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

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  14
  15 include "basic_2/reducibility/lfpr_lfpr.ma".
  16 include "basic_2/computation/lfprs_cprs.ma".
  17
  18 (* FOCALIZED PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *********************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lfprs_strip: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡ ⦃L2⦄ →
  23                    ∃∃L0. ⦃L1⦄ ➡ ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
  24 /3 width=3/ qed.
  25
  26 (* Main properties **********************************************************)
  27
  28 theorem lfprs_conf: ∀L,L1. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ →
  29                     ∃∃L0. ⦃L1⦄ ➡* ⦃L0⦄ & ⦃L2⦄ ➡* ⦃L0⦄.
  30 /3 width=3/ qed.
  31
  32 theorem lfprs_trans: ∀L1,L. ⦃L1⦄ ➡* ⦃L⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ➡* ⦃L2⦄.
  33 /2 width=3/ qed.
  34
  35 lemma lfprs_pair: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ → ∀V1,V2. L2 ⊢ V1 ➡* V2 →
  36                   ∀I. ⦃L1. ⓑ{I} V1⦄ ➡* ⦃L2. ⓑ{I} V2⦄.
  37 #L1 #L2 #H @(lfprs_ind … H) -L2 /2 width=1/
  38 #L #L2 #_ #HL2 #IHL1 #V1 #V2 #HV12 #I
  39 @(lfprs_trans … (L.ⓑ{I}V1)) /2 width=1/
  40 qed.