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

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  14
  15 include "basic_2/unwind/sstas.ma".
  16 include "basic_2/computation/cprs.ma".
  17
  18 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  19
  20 definition dxprs: ∀h. sd h → lenv → relation term ≝ λh,g,L,T1,T2.
  21                   ∃∃T. ⦃h, L⦄ ⊢ T1 •*[g] T & L ⊢ T ➡* T2.
  22
  23 interpretation "decomposed extended parallel computation (term)"
  24    'DecomposedXPRedStar h g L T1 T2 = (dxprs h g L T1 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma dxprs_refl: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l] U → ⦃h, L⦄ ⊢ T •*➡*[g] T.
  29 /3 width=3/ qed.
  30
  31 lemma sstas_dxprs: ∀h,g,L,T1,T2. ⦃h, L⦄ ⊢ T1 •*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  32 /2 width=3/ qed.
  33
  34 lemma cprs_dxprs: ∀h,g,L,T1,T2,U,l. ⦃h, L⦄ ⊢ T1 •[g, l] U → L ⊢ T1 ➡* T2 →
  35                   ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  36 /3 width=3/ qed.
  37
  38 lemma dxprs_strap1: ∀h,g,L,T1,T,T2.
  39                     ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡ T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  40 #h #g #L #T1 #T #T2 * /3 width=5/
  41 qed.
  42
  43 lemma dxprs_strap2: ∀h,g,L,T1,T,T2,l.
  44                     ⦃h, L⦄ ⊢ T1 •[g, l+1] T → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  45 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/
  46 qed.