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

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  14
  15 include "basic_2/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/reducibility/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  19
  20 (* Properties concerning sn partial unfold on local environments ************)
  21
  22 lemma ltpss_sn_cpr_trans: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  23                           ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
  24 #L1 #L2 #d #e #HL12 #T1 #T2 *
  25 lapply (ltpss_sn_weak_full … HL12)
  26 <(ltpss_sn_fwd_length … HL12) -HL12 /3 width=5/
  27 qed.
  28
  29 lemma ltpss_sn_cpr_conf: ∀L1,T,U1. L1 ⊢ T ➡ U1 →
  30                          ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  31                          ∃∃U2. L2 ⊢ T ➡ U2 & L1 ⊢ U1 ▶* [d, e] U2.
  32 #L1 #T #U1 * #U #HTU #HU1 #L2 #d #e #HL12
  33 lapply (ltpss_sn_fwd_length … HL12) #H >H in HU1; -H #HU1
  34 elim (ltpss_sn_tpss_conf … HU1 … HL12) -HU1 -HL12 /3 width=3/
  35 qed-.