-lemma structure_lift_path (p) (f):
- ⊗p = ⊗↑[f]p.
-#p elim p -p //
-* [ #n ] #p #IH #f //
-[ <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 //
+lemma structure_lift_path (f) (p):
+ ⊗p = ⊗🠡[f]p.
+#f #p elim p -p //
+* [ #k ] #p #IH //
+[ <lift_path_d_dx <structure_d_dx <structure_d_dx //
+| <lift_path_m_dx <structure_m_dx <structure_m_dx //