matita/matita/contribs/lambdadelta/basic_2/computation/cpe.ma

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  14
  15 include "basic_2/computation/cprs.ma".
  16 include "basic_2/computation/csn.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL EVALUATION ON TERMS **************************)
  19
  20 definition cpe: lenv → relation term ≝
  21                 λL,T1,T2. L ⊢ T1 ➡* T2 ∧ L ⊢ 𝐍⦃T2⦄.
  22
  23 interpretation "context-sensitive parallel evaluation (term)"
  24    'PEval L T1 T2 = (cpe L T1 T2).
  25
  26 (* Basic_properties *********************************************************)
  27
  28 (* Basic_1: was: nf2_sn3 *)
  29 lemma cpe_csn: ∀L,T1. L ⊢ ⬊* T1 → ∃T2. L ⊢ T1 ➡* 𝐍⦃T2⦄.
  30 #L #T1 #H @(csn_ind … H) -T1
  31 #T1 #_ #IHT1
  32 elim (cnf_dec L T1) /3 width=3/
  33 * #T #H1T1 #H2T1
  34 elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1 #T2 * /4 width=3/
  35 qed.