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

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  14
  15 include "basic_2/rt_transition/lfpx_fqup.ma".
  16 include "basic_2/rt_computation/lfpxs.ma".
  17
  18 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
  19
  20 (* Advanced eliminators *****************************************************)
  21
  22 (* Basic_2A1: was just: lpxs_ind *)
  23 lemma lfpxs_ind: ∀h,G,L1,T. ∀R:predicate lenv. R L1 →
  24                  (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L → ⦃G, L⦄ ⊢ ⬈[h, T] L2 → R L → R L2) →
  25                  ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L2.
  26 #h #G #L1 #T #R #HL1 #IHL1 #L2 #HL12
  27 @(TC_star_ind … HL1 IHL1 … HL12) //
  28 qed-.
  29
  30 (* Basic_2A1: was just: lpxs_ind_dx *)
  31 lemma lfpxs_ind_dx: ∀h,G,L2,T. ∀R:predicate lenv. R L2 →
  32                     (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h, T] L → ⦃G, L⦄ ⊢ ⬈*[h, T] L2 → R L → R L1) →
  33                     ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → R L1.
  34 #h #o #G #L2 #R #HL2 #IHL2 #L1 #HL12
  35 @(TC_star_ind_dx … HL2 IHL2 … HL12) //
  36 qed-.
  37
  38 (* Advanced properties ******************************************************)
  39
  40 (* Basic_2A1: was just: lpxs_refl *)
  41 lemma lfpxs_refl: ∀h,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h, T] L.
  42 /2 width=1 by lfpx_lfpxs/ qed.