(* Properties about atomic arity assignment on terms ************************)
-lemma cpxs_aaa_conf: ∀h,g,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A →
- ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
-#h #g #G #L #T1 #A #HT1 #T2 #HT12
+lemma cpxs_aaa_conf: ∀h,o,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A →
+ ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, o] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
+#h #o #G #L #T1 #A #HT1 #T2 #HT12
@(TC_Conf3 … HT1 ? HT12) -A -T1 -T2 /2 width=5 by cpx_aaa_conf/
qed-.