matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_lpr.ma

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  14
  15 include "basic_2/rt_computation/cpms_lpr.ma".
  16 include "basic_2/rt_computation/cprs_cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
  19
  20 (* Properties concerning sn parallel reduction on local environments ********)
  21
  22 (* Basic_1: uses: pr3_pr2_pr2_t *)
  23 (* Basic_1: includes: pr3_pr0_pr2_t *)
  24 lemma lpr_cpr_trans (h) (G):
  25       s_r_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
  26 /3 width=4 by cprs_inv_CTC, lpr_cpm_trans, ltc_inv_CTC/
  27 qed-.
  28
  29 (* Basic_1: uses: pr3_pr2_pr3_t pr3_wcpr0_t *)
  30 lemma lpr_cprs_trans (h) (G):
  31       s_rs_transitive … (λL. cpm h G L 0) (λ_. lpr h 0 G).
  32 #h #G @s_r_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
  33 qed-.
  34
  35 lemma cprs_lpr_conf_dx (h) (G):
  36       ∀L0,T0,T1. ❨G,L0❩ ⊢ T0 ➡*[h,0] T1 → ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 →
  37       ∃∃T. ❨G,L1❩ ⊢ T1 ➡*[h,0] T & ❨G,L1❩ ⊢ T0 ➡*[h,0] T.
  38 #h #G #L0 #T0 #T1 #H
  39 @(cprs_ind_dx … H) -T1 /2 width=3 by ex2_intro/
  40 #T #T1 #_ #HT1 #IHT0 #L1 #HL01
  41 elim (IHT0 … HL01) #T2 #HT2 #HT02
  42 elim (lpr_cpr_conf_dx … HT1 … HL01) -L0 #T3 #HT3 #HT13
  43 elim (cprs_strip … HT2 … HT3) -T
  44 /3 width=5 by cprs_step_dx, cprs_step_sn, ex2_intro/
  45 qed-.
  46
  47 lemma cprs_lpr_conf_sn (h) (G):
  48       ∀L0,T0,T1. ❨G,L0❩ ⊢ T0 ➡*[h,0] T1 →
  49       ∀L1. ❨G,L0❩ ⊢ ➡[h,0] L1 →
  50       ∃∃T. ❨G,L0❩ ⊢ T1 ➡*[h,0] T & ❨G,L1❩ ⊢ T0 ➡*[h,0] T.
  51 #h #G #L0 #T0 #T1 #HT01 #L1 #HL01
  52 elim (cprs_lpr_conf_dx … HT01 … HL01) -HT01 #T #HT1 #HT0
  53 /3 width=3 by lpr_cpms_trans, ex2_intro/
  54 qed-.