: was: pr3_step *)
  45 lemma cprs_strap2: ∀L,T1,T,T2.
  46                    L ⊢ T1 ➡ T → L ⊢ T ➡* T2 → L ⊢ T1 ➡* T2.
  47 /2 width=3/ qed.
  48
  49 (* Note: it does not hold replacing |L1| with |L2| *)
  50 lemma cprs_lsubs_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡* T2 →
  51                        ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡* T2.
  52 /3 width=3/
  53 qed.
  54
  55 (* Basic_1: removed theorems 2: clear_pr3_trans pr3_cflat *)