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

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  14
  15 include "basic_2/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/computation/cprs_ltpss_dx.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties concerning sn partial unfold on local environments ************)
  21
  22 lemma cprs_ltpss_sn_conf: ∀L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  23                           ∀T,U1. L1 ⊢ T ➡* U1 →
  24                           ∃∃U2. L2 ⊢ T ➡* U2 & L1 ⊢ U1 ▶* [d, e] U2.
  25 #L1 #L2 #d #e #H
  26 lapply (ltpss_sn_ltpssa … H) -H #H @(ltpssa_ind … H) -L2 /2 width=3/
  27 #L #L2 #HL1 #HL2 #IHL1 #T #U1 #HTU1
  28 lapply (ltpssa_ltpss_sn … HL1) -HL1 #HL1
  29 lapply (ltpss_sn_dx_trans_eq … HL1 … HL2) -HL1 #HL12
  30 elim (IHL1 … HTU1) -IHL1 -HTU1 #U #HTU #HU1
  31 elim (cprs_ltpss_dx_conf … HTU … HL2) -HTU -HL2 #U2 #HTU2 #HU2
  32 lapply (ltpss_sn_tpss_trans_eq … HU2 … HL12) -HU2 -HL12 #HU2
  33 lapply (tpss_trans_eq … HU1 HU2) -U /2 width=3/
  34 qed-.