matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/dxprs_ltpss_sn.etc

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  14
  15 include "basic_2/unfold/ltpss_sn_alt.ma".
  16 include "basic_2/computation/dxprs_ltpss_dx.ma".
  17
  18 (* DECOMPOSED EXTENDED PARALLEL COMPUTATION ON TERMS ************************)
  19
  20 (* Properties about sn parallel unfold **************************************)
  21
  22 lemma dxprs_ltpss_sn_conf: ∀h,g,L1,L2,d,e. L1 ⊢ ▶* [d, e] L2 →
  23                            ∀T,U1. ⦃h, L1⦄ ⊢ T •*➡*[g] U1 →
  24                            ∃∃U2. ⦃h, L2⦄ ⊢ T •*➡*[g] U2 & L1 ⊢ U1 ▶* [d, e] U2.
  25 #h #g #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 (dxprs_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-.