- [ #V3 #T3 #HV3 #HLT3 #H0 destruct
- elim (lift_total V0 0 1) #V4 #HV04
- elim (eq_term_dec (ⓓ{a}V.ⓐV2.T) (ⓓ{a}V3.ⓐV4.T3))
- [ -IHVT #H0 destruct
- elim (eq_false_inv_tpair_sn … H) -H
- [ -HLV10 -HV3 -HLT3 -HVT
- >(lift_inj … HV12 … HV04) -V4
- #H elim H //
- | * #_ #H elim H //
- ]
- | -H -HVT #H
- lapply (cpx_lift … HLV10 (L.ⓓV) (Ⓕ) … HV12 … HV04) -HLV10 -HV12 /2 width=1 by drop_drop/ #HV24
- @(IHVT … H … HV04) -IHVT /4 width=1 by cpx_cpxs, cpx_bind, cpx_flat/
+ [ -HVT #V3 #T3 #HV3 #HLT3 #H0 destruct
+ elim (cpx_lifts_sn … HLV10 (Ⓣ) … (L.ⓓV) … HV12) -HLV10 /3 width=1 by drops_refl, drops_drop/ #V4 #HV04 #HV24
+ elim (tdeq_dec h o (ⓓ{p}V.ⓐV2.T) (ⓓ{p}V3.ⓐV4.T3)) #H0
+ [ -IHVT -HV3 -HV24 -HLT3
+ elim (tdeq_inv_pair … H0) -H0 #_ #HV3 #H0
+ elim (tdeq_inv_pair … H0) -H0 #_ #HV24 #HT3
+ elim (tdneq_inv_pair … H) -H #H elim H -H -G -L
+ /3 width=6 by tdeq_inv_lifts_bi, tdeq_pair/
+ | -V1 @(IHVT … H0 … HV04) -o -V0 /4 width=1 by cpx_cpxs, cpx_flat, cpx_bind/