+#V1s elim V1s -V1s normalize
+[ #T1 #T2 #des #HT12
+ @(ex3_2_intro) [3,4: // |1,2: skip | // ] (**) (* explicit constructor *)
+| #V1 #V1s #IHV1s #T1 #X #des #H
+ elim (lifts_inv_flat1 … H) -H #V2 #Y #HV12 #HY #H destruct
+ elim (IHV1s … HY) -IHV1s -HY #V2s #T2 #HV12s #HT12 #H destruct
+ @(ex3_2_intro) [4: // |3: /2 width=2/ |1,2: skip | // ] (**) (* explicit constructor *)
+]
+qed-.