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

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  14
  15 include "basic_2/notation/relations/predsnstar_4.ma".
  16 include "basic_2/relocation/lex.ma".
  17 include "basic_2/rt_computation/cprs_ext.ma".
  18
  19 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
  20
  21 definition lprs (h) (G): relation lenv ≝
  22                          lex (λL.cpms h G L 0).
  23
  24 interpretation
  25    "parallel r-computation on all entries (local environment)"
  26    'PRedSnStar h G L1 L2 = (lprs h G L1 L2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma lprs_refl (h) (G): ∀L. ⦃G, L⦄ ⊢ ➡*[h] L.
  31 /2 width=1 by lex_refl/ qed.
  32
  33 (* Basic_2A1: uses: lprs_pair_refl *)
  34 lemma lprs_bind_refl_dx (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ➡*[h] L2 →
  35                                  ∀I. ⦃G, L1.ⓘ{I}⦄ ⊢ ➡*[h] L2.ⓘ{I}.
  36 /2 width=1 by lex_bind_refl_dx/ qed.
  37
  38 (* Basic inversion lemmas ***************************************************)
  39
  40 (* Basic_2A1: uses: lprs_inv_atom1 *)
  41 lemma lprs_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ➡*[h] L2 → L2 = ⋆.
  42 /2 width=2 by lex_inv_atom_sn/ qed-.
  43
  44 (* Basic_2A1: uses: lprs_inv_atom2 *)
  45 lemma lprs_inv_atom_dx (h) (G): ∀L1. ⦃G, L1⦄ ⊢ ➡*[h] ⋆ → L1 = ⋆.
  46 /2 width=2 by lex_inv_atom_dx/ qed-.