-lemma snv_inv_bind_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀a,I,V,T. X = ⓑ{a,I}V.T →
- ⦃h, L⦄ ⊩ V :[g] ∧ ⦃h, L.ⓑ{I}V⦄ ⊩ T :[g].
+fact snv_inv_lref_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀i. X = #i →
+ ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃h, K⦄ ⊩ V :[g].
+#h #g #L #X * -L -X
+[ #L #k #i #H destruct
+| #I #L #K #V #i0 #HLK #HV #i #H destruct /2 width=5/
+| #a #I #L #V #T #_ #_ #i #H destruct
+| #a #L #V #W #W0 #T #U #l #_ #_ #_ #_ #_ #i #H destruct
+| #L #W #T #U #l #_ #_ #_ #_ #i #H destruct
+]
+qed.
+
+lemma snv_inv_lref: ∀h,g,L,i. ⦃h, L⦄ ⊩ #i :[g] →
+ ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V & ⦃h, K⦄ ⊩ V :[g].
+/2 width=3/ qed-.
+
+fact snv_inv_bind_aux: ∀h,g,L,X. ⦃h, L⦄ ⊩ X :[g] → ∀a,I,V,T. X = ⓑ{a,I}V.T →
+ ⦃h, L⦄ ⊩ V :[g] ∧ ⦃h, L.ⓑ{I}V⦄ ⊩ T :[g].