+ lapply (da_inv_lift … Hl … HLK … HTU) -Hl #Hl
+ elim (ssta_inv_lift1 … HUW … HLK … HTU) -HUW #V #HVW #HTV
+ lapply (cpcs_inv_lift G … HLK … HVW … HVW0 ?) // -W /3 width=4/
+]
+qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma snv_fqu_conf: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ¡[h, g] → ⦃G2, L2⦄ ⊢ T2 ¡[h, g].
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+[ #I1 #G1 #L1 #V1 #H
+ elim (snv_inv_lref … H) -H #I2 #L2 #V2 #H #HV2
+ lapply (ldrop_inv_O2 … H) -H #H destruct //
+|2: *
+|5,6: /3 width=7 by snv_inv_lift/
+]
+[1,3: #a #I #G1 #L1 #V1 #T1 #H elim (snv_inv_bind … H) -H //
+|2,4: * #G1 #L1 #V1 #T1 #H
+ [1,3: elim (snv_inv_appl … H) -H //
+ |2,4: elim (snv_inv_cast … H) -H //
+ ]