| #L1 #L2 #V #W #A #HV #H1W #H2W #_ #IHL12 #X #s #e #H
elim (drop_inv_O1_pair1 … H) -H * #He #H destruct
[ elim (IHL12 L2 s 0) -IHL12 // #X #H <(drop_inv_O2 … H) -H
- /3 width=8 by lsubc_abbr, drop_pair, ex2_intro/
+ /3 width=8 by lsubc_beta, drop_pair, ex2_intro/
| elim (IHL12 … H) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
]
]
elim (lsubc_inv_pair1 … H) -H *
[ #K1 #HLK1 #H destruct /3 width=3 by lsubc_pair, drop_pair, ex2_intro/
| #K1 #V #W1 #A #HV1 #H1W1 #H2W1 #HLK1 #H1 #H2 #H3 destruct
- /3 width=4 by lsubc_abbr, drop_pair, ex2_intro/
+ /3 width=4 by lsubc_beta, drop_pair, ex2_intro/
]
| #I #L1 #K1 #V1 #e #_ #IHLK1 #K2 #HK12
elim (IHLK1 … HK12) -K1 /3 width=5 by lsubc_pair, drop_drop, ex2_intro/
lapply (aacr_acr … Hacp Hacr A) -Hacp -Hacr #HA
lapply (s0 … HA … HV2 … HLK1 HV3) -HV2
lapply (s0 … HA … H1W2 … HLK1 HW23) -H1W2
- /4 width=11 by lsubc_abbr, aaa_lift, drop_skip, ex2_intro/
+ /4 width=11 by lsubc_beta, aaa_lift, drop_skip, ex2_intro/
]
]
qed-.