matita/matita/contribs/lambdadelta/basic_2A/etc/fpr/lfprs_fprs.etc

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  14
  15 include "basic_2/reducibility/lfpr_fpr.ma".
  16 include "basic_2/computation/fprs_fprs.ma".
  17 include "basic_2/computation/lfprs.ma".
  18
  19 (* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
  20
  21 (* Inversion lemmas on context-free parallel reduction for closures *********)
  22
  23 lemma lfprs_inv_fprs: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ → ∀T. ⦃L1, T⦄ ➡* ⦃L2, T⦄.
  24 #L1 #L2 #H @(lfprs_ind … H) -L2 //
  25 #L #L2 #_ #HL2 #IHL1 #T
  26 lapply (lfpr_inv_fpr … HL2 T) -HL2 /3 width=4/
  27 qed-.
  28
  29 (* Properties on context-free parallel computation for closures *************)
  30
  31 lemma fprs_lfprs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.
  32 #L1 #L2 #T1 #T2 #H @(fprs_ind … H) -L2 -T2 // /3 width=5/
  33 qed.
  34
  35 lemma lfprs_fprs_trans: ∀L1,L,L2,T1,T2. ⦃L1⦄ ➡* ⦃L⦄ → ⦃L, T1⦄ ➡* ⦃L2, T2⦄ → ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  36 #L1 #L #L2 #T1 #T2 #HL1 #HL2
  37 lapply (lfprs_inv_fprs … HL1 T1) -HL1 /2 width=4/
  38 qed.
  39 (*
  40 lamma lfprs_cprs_conf: ∀L1,L,L2,T1,T2. ⦃L1⦄ ➡* ⦃L2⦄ → L1 ⊢ T1 ➡* T2 → ⦃L1, T1⦄ ➡* ⦃L2, T2⦄.
  41 *)