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

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  14
  15 include "basic_2/notation/relations/predtysnstar_5.ma".
  16 include "basic_2/rt_transition/lfpx.ma".
  17
  18 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
  19
  20 definition lfpxs: ∀h. relation4 genv term lenv lenv ≝
  21                   λh,G,T. TC … (lfpx h G T).
  22
  23 interpretation
  24    "uncounted parallel rt-computation on referred entries (local environment)"
  25    'PRedTySnStar h T G L1 L2 = (lfpxs h G T L1 L2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 (* Basic_2A1: was just: lpx_lpxs *)
  30 lemma lfpx_lfpxs: ∀h,G,T,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
  31 /2 width=1 by inj/ qed.
  32
  33 (* Basic_2A1: was just: lpxs_strap1 *)
  34 lemma lfpxs_strap1: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
  35 /2 width=3 by step/ qed.
  36
  37 (* Basic_2A1: was just: lpxs_strap2 *)
  38 lemma lfpxs_strap2: ∀h,G,T,L1,L,L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → ⦃G, L1⦄ ⊢ ⬈*[h, T] L2.
  39 /2 width=3 by TC_strap/ qed.
  40 (*
  41 (* Basic_2A1: was just: lpxs_pair_refl *)
  42 lemma lfpxs_pair_refl: ∀h,G,T,L1,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈*[h, T] L2.ⓑ{I}V.
  43 /2 width=1 by TC_lpx_sn_pair_refl/ qed.
  44
  45 (* Basic inversion lemmas ***************************************************)
  46
  47 (* Basic_2A1: was just: lpxs_inv_atom1 *)
  48 lemma lfpxs_inv_atom1: ∀h,G,L2.T. ⦃G, ⋆⦄ ⊢ ⬈*[h, T] L2 → L2 = ⋆.
  49 /2 width=2 by TC_lpx_sn_inv_atom1/ qed-.
  50
  51 (* Basic_2A1: was just: lpxs_inv_atom2 *)
  52 lemma lfpxs_inv_atom2: ∀h,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] ⋆ → L1 = ⋆.
  53 /2 width=2 by TC_lpx_sn_inv_atom2/ qed-.
  54 *)