elim (cprs_inv_abst1 … H) -H #W #U2 #HW3 #_ #H destruct -U3
lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ #HW2
lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ #HV0
lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -L1 #HT2
lapply (snv_lift … HV0 (L2.ⓓW2) (Ⓕ) … HV02) /2 width=1 by drop_drop/ -HV0 #HV2
elim (lift_total XV 0 1) #XW #HXVW
elim (cprs_inv_abst1 … H) -H #W #U2 #HW3 #_ #H destruct -U3
lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ #HW2
lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ #HV0
lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -L1 #HT2
lapply (snv_lift … HV0 (L2.ⓓW2) (Ⓕ) … HV02) /2 width=1 by drop_drop/ -HV0 #HV2
elim (lift_total XV 0 1) #XW #HXVW