(* Properties about atomic arity assignment on terms ************************)
-lemma aaa_lpxs_conf: ∀h,g,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
+lemma lpxs_aaa_conf: ∀h,g,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
∀L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
#h #g #G #L1 #T #A #HT #L2 #HL12
-@(TC_Conf3 … (λL,A. ⦃G, L⦄ ⊢ T ⁝ A) … HT ? HL12) /2 width=5 by aaa_lpx_conf/
+@(TC_Conf3 … (λL,A. ⦃G, L⦄ ⊢ T ⁝ A) … HT ? HL12) /2 width=5 by lpx_aaa_conf/
qed-.
-lemma aaa_lprs_conf: ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
+lemma lprs_aaa_conf: ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
∀L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
-/3 width=5 by lprs_lpxs, aaa_lpxs_conf/ qed-.
+/3 width=5 by lprs_lpxs, lpxs_aaa_conf/ qed-.