+[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 //
+ ]
+]
+qed-.
+
+lemma snv_fquq_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ¡[h, o] → ⦃G2, L2⦄ ⊢ T2 ¡[h, o].
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fquq_inv_gen … H) -H [|*]
+/2 width=5 by snv_fqu_conf/
+qed-.
+
+lemma snv_fqup_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ¡[h, o] → ⦃G2, L2⦄ ⊢ T2 ¡[h, o].
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/3 width=5 by fqup_strap1, snv_fqu_conf/
+qed-.
+
+lemma snv_fqus_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+ ⦃G1, L1⦄ ⊢ T1 ¡[h, o] → ⦃G2, L2⦄ ⊢ T2 ¡[h, o].
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqus_inv_gen … H) -H [|*]
+/2 width=5 by snv_fqup_conf/