-lemma lpxs_aaa_conf: ∀h,o,G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A →
- ∀L2. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 → ⦃G, L2⦄ ⊢ T ⁝ A.
-#h #o #G #L1 #T #A #HT #L2 #HL12
-@(TC_Conf3 … (λL,A. ⦃G, L⦄ ⊢ T ⁝ A) … HT ? HL12) /2 width=5 by lpx_aaa_conf/
+lemma lpxs_aaa_conf (G) (T):
+ Conf3 … (λL. aaa G L T) (lpxs G).
+#G #T #A #L1 #HT #L2 #H
+lapply (lex_inv_CTC … H) -H //
+@TC_Conf3 [4: // |*: /2 width=4 by lpx_aaa_conf/ ]