-lemma aaa_cpxs_conf: ∀h,g,G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A →
+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
∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
#h #g #G #L #T1 #A #HT1 #T2 #HT12
-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-.
+lemma cprs_aaa_conf: ∀G,L,T1,A. ⦃G, L⦄ ⊢ T1 ⁝ A → ∀T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T2 ⁝ A.
+/3 width=5 by cpxs_aaa_conf, cprs_cpxs/ qed-.