matita/matita/contribs/lambdadelta/basic_2/etc/cpr/tprs_tprs.etc

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/reducibility/tpr_tpr.ma".
  16 include "basic_2/computation/tprs.ma".
  17
  18 (* CONTEXT-FREE PARALLEL COMPUTATION ON TERMS *******************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 (* Basic_1: was: pr1_strip *)
  23 lemma tprs_strip: ∀T1,T. T ➡* T1 → ∀T2. T ➡ T2 →
  24                   ∃∃T0. T1 ➡ T0 & T2 ➡* T0.
  25 /3 width=3 by TC_strip1, tpr_conf/ qed.
  26
  27 (* Main propertis ***********************************************************)
  28
  29 (* Basic_1: was: pr1_confluence *)
  30 theorem tprs_conf: confluent … tprs.
  31 /3 width=3/ qed.
  32
  33 (* Basic_1: was: pr1_t *)
  34 theorem tprs_trans: Transitive … tprs.
  35 /2 width=3/ qed.
  36
  37 (* Basic_1: was: pr1_comp *)
  38 lemma tprs_pair: ∀I,V1,V2. V1 ➡* V2 → ∀T1,T2. T1 ➡* T2 →
  39                  ②{I} V1. T1 ➡* ②{I} V2. T2.
  40 #I #V1 #V2 #H @(tprs_ind … H) -V2 /2 width=1/
  41 #V #V2 #_ #HV2 #IHV1 #T1 #T2 #HT12
  42 @(tprs_trans … (②{I}V.T2)) /2 width=1/
  43 qed.