matita/matita/contribs/lambdadelta/basic_2A/etc/cpr/cprs_ltpss_dx.etc

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  14
  15 include "basic_2/reducibility/cpr_ltpss_dx.ma".
  16 include "basic_2/computation/cprs_tpss.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON TERMS **************************)
  19
  20 (* Properties concerning dx partial unfold on local environments ************)
  21
  22 lemma cprs_ltpss_dx_conf: ∀L1,T,U1. L1 ⊢ T ➡* U1 →
  23                           ∀L2,d,e. L1 ▶* [d, e] L2 →
  24                           ∃∃U2. L2 ⊢ T ➡* U2 & L2 ⊢ U1 ▶* [d, e] U2.
  25 #L1 #T #U1 #H @(cprs_ind … H) -U1 /2 width=3/
  26 #T1 #U1 #_ #HTU1 #IHT1 #L2 #d #e #HL12
  27 elim (IHT1 … HL12) -IHT1 #U #HTU #HT1U
  28 elim (ltpss_dx_cpr_conf … HTU1 … HL12) -L1 #U0 #HT1U0 #HU10
  29 elim (cpr_tpss_conf … HT1U0 … HT1U) -T1 #U2 #HU02 #HU2
  30 lapply (tpss_trans_eq … HU10 HU02) -U0 /3 width=3/
  31 qed-.
  32
  33 lemma cprs_ltpss_dx_tpss_conf: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 →
  34                                ∀L2,d,e. L1 ▶* [d, e] L2 →
  35                                ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
  36                                ∃∃U2. L2 ⊢ T2 ➡* U2 & L2 ⊢ U1 ▶* [d, e] U2.
  37 #L1 #T1 #U1 #HTU1 #L2 #d #e #HL12 #T2 #HT12
  38 elim (cprs_ltpss_dx_conf … HTU1 … HL12) -L1 #U #HT1U #HU1
  39 elim (cprs_tpss_conf … HT1U … HT12) -T1 #T #HUT #HT2
  40 lapply (tpss_trans_eq … HU1 HUT) -U /2 width=3/
  41 qed-.
  42
  43 lemma cprs_ltpss_dx_tpss2_conf: ∀L1,T1,U1. L1 ⊢ T1 ➡* U1 →
  44                                 ∀L2,d,e. L1 ▶* [d, e] L2 →
  45                                 ∀T2. L2 ⊢ T1 ▶* [d, e] T2 →
  46                                 ∀U2. L2 ⊢ U1 ▶* [d, e] U2 →
  47                                 ∃∃U. L2 ⊢ T2 ➡* U & L2 ⊢ U2 ▶* [d, e] U.
  48 #L1 #T1 #U1 #HTU1 #L2 #d #e #HL12 #T2 #HT12 #U2 #HU12
  49 elim (cprs_ltpss_dx_tpss_conf … HTU1 … HL12 … HT12) -L1 -T1 #U #HT2U #HU1
  50 elim (tpss_conf_eq … HU12 … HU1) -U1 #U0 #HU20 #HU0
  51 lapply (cprs_tpss_trans … HT2U … HU0) -U /2 width=3/
  52 qed-.