matita/matita/contribs/lambdadelta/basic_2A/etc/xpr/xprs.etc

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ break term 46 T1 • ➡ * break [ term 46 g ] break term 46 T2 )"
  16    non associative with precedence 45
  17    for @{ 'XPRedStar $h $g $L $T1 $T2 }.
  18
  19 notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ • ⬊ * break [ term 46 g ] break term 46 T2 )"
  20    non associative with precedence 45
  21    for @{ 'XSN $h $g $L $T }.
  22
  23 include "basic_2/static/lsubss.ma".
  24 include "basic_2/reducibility/xpr.ma".
  25 (*
  26 include "basic_2/reducibility/cnf.ma".
  27 *)
  28 (* EXTENDED PARALLEL COMPUTATION ON TERMS ***********************************)
  29
  30 definition xprs: ∀h. sd h → lenv → relation term ≝
  31                  λh,g,L. TC … (xpr h g L).
  32
  33 interpretation "extended parallel computation (term)"
  34    'XPRedStar h g L T1 T2 = (xprs h g L T1 T2).
  35
  36 (* Basic eliminators ********************************************************)
  37
  38 lemma xprs_ind: ∀h,g,L,T1. ∀R:predicate term. R T1 →
  39                 (∀T,T2. ⦃h, L⦄ ⊢ T1 •➡*[g] T → ⦃h, L⦄ ⊢ T •➡[g] T2 → R T → R T2) →
  40                 ∀T2. ⦃h, L⦄ ⊢ T1 •➡*[g] T2 → R T2.
  41 #h #g #L #T1 #R #HT1 #IHT1 #T2 #HT12
  42 @(TC_star_ind … HT1 IHT1 … HT12) //
  43 qed-.
  44
  45 lemma xprs_ind_dx: ∀h,g,L,T2. ∀R:predicate term. R T2 →
  46                    (∀T1,T. ⦃h, L⦄ ⊢ T1 •➡[g] T → ⦃h, L⦄ ⊢ T •➡*[g] T2 → R T → R T1) →
  47                    ∀T1. ⦃h, L⦄ ⊢ T1 •➡*[g] T2 → R T1.
  48 #h #g #L #T2 #R #HT2 #IHT2 #T1 #HT12
  49 @(TC_star_ind_dx … HT2 IHT2 … HT12) //
  50 qed-.
  51
  52 (* Basic properties *********************************************************)
  53
  54 lemma xprs_refl: ∀h,g,L. reflexive … (xprs h g L).
  55 /2 width=1/ qed.
  56
  57 lemma xprs_strap1: ∀h,g,L,T1,T,T2.
  58                    ⦃h, L⦄ ⊢ T1 •➡*[g] T → ⦃h, L⦄ ⊢ T •➡[g] T2 → ⦃h, L⦄ ⊢ T1 •➡*[g] T2.
  59 /2 width=3/ qed.
  60
  61 lemma xprs_strap2: ∀h,g,L,T1,T,T2.
  62                    ⦃h, L⦄ ⊢ T1 •➡[g] T → ⦃h, L⦄ ⊢ T •➡*[g] T2 → ⦃h, L⦄ ⊢ T1 •➡*[g] T2.
  63 /2 width=3/ qed.
  64
  65 (* Basic inversion lemmas ***************************************************)
  66 (*
  67 axiom xprs_inv_cnf1: ∀L,T,U. L ⊢ T ➡* U → L ⊢ 𝐍⦃T⦄ → T = U.
  68 #L #T #U #H @(xprs_ind_dx … H) -T //
  69 #T0 #T #H1T0 #_ #IHT #H2T0
  70 lapply (H2T0 … H1T0) -H1T0 #H destruct /2 width=1/
  71 qed-.
  72 *)