(* Properties about atomic arity assignment on terms ************************)
-lemma aaa_lcprs_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2. L1 ⊢ ➡* L2 → L2 ⊢ T ÷ A.
+lemma aaa_lcprs_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ⊢ ➡* L2 → L2 ⊢ T ⁝ A.
#L1 #T #A #HT #L2 #HL12
-@(TC_Conf3 … (λL,A. L ⊢ T ÷ A) … HT ? HL12) /2 width=3/
+@(TC_Conf3 … (λL,A. L ⊢ T ⁝ A) … HT ? HL12) /2 width=3/
qed.
-lemma aaa_cprs_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2. L ⊢ T1 ➡* T2 → L ⊢ T2 ÷ A.
+lemma aaa_cprs_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡* T2 → L ⊢ T2 ⁝ A.
#L #T1 #A #HT1 #T2 #HT12
@(TC_Conf3 … HT1 ? HT12) /2 width=3/
qed.
-lemma aaa_lcprs_cprs_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2. L1 ⊢ ➡* L2 →
- ∀T2. L2 ⊢ T1 ➡* T2 → L2 ⊢ T2 ÷ A.
+lemma aaa_lcprs_cprs_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ⊢ ➡* L2 →
+ ∀T2. L2 ⊢ T1 ➡* T2 → L2 ⊢ T2 ⁝ A.
/3 width=3/ qed.