#h #g #G #L1 #U1 @(fqup_wf_ind_eq … G L1 U1) -G -L1 -U1
#G0 #L0 #U0 #IH #G #L1 * *
[ -IH #k #HG #HL #HU #U2 #H1 #L2 #_ #i #H2 elim (cpx_inv_sort1 … H1) -H1
#h #g #G #L1 #U1 @(fqup_wf_ind_eq … G L1 U1) -G -L1 -U1
#G0 #L0 #U0 #IH #G #L1 * *
[ -IH #k #HG #HL #HU #U2 #H1 #L2 #_ #i #H2 elim (cpx_inv_sort1 … H1) -H1
| #j #HG #HL #HU #U2 #H1 #L2 #HL12 #i #H2 elim (cpx_inv_lref1 … H1) -H1
[ #H destruct elim (frees_inv_lref … H2) -H2 //
* #I #K2 #W2 #Hj #Hji #HLK2 #HW2
| #j #HG #HL #HU #U2 #H1 #L2 #HL12 #i #H2 elim (cpx_inv_lref1 … H1) -H1
[ #H destruct elim (frees_inv_lref … H2) -H2 //
* #I #K2 #W2 #Hj #Hji #HLK2 #HW2
elim (frees_inv_bind … Hi) -Hi #Hi
[ elim (frees_inv_flat … Hi) -Hi
/4 width=7 by frees_flat_dx, frees_flat_sn, frees_bind_sn/
elim (frees_inv_bind … Hi) -Hi #Hi
[ elim (frees_inv_flat … Hi) -Hi
/4 width=7 by frees_flat_dx, frees_flat_sn, frees_bind_sn/
lapply (frees_weak … HU2 0 ?) -HU2
/5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/
]
lapply (frees_weak … HU2 0 ?) -HU2
/5 width=7 by frees_bind_dx_O, frees_flat_dx, lpx_pair/
]