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

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  14
  15 include "static_2/syntax/term_vector.ma".
  16 include "basic_2/rt_computation/csx.ma".
  17
  18 (* STRONGLY NORMALIZING TERMS VECTORS FOR UNBOUND PARALLEL RT-TRANSITION ****)
  19
  20 definition csxv: ∀h. sd h → relation3 genv lenv (list term) ≝
  21                  λh,o,G,L. all … (csx h o G L).
  22
  23 interpretation
  24    "strong normalization for unbound context-sensitive parallel rt-transition (term vector)"
  25    'PRedTyStrong h o G L Ts = (csxv h o G L Ts).
  26
  27 (* Basic inversion lemmas ***************************************************)
  28
  29 lemma csxv_inv_cons: ∀h,o,G,L,T,Ts. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⨮Ts⦄ →
  30                      ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄ ∧ ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃Ts⦄.
  31 normalize // qed-.
  32
  33 (* Basic forward lemmas *****************************************************)
  34
  35 lemma csx_fwd_applv: ∀h,o,G,L,T,Vs. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⒶVs.T⦄ →
  36                      ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃Vs⦄ ∧ ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
  37 #h #o #G #L #T #Vs elim Vs -Vs /2 width=1 by conj/
  38 #V #Vs #IHVs #HVs
  39 lapply (csx_fwd_pair_sn … HVs) #HV
  40 lapply (csx_fwd_flat_dx … HVs) -HVs #HVs
  41 elim (IHVs HVs) -IHVs -HVs /3 width=1 by conj/
  42 qed-.