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

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  14
  15 include "basic_2/reducibility/ltpr_tpss.ma".
  16 include "basic_2/reducibility/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  19
  20 (* Properties on partial unfold for terms ***********************************)
  21
  22 lemma cpr_tpss_trans: ∀L,T1,T. L ⊢ T1 ➡ T →
  23                       ∀T2,d,e. L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
  24 #L #T1 #T * #T0 #HT10 #HT0 #T2 #d #e #HT2
  25 lapply (tpss_weak_full … HT2) -HT2 #HT2
  26 lapply (tpss_trans_eq … HT0 HT2) -T /2 width=3/
  27 qed.
  28
  29 lemma cpr_tps_trans: ∀L,T1,T. L ⊢ T1 ➡ T →
  30                      ∀T2,d,e. L ⊢ T ▶ [d, e] T2 → L ⊢ T1 ➡ T2.
  31 /3 width=5/ qed.
  32
  33 lemma cpr_tpss_conf: ∀L,T0,T1. L ⊢ T0 ➡ T1 →
  34                      ∀T2,d,e. L ⊢ T0 ▶* [d, e] T2 →
  35                      ∃∃T. L ⊢ T1 ▶* [d, e] T & L ⊢ T2 ➡ T.
  36 #L #T0 #T1 * #U0 #HTU0 #HU0T1 #T2 #d #e #HT02
  37 elim (tpr_tpss_conf … HTU0 … HT02) -T0 #T0 #HT20 #HUT0
  38 elim (tpss_conf_eq … HU0T1 … HUT0) -U0 /3 width=5/
  39 qed-.