(* Properties on atomic arity assignment for terms **************************)
-lemma aaa_fpb_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+lemma fpb_aaa_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
-/3 width=6 by aaa_lleq_conf, aaa_lpx_conf, aaa_cpx_conf, aaa_fquq_conf, ex_intro/
+/3 width=6 by aaa_lleq_conf, lpx_aaa_conf, cpx_aaa_conf, aaa_fquq_conf, ex_intro/
qed-.