-lemma snv_fwd_sta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] → ∃U. ⦃G, L⦄ ⊢ T •[h] U.
-#h #g #G #L #T #H elim (snv_fwd_aaa … H) -H /2 width=2 by aaa_sta/
-qed-.
-
-lemma snv_lstas_fwd_correct: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ¡[h, g] → ⦃G, L⦄ ⊢ T1 •* [h, l] T2 →
- ∃U2. ⦃G, L⦄ ⊢ T2 •[h] U2.
-#h #g #G #L #T1 #T2 #l #HT1 #HT12
-elim (snv_fwd_sta … HT1) -HT1 /2 width=5 by lstas_fwd_correct/
+lemma snv_fwd_lstas: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
+ ∀l. ∃U. ⦃G, L⦄ ⊢ T •*[h, l] U.
+#h #g #G #L #T #H #l elim (snv_fwd_aaa … H) -H
+#A #HT elim (aaa_lstas h … HT l) -HT /2 width=2 by ex_intro/