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

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  14
  15 include "basic_2/rt_computation/lprs_tc.ma".
  16
  17 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
  18
  19 (* Eliminators with r-transition for full local environments ****************)
  20
  21 (* Basic_2A1: was: lprs_ind_dx *)
  22 lemma lprs_ind_sn (h) (G) (L2):
  23       ∀Q:predicate lenv. Q L2 →
  24       (∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L → ❪G,L❫ ⊢ ➡*[h,0] L2 → Q L → Q L1) →
  25       ∀L1. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L1.
  26 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
  27
  28 (* Basic_2A1: was: lprs_ind *)
  29 lemma lprs_ind_dx (h) (G) (L1):
  30       ∀Q:predicate lenv. Q L1 →
  31       (∀L,L2. ❪G,L1❫ ⊢ ➡*[h,0] L → ❪G,L❫ ⊢ ➡[h,0] L2 → Q L → Q L2) →
  32       ∀L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L2.
  33 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
  34
  35 (* Properties with extended rt-transition for full local environments *******)
  36
  37 lemma lpr_lprs (h) (G):
  38       ∀L1,L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
  39 /4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
  40
  41 (* Basic_2A1: was: lprs_strap2 *)
  42 lemma lprs_step_sn (h) (G):
  43       ∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L →
  44       ∀L2.❪G,L❫ ⊢ ➡*[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
  45 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_sn/ qed-.
  46
  47 (* Basic_2A1: was: lpxs_strap1 *)
  48 lemma lprs_step_dx (h) (G):
  49       ∀L1,L. ❪G,L1❫ ⊢ ➡*[h,0] L →
  50       ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
  51 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.
  52
  53 lemma lprs_strip (h) (G):
  54       confluent2 … (lprs h 0 G) (lpr h 0 G).
  55 #h #G #L0 #L1 #HL01 #L2 #HL02
  56 elim (TC_strip1 … L1 ?? HL02) -HL02
  57 [ /3 width=3 by lprs_TC, ex2_intro/ | skip
  58 | /2 width=1 by lprs_inv_TC/
  59 | /2 width=3 by lpr_conf/
  60 ]
  61 qed-.