matita/matita/contribs/lambdadelta/basic_2/etc/referred/lfpxs_fqup.etc

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  14
  15 include "basic_2/i_static/tc_lfxs_fqup.ma".
  16 include "basic_2/rt_computation/lfpxs.ma".
  17
  18 (* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma lfpxs_refl: ∀h,G,T. reflexive … (lfpxs h G T).
  23 /2 width=1 by tc_lfxs_refl/ qed.
  24
  25 (* Advanced forward lemmas **************************************************)
  26
  27 lemma lfpxs_fwd_bind_dx: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
  28                          ⦃G, L1.ⓑ{I}V⦄ ⊢ ⬈*[h, T] L2.ⓑ{I}V.
  29 /2 width=2 by tc_lfxs_fwd_bind_dx/ qed-.
  30
  31 lemma lfpxs_fwd_bind_dx_void: ∀h,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈*[h, ⓑ{p,I}V.T] L2 →
  32                               ⦃G, L1.ⓧ⦄ ⊢ ⬈*[h, T] L2.ⓧ.
  33 /2 width=4 by tc_lfxs_fwd_bind_dx_void/ qed-.
  34
  35 (* Advanced eliminators *****************************************************)
  36
  37 (* Basic_2A1: uses: lpxs_ind *)
  38 lemma lfpxs_ind_sn: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
  39                     (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
  40                     ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
  41 #h #G @tc_lfxs_ind_sn // (**) (* auto fails *)
  42 qed-.
  43
  44 (* Basic_2A1: uses: lpxs_ind_dx *)
  45 lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
  46                     (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
  47                     ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
  48 #h #G @tc_lfxs_ind_dx // (**) (* auto fails *)
  49 qed-.