(* Properties about atomic arity assignment on terms ************************)
-lemma aaa_cpxs_conf: ∀h,g,L,T1,A. L ⊢ T1 ⁝ A →
- ∀T2. ⦃h, L⦄ ⊢ T1 ➡*[g] T2 → L ⊢ T2 ⁝ A.
-#h #g #L #T1 #A #HT1 #T2 #HT12
+lemma aaa_cpxs_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
@(TC_Conf3 … HT1 ? HT12) -A -T1 -T2 /2 width=5 by aaa_cpx_conf/
qed-.
-lemma aaa_cprs_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡* T2 → L ⊢ T2 ⁝ A.
+lemma aaa_cprs_conf: ∀G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
/3 width=5 by aaa_cpxs_conf, cprs_cpxs/ qed-.