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

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/relocation/lex_tc.ma".
  16 include "basic_2/rt_computation/cprs_lpr.ma".
  17 include "basic_2/rt_computation/lprs_ctc.ma".
  18
  19 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
  20
  21 (* Eliminators with r-transition for full local environments ****************)
  22
  23 (* Basic_2A1: was: lprs_ind_dx *)
  24 lemma lprs_ind_sn (h) (G) (L2): ∀R:predicate lenv. R L2 →
  25                                 (∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L → ⦃G, L⦄ ⊢ ➡*[h] L2 → R L → R L1) →
  26                                 ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R L1.
  27 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
  28
  29 (* Basic_2A1: was: lprs_ind *)
  30 lemma lprs_ind_dx (h) (G) (L1): ∀R:predicate lenv. R L1 →
  31                                 (∀L,L2. ⦃G, L1⦄ ⊢ ➡*[h] L → ⦃G, L⦄ ⊢ ➡[h] L2 → R L → R L2) →
  32                                 ∀L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 → R 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 unbound rt-transition for full local environments ********)
  36
  37 lemma lpr_lprs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
  38 /4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
  39
  40 (* Basic_2A1: was: lprs_strap2 *)
  41 lemma lprs_step_sn (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡[h] L →
  42                             ∀L2.⦃G, L⦄ ⊢ ➡*[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
  43 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_sn/ qed-.
  44
  45 (* Basic_2A1: was: lpxs_strap1 *)
  46 lemma lprs_step_dx (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ➡*[h] L →
  47                             ∀L2. ⦃G, L⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ ➡*[h] L2.
  48 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.