(* Properties on atomic arity assignment for terms **************************)
-lemma ssta_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ∀U,l. ⦃h, L⦄ ⊢ T •[g, l] U → L ⊢ U ⁝ A.
+lemma ssta_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ∀U,l. ⦃h, L⦄ ⊢ T •[g] ⦃l, U⦄ → L ⊢ U ⁝ A.
#h #g #L #T #A #H elim H -L -T -A
[ #L #k #U #l #H
elim (ssta_inv_sort1 … H) -H #_ #H destruct //
lapply (ssta_inv_cast1 … H) -H /2 width=2/
]
qed.
-