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

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  14
  15 include "basic_2/static/lfdeq_lfeq.ma".
  16 include "basic_2/rt_transition/lfpx_lpx.ma".
  17 include "basic_2/rt_computation/lfsx_lfsx.ma".
  18
  19 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
  20
  21 (* Properties with unbound rt-transition ************************************)
  22
  23 lemma lfsx_intro_lpx: ∀h,o,G,L1,T.
  24                       (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄) →
  25                       G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄.
  26 #h #o #G #L1 #T #HT
  27 @lfsx_intro #L2 #H
  28 elim (lfpx_inv_lpx_lfeq … H) -H
  29 /6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfeq_lfdeq/
  30 qed-.
  31
  32 lemma lfsx_lpx_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
  33                       ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
  34 /3 width=3 by lfsx_lfpx_trans, lfpx_lpx/ qed-.
  35
  36 (* Eliminators with unbound rt-transition ***********************************)
  37
  38 lemma lfsx_ind_lpx: ∀h,o,G,T. ∀R:predicate lenv.
  39                     (∀L1. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
  40                           (∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) → R L2) →
  41                           R L1
  42                     ) →
  43                     ∀L. G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄  → R L.
  44 /5 width=6 by lfsx_ind, lfpx_lpx/ qed-.