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

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  14
  15 include "static_2/static/rdeq_length.ma".
  16 include "basic_2/rt_transition/lpx_length.ma".
  17 include "basic_2/rt_computation/rdsx.ma".
  18
  19 (* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 (* Basic_2A1: uses: lsx_sort *)
  24 lemma rdsx_sort (h) (o) (G): ∀L,s. G ⊢ ⬈*[h, o, ⋆s] 𝐒⦃L⦄.
  25 #h #o #G #L1 #s @rdsx_intro #L2 #H #Hs
  26 elim Hs -Hs /3 width=3 by lpx_fwd_length, rdeq_sort_length/
  27 qed.
  28
  29 (* Basic_2A1: uses: lsx_gref *)
  30 lemma rdsx_gref (h) (o) (G): ∀L,l. G ⊢ ⬈*[h, o, §l] 𝐒⦃L⦄.
  31 #h #o #G #L1 #s @rdsx_intro #L2 #H #Hs
  32 elim Hs -Hs /3 width=3 by lpx_fwd_length, rdeq_gref_length/
  33 qed.
  34
  35 lemma rdsx_unit (h) (o) (G): ∀I,L. G ⊢ ⬈*[h, o, #0] 𝐒⦃L.ⓤ{I}⦄.
  36 #h #o #G #I #L1 @rdsx_intro
  37 #Y #HY #HnY elim HnY -HnY
  38 elim (lpx_inv_unit_sn … HY) -HY #L2 #HL12 #H destruct
  39 /3 width=3 by lpx_fwd_length, rdeq_unit_length/
  40 qed.