(* Properties on atomic arity assignment for terms **************************)
-lemma aaa_lstas: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀l.
- ∃∃U. ⦃G, L⦄ ⊢ T •*[h, l] U & ⦃G, L⦄ ⊢ U ⁝ A.
+lemma aaa_lstas: ∀h,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∀d.
+ ∃∃U. ⦃G, L⦄ ⊢ T •*[h, d] U & ⦃G, L⦄ ⊢ U ⁝ A.
#h #G #L #T #A #H elim H -G -L -T -A
[ /2 width=3 by ex2_intro/
-| * #G #L #K #V #B #i #HLK #HV #IHV #l
- [ elim (IHV l) -IHV #W
+| * #G #L #K #V #B #i #HLK #HV #IHV #d
+ [ elim (IHV d) -IHV #W
elim (lift_total W 0 (i+1))
lapply (drop_fwd_drop2 … HLK)
/3 width=10 by lstas_ldef, aaa_lift, ex2_intro/
- | @(nat_ind_plus … l) -l
+ | @(nat_ind_plus … d) -d
[ elim (IHV 0) -IHV /3 width=7 by lstas_zero, aaa_lref, ex2_intro/
- | #l #_ elim (IHV l) -IHV #W
+ | #d #_ elim (IHV d) -IHV #W
elim (lift_total W 0 (i+1))
lapply (drop_fwd_drop2 … HLK)
/3 width=10 by lstas_succ, aaa_lift, ex2_intro/
]
]
-| #a #G #L #V #T #B #A #HV #_ #_ #IHT #l elim (IHT l) -IHT
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
/3 width=7 by lstas_bind, aaa_abbr, ex2_intro/
-| #a #G #L #V #T #B #A #HV #_ #_ #IHT #l elim (IHT l) -IHT
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
/3 width=6 by lstas_bind, aaa_abst, ex2_intro/
-| #G #L #V #T #B #A #HV #_ #_ #IHT #l elim (IHT l) -IHT
+| #G #L #V #T #B #A #HV #_ #_ #IHT #d elim (IHT d) -IHT
/3 width=6 by lstas_appl, aaa_appl, ex2_intro/
-| #G #L #W #T #A #HW #_ #_ #IHT #l elim (IHT l) -IHT
+| #G #L #W #T #A #HW #_ #_ #IHT #d elim (IHT d) -IHT
/3 width=3 by lstas_cast, aaa_cast, ex2_intro/
]
qed-.
-lemma lstas_aaa_conf: ∀h,G,L,l. Conf3 … (aaa G L) (lstas h l G L).
-#h #G #L #l #A #T #HT #U #HTU
-elim (aaa_lstas h … HT l) -HT #X #HTX
+lemma lstas_aaa_conf: ∀h,G,L,d. Conf3 … (aaa G L) (lstas h d G L).
+#h #G #L #d #A #T #HT #U #HTU
+elim (aaa_lstas h … HT d) -HT #X #HTX
lapply (lstas_mono … HTX … HTU) -T //
qed-.