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

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  14
  15 include "basic_2/notation/relations/dpredstar_6.ma".
  16 include "basic_2/unfold/lsstas.ma".
  17 include "basic_2/computation/cprs.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  20
  21 definition cpds: ∀h. sd h → relation4 genv lenv term term ≝
  22                  λh,g,G,L,T1,T2.
  23                  ∃∃T,l1,l2. l2 ≤ l1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 & ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T & ⦃G, L⦄ ⊢ T ➡* T2.
  24
  25 interpretation "decomposed extended parallel computation (term)"
  26    'DPRedStar h g G L T1 T2 = (cpds h g G L T1 T2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma ssta_cprs_cpds: ∀h,g,G,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T1 •[h, g] T →
  31                       ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  32 /3 width=7/ qed.
  33
  34 lemma lsstas_cpds: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 •*[h, g, l] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  35 /2 width=7/ qed.
  36
  37 lemma cprs_cpds: ∀h,g,G,L,T1,T2,l.  ⦃G, L⦄ ⊢ T1 ▪[h, g] l → ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  38 /2 width=7/ qed.
  39
  40 lemma cpds_refl: ∀h,g,G,L,T,l. ⦃G, L⦄ ⊢ T ▪[h, g] l → ⦃G, L⦄ ⊢ T •*➡*[h, g] T.
  41 /2 width=2/ qed.
  42
  43 lemma cpds_strap1: ∀h,g,G,L,T1,T,T2.
  44                    ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  45 #h #g #G #L #T1 #T #T2 * /3 width=9/
  46 qed.