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

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  14
  15 include "basic_2/notation/relations/dpredstar_5.ma".
  16 include "basic_2/unfold/sstas.ma".
  17 include "basic_2/computation/cprs.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  20
  21 definition cpds: ∀h. sd h → lenv → relation term ≝ λh,g,L,T1,T2.
  22                  ∃∃T. ⦃G, L⦄ ⊢ T1 •*[h, g] T & ⦃G, L⦄ ⊢ T ➡* T2.
  23
  24 interpretation "decomposed extended parallel computation (term)"
  25    'DPRedStar h g L T1 T2 = (cpds h g L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma cpds_refl: ∀h,g,L. reflexive … (cpds h g L).
  30 /2 width=3/ qed.
  31
  32 lemma sstas_cpds: ∀h,g,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  33 /2 width=3/ qed.
  34
  35 lemma cprs_cpds: ∀h,g,L,T1,T2.  ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  36 /2 width=3/ qed.
  37
  38 lemma cpds_strap1: ∀h,g,L,T1,T,T2.
  39                    ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  40 #h #g #L #T1 #T #T2 * /3 width=5/
  41 qed.
  42
  43 lemma cpds_strap2: ∀h,g,L,T1,T,T2,l.
  44                    ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ → ⦃G, L⦄ ⊢ T •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  45 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/
  46 qed.
  47
  48 lemma ssta_cprs_cpds: ∀h,g,L,T1,T,T2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, T⦄ →
  49                       ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2.
  50 /3 width=3/ qed.