matita/matita/contribs/lambdadelta/basic_2A/unfold/lstas_aaa.ma

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  14
  15 include "basic_2A/static/aaa_lift.ma".
  16 include "basic_2A/unfold/lstas_lstas.ma".
  17
  18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
  19
  20 (* Properties on atomic arity assignment for terms **************************)
  21
  22 lemma aaa_lstas: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀d.
  23                  ∃∃U. ⦃G, L⦄ ⊢ T •*[h, d] U & ⦃G, L⦄ ⊢ U ⁝ A.
  24 #h #G #L #T #A #H elim H -G -L -T -A
  25 [ /2 width=3 by ex2_intro/
  26 | * #G #L #K #V #B #i #HLK #HV #IHV #d
  27   [ elim (IHV d) -IHV #W
  28     elim (lift_total W 0 (i+1))
  29     lapply (drop_fwd_drop2 … HLK)
  30     /3 width=10 by lstas_ldef, aaa_lift, ex2_intro/
  31   | @(nat_ind_plus … d) -d
  32     [ elim (IHV 0) -IHV /3 width=7 by lstas_zero, aaa_lref, ex2_intro/
  33     | #d #_ elim (IHV d) -IHV #W
  34       elim (lift_total W 0 (i+1))
  35       lapply (drop_fwd_drop2 … HLK)
  36       /3 width=10 by lstas_succ, aaa_lift, ex2_intro/
  37     ]
  38   ]
  39 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
  40   /3 width=7 by lstas_bind, aaa_abbr, ex2_intro/
  41 | #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
  42   /3 width=6 by lstas_bind, aaa_abst, ex2_intro/
  43 | #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
  44   /3 width=6 by lstas_appl, aaa_appl, ex2_intro/
  45 | #G #L #W #T #A #HW #_ #_ #IHT #d elim (IHT d) -IHT
  46   /3 width=3 by lstas_cast, aaa_cast, ex2_intro/
  47 ]
  48 qed-.
  49
  50 lemma lstas_aaa_conf: ∀h,G,L,d. Conf3 … (aaa G L) (lstas h d G L).
  51 #h #G #L #d #A #T #HT #U #HTU
  52 elim (aaa_lstas h … HT d) -HT #X #HTX
  53 lapply (lstas_mono … HTX … HTU) -T //
  54 qed-.