⊗p = ⊗↑[f]p.
#p elim p -p //
* [ #n ] #p #IH #f //
-[ <lift_path_m_sn <structure_m_sn <structure_m_sn //
+[ <lift_path_d_sn <structure_d_sn <structure_d_sn //
+| <lift_path_m_sn <structure_m_sn <structure_m_sn //
| <lift_path_L_sn <structure_L_sn <structure_L_sn //
]
qed.