- elim (lift_total W 0 (i+1)) /3 width=7/
-| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2/
-| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2/
-| #G #L #V #T #B #A #_ #_ #_ * /3 width=2/
-| #G #L #W #T #A #_ #_ #_ * /3 width=2/
+ elim (lift_total W 0 (i+1)) /3 width=7 by sta_ldef, sta_ldec, ex_intro/
+| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_bind, ex_intro/
+| #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_bind, ex_intro/
+| #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by sta_appl, ex_intro/
+| #G #L #W #T #A #_ #_ #_ * /3 width=2 by sta_cast, ex_intro/
+]
+qed-.
+
+lemma sta_aaa_conf: ∀h,G,L. Conf3 … (aaa G L) (sta h G L).
+#h #G #L #T #A #H elim H -G -L -T -A
+[ #G #L #k #U #H
+ lapply (sta_inv_sort1 … H) -H #H destruct //
+| #I #G #L #K #V #B #i #HLK #HV #IHV #U #H
+ elim (sta_inv_lref1 … H) -H * #K0 #V0 #W0 #HLK0 #HVW0 #HU
+ lapply (drop_mono … HLK0 … HLK) -HLK0 #H0 destruct
+ lapply (drop_fwd_drop2 … HLK) -HLK #HLK
+ @(aaa_lift … HLK … HU) -HU -L /2 width=2 by/
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+ elim (sta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2 by aaa_abbr/
+| #a #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+ elim (sta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2 by aaa_abst/
+| #G #L #V #T #B #A #HV #_ #_ #IHT #X #H
+ elim (sta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3 by aaa_appl/
+| #G #L #V #T #A #_ #_ #IHV #IHT #X #H
+ lapply (sta_inv_cast1 … H) -H /2 width=2 by/