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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2A/static/aaa_lift.ma".
16 include "basic_2A/unfold/lstas_lstas.ma".
18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
20 (* Properties on atomic arity assignment for terms **************************)
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/
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/
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 //