matita/matita/contribs/lambdadelta/basic_2A/computation/scpds.ma

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  14
  15 include "ground_2/xoa/ex_4_2.ma".
  16 include "basic_2A/notation/relations/dpredstar_7.ma".
  17 include "basic_2A/static/da.ma".
  18 include "basic_2A/computation/cprs.ma".
  19
  20 (* STRATIFIED DECOMPOSED PARALLEL COMPUTATION ON TERMS **********************)
  21
  22 definition scpds: ∀h. sd h → nat → relation4 genv lenv term term ≝
  23                   λh,g,d2,G,L,T1,T2.
  24                   ∃∃T,d1. d2 ≤ d1 & ⦃G, L⦄ ⊢ T1 ▪[h, g] d1 & ⦃G, L⦄ ⊢ T1 •*[h, d2] T & ⦃G, L⦄ ⊢ T ➡* T2.
  25
  26 interpretation "stratified decomposed parallel computation (term)"
  27    'DPRedStar h g d G L T1 T2 = (scpds h g d G L T1 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma sta_cprs_scpds: ∀h,g,G,L,T1,T,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, g] d+1 → ⦃G, L⦄ ⊢ T1 •*[h, 1] T →
  32                       ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 1] T2.
  33 /2 width=6 by ex4_2_intro/ qed.
  34
  35 lemma lstas_scpds: ∀h,g,G,L,T1,T2,d1. ⦃G, L⦄ ⊢ T1 ▪[h, g] d1 →
  36                    ∀d2. d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d2] T2.
  37 /2 width=6 by ex4_2_intro/ qed.
  38
  39 lemma scpds_strap1: ∀h,g,G,L,T1,T,T2,d.
  40                     ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T → ⦃G, L⦄ ⊢ T ➡ T2 → ⦃G, L⦄ ⊢ T1 •*➡*[h, g, d] T2.
  41 #h #g #G #L #T1 #T #T2 #d * /3 width=8 by cprs_strap1, ex4_2_intro/
  42 qed.
  43
  44 (* Basic forward lemmas *****************************************************)
  45
  46 lemma scpds_fwd_cprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g, 0] T2 →
  47                       ⦃G, L⦄ ⊢ T1 ➡* T2.
  48 #h #g #G #L #T1 #T2 * /3 width=3 by cprs_strap2, lstas_cpr/
  49 qed-.