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

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  14
  15 include "basic_2/unfold/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    'DecomposedPRedStar h g L T1 T2 = (dxprs h g L T1 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma dxprs_refl: ∀h,g,L. reflexive … (dxprs h g L).
  29 /2 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.  L ⊢ T1 ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  35 /2 width=3/ qed.
  36
  37 lemma dxprs_strap1: ∀h,g,L,T1,T,T2.
  38                     ⦃h, L⦄ ⊢ T1 •*➡*[g] T → L ⊢ T ➡ T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  39 #h #g #L #T1 #T #T2 * /3 width=5/
  40 qed.
  41
  42 lemma dxprs_strap2: ∀h,g,L,T1,T,T2,l.
  43                     ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, T⦄ → ⦃h, L⦄ ⊢ T •*➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  44 #h #g #L #T1 #T #T2 #l #HT1 * /3 width=4/
  45 qed.
  46
  47 lemma ssta_cprs_dxprs: ∀h,g,L,T1,T,T2,l. ⦃h, L⦄ ⊢ T1 •[g] ⦃l+1, T⦄ →
  48                        L ⊢ T ➡* T2 → ⦃h, L⦄ ⊢ T1 •*➡*[g] T2.
  49 /3 width=3/ qed.
  50
  51 (* Basic inversion lemmas ***************************************************)
  52
  53 lemma dxprs_inv_abst1: ∀h,g,a,L,V1,T1,U2. ⦃h, L⦄ ⊢ ⓛ{a}V1. T1 •*➡*[g] U2 →
  54                        ∃∃V2,T2. L ⊢ V1 ➡* V2 & ⦃h, L.ⓛV1⦄ ⊢ T1 •*➡*[g] T2 &
  55                                 U2 = ⓛ{a}V2. T2.
  56 #h #g #a #L #V1 #T1 #U2 * #X #H1 #H2
  57 elim (sstas_inv_bind1 … H1) -H1 #U #HTU1 #H destruct
  58 elim (cprs_fwd_abst1 … H2 Abst V1) -H2 #V2 #T2 #HV12 #HUT2 #H destruct /3 width=5/
  59 qed-.