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

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  14
  15 include "basic_2/static/lfdeq_lfeq.ma".
  16 include "basic_2/rt_computation/lfpxs_lpxs.ma".
  17 include "basic_2/rt_computation/lfsx_lfpxs.ma".
  18
  19 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
  20
  21 (* Properties with unbound rt-computation ***********************************)
  22
  23 lemma lfsx_intro_lpxs: ∀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_lfpxs #L2 #H
  28 elim (lfpxs_inv_lpxs_lfeq … H) -H
  29 /6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfeq_lfdeq/
  30 qed-.
  31
  32 lemma lfsx_lpxs_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_lfpxs_trans, lfpxs_lpxs/ qed-.
  35
  36 (* Eliminators with unbound rt-computation **********************************)
  37
  38 lemma lfsx_ind_lpxs: ∀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_lfpxs, lfpxs_lpxs/ qed-.