matita/matita/contribs/lambda_delta/basic_2/computation/fprs_cprs.ma

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  14
  15 include "basic_2/reducibility/fpr_cpr.ma".
  16 include "basic_2/computation/cprs.ma".
  17 include "basic_2/computation/fprs.ma".
  18
  19 (* CONTEXT-FREE PARALLEL COMPUTATION ON CLOSURES ****************************)
  20
  21 (* Properties on context-sensitive parallel computation for terms ***********)
  22
  23 lemma cprs_fprs: ∀L,T1,T2. L ⊢ T1 ➡* T2 → ⦃L, T1⦄ ➡* ⦃L, T2⦄.
  24 #L #T1 #T2 #H @(cprs_ind … H) -T2 // /3 width=4/
  25 qed.
  26 (*
  27 (* Advanced propertis *******************************************************)
  28
  29 lamma fpr_bind_sn: ∀L1,L2,V1,V2. ⦃L1, V1⦄ ➡ ⦃L2, V2⦄ → ∀T1,T2. T1 ➡ T2 →
  30                    ∀a,I. ⦃L1, ⓑ{a,I}V1.T1⦄ ➡ ⦃L2, ⓑ{a,I}V2.T2⦄.
  31 #L1 #L2 #V1 #V2 #H #T1 #T2 #HT12 #a #I
  32 elim (fpr_inv_all … H) /3 width=4/
  33 qed.
  34
  35 (* Advanced forward lemmas **************************************************)
  36
  37 lamma fpr_fwd_shift_bind_minus: ∀I1,I2,L1,L2,V1,V2,T1,T2.
  38                                 ⦃L1, -ⓑ{I1}V1.T1⦄ ➡ ⦃L2, -ⓑ{I2}V2.T2⦄ →
  39                                 ⦃L1, V1⦄ ➡ ⦃L2, V2⦄ ∧ I1 = I2.
  40 * #I2 #L1 #L2 #V1 #V2 #T1 #T2 #H
  41 elim (fpr_inv_all … H) -H #L #HL1 #H #HL2
  42 [ elim (cpr_inv_abbr1 … H) -H *
  43   [ #V #V0 #T #HV1 #HV0 #_ #H destruct /4 width=4/
  44   | #T #_ #_ #H destruct
  45   ]
  46 | elim (cpr_inv_abst1 … H Abst V2) -H
  47   #V #T #HV1 #_ #H destruct /3 width=4/
  48 ]
  49 qed-.
  50
  51 (* Advanced inversion lemmas ************************************************)
  52
  53 lamma fpr_inv_pair1: ∀I,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I}V1, T1⦄ ➡ ⦃L2, T2⦄ →
  54                      ∃∃K2,V2. ⦃K1, V1⦄  ➡ ⦃K2, V2⦄ &
  55                               ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
  56                               L2 = K2.ⓑ{I}V2.
  57 #I1 #K1 #X #V1 #T1 #T2 #H
  58 elim (fpr_fwd_pair1 … H) -H #I2 #K2 #V2 #HT12 #H destruct
  59 elim (fpr_fwd_shift_bind_minus … HT12) #HV12 #H destruct /2 width=5/
  60 qed-.
  61
  62 lamma fpr_inv_pair3: ∀I,L1,K2,V2,T1,T2. ⦃L1, T1⦄ ➡ ⦃K2.ⓑ{I}V2, T2⦄ →
  63                      ∃∃K1,V1. ⦃K1, V1⦄  ➡ ⦃K2, V2⦄ &
  64                               ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
  65                               L1 = K1.ⓑ{I}V1.
  66 #I2 #X #K2 #V2 #T1 #T2 #H
  67 elim (fpr_fwd_pair3 … H) -H #I1 #K1 #V1 #HT12 #H destruct
  68 elim (fpr_fwd_shift_bind_minus … HT12) #HV12 #H destruct /2 width=5/
  69 qed-.
  70 *)