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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  14
  15 include "basic_2/rt_transition/cpx_rdeq.ma".
  16 include "basic_2/rt_computation/csx_csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
  19
  20 (* Properties with sort-irrelevant equivalence for local environments *******)
  21
  22 (* Basic_2A1: uses: csx_lleq_conf *)
  23 lemma csx_rdeq_conf: ∀h,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →
  24                      ∀L2. L1 ≛[T] L2 → ⦃G, L2⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
  25 #h #G #L1 #T #H
  26 @(csx_ind … H) -T #T1 #_ #IH #L2 #HL12
  27 @csx_intro #T2 #HT12 #HnT12
  28 elim (rdeq_cpx_trans … HL12 … HT12) -HT12
  29 /5 width=5 by cpx_rdeq_conf_sn, csx_tdeq_trans, tdeq_trans/
  30 qed-.
  31
  32 (* Basic_2A1: uses: csx_lleq_conf *)
  33 lemma csx_rdeq_trans: ∀h,L1,L2,T. L1 ≛[T] L2 →
  34                       ∀G. ⦃G, L2⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G, L1⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
  35 /3 width=3 by csx_rdeq_conf, rdeq_sym/ qed-.