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

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  14
  15 include "basic_2/notation/relations/peval_5.ma".
  16 include "basic_2/computation/cpxs.ma".
  17 include "basic_2/computation/csn.ma".
  18
  19 (* CONTEXT-SENSITIVE EXTENDED PARALLEL EVALUATION ON TERMS ******************)
  20
  21 definition cpxe: ∀h. sd h → lenv → relation term ≝
  22                  λh,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 ∧ ⦃h, L⦄ ⊢ 𝐍[g]⦃T2⦄.
  23
  24 interpretation "context-sensitive extended parallel evaluation (term)"
  25    'PEval h g L T1 T2 = (cpxe h g L T1 T2).
  26
  27 (* Basic_properties *********************************************************)
  28
  29 lemma csn_cpxe: ∀h,g,L,T1. ⦃h, L⦄ ⊢ ⬊*[g] T1 → ∃T2. ⦃h, L⦄ ⊢ T1 ➡*[g] 𝐍⦃T2⦄.
  30 #h #g #L #T1 #H @(csn_ind … H) -T1
  31 #T1 #_ #IHT1
  32 elim (cnx_dec h g L T1) /3 width=3/
  33 * #T #H1T1 #H2T1
  34 elim (IHT1 … H1T1 H2T1) -IHT1 -H2T1 #T2 * /4 width=3/
  35 qed-.