-lemma snv_lsstas_fwd_correct: ∀h,g,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 ¡[h, g] → ⦃G, L⦄ ⊢ T1 •* [h, g, l] T2 →
- ∃U2. ⦃G, L⦄ ⊢ T2 •[h, g] U2.
-#h #g #G #L #T1 #T2 #l #HT1 #HT12
-elim (snv_fwd_ssta … HT1) -HT1 /2 width=5 by lsstas_fwd_correct/
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma snv_scast: ∀h,g,G,L,V,W,l. ⦃G, L⦄ ⊢ V ¡[h, g] → ⦃G, L⦄ ⊢ W ¡[h, g] →
- scast h g l G L V W → ⦃G, L⦄ ⊢V ▪[h, g] l+1 → ⦃G, L⦄ ⊢ ⓝW.V ¡[h, g].
-#h #g #G #L #V #W #l #HV #HW #H #Hl
-elim (snv_fwd_ssta … HV) /4 width=6 by snv_cast, ssta_lsstas/
+lemma snv_fwd_lstas: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] →
+ ∀d. ∃U. ⦃G, L⦄ ⊢ T •*[h, d] U.
+#h #o #G #L #T #H #d elim (snv_fwd_aaa … H) -H
+#A #HT elim (aaa_lstas h … HT d) -HT /2 width=2 by ex_intro/