theorem lsubr_trans: Transitive … lsubr.
#L1 #L #H elim H -L1 -L //
[ #I #L1 #L #_ #IH #X #H elim (lsubr_inv_bind1 … H) -H *
- [ #L2 #HL2 #H | #L2 #V #W #HL2 #H1 #H2 | #I1 #I2 #L2 #V #Hl2 #H1 #H2 ]
+ [ #L2 #HL2 #H | #L2 #V #W #HL2 #H1 #H2 | #I1 #I2 #L2 #V #HL2 #H1 #H2 ]
destruct /3 width=1 by lsubr_bind, lsubr_beta, lsubr_unit/
| #L1 #L #V #W #_ #IH #X #H elim (lsubr_inv_abst1 … H) -H *
[ #L2 #HL2 #H | #I #L2 #HL2 #H ]
destruct /3 width=1 by lsubr_beta, lsubr_unit/
| #I1 #I2 #L1 #L #V #_ #IH #X #H elim (lsubr_inv_unit1 … H) -H
- /4 width=1 by lsubr_unit/
+ #L2 #HL2 #H destruct /4 width=1 by lsubr_unit/
]
qed-.