matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fprs.etc

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  14
  15 notation "hvbox( ⦃ term 46 L1 , term 46 T1 ⦄ ➡ * break ⦃ term 46 L2 , term 46 T2 ⦄ )"
  16    non associative with precedence 45
  17    for @{ 'FocalizedPRedStar $L1 $T1 $L2 $T2 }.
  18
  19 notation "hvbox( ⦃ term 46 L1 , term 46 T1 ⦄ ➡ ➡ * break ⦃ term 46 L2 , term 46 T2 ⦄ )"
  20    non associative with precedence 45
  21    for @{ 'FocalizedPRedStarAlt $L1 $T1 $L2 $T2 }.
  22
  23 include "basic_2/reducibility/fpr.ma".
  24
  25 (* CONTEXT-FREE PARALLEL COMPUTATION ON CLOSURES ****************************)
  26
  27 definition fprs: bi_relation lenv term ≝ bi_TC … fpr.
  28
  29 interpretation "context-free parallel computation (closure)"
  30    'FocalizedPRedStar L1 T1 L2 T2 = (fprs L1 T1 L2 T2).
  31
  32 (* Basic eliminators ********************************************************)
  33
  34 lemma fprs_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
  35                 (∀L,L2,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ → R L T → R L2 T2) →
  36                 ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L2 T2.
  37 /3 width=7 by bi_TC_star_ind/ qed-.
  38
  39 lemma fprs_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
  40                    (∀L1,L,T1,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ → R L T → R L1 T1) →
  41                    ∀L1,T1. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → R L1 T1.
  42 /3 width=7 by bi_TC_star_ind_dx/ qed-.
  43
  44 (* Basic properties *********************************************************)
  45
  46 lemma fpr_fprs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  47 /2 width=1/ qed.
  48
  49 lemma fprs_refl: bi_reflexive … fprs.
  50 /2 width=1/ qed.
  51
  52 lemma fprs_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡* ⦃L, T⦄ → ⦃L, T⦄ ➡ ⦃L2, T2⦄ →
  53                    ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  54 /2 width=4/ qed.
  55
  56 lemma fprs_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ➡ ⦃L, T⦄ → ⦃L, T⦄ ➡* ⦃L2, T2⦄ →
  57                    ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  58 /2 width=4/ qed.