End PartialTreeboxRep_WandFrame.
Module PartialTreeboxRep_WandQFrame_Ind_Hole.
Definition partial_treebox_rep (pt: partial_tree val) (p_root p_in: val): mpred :=
ALL t: tree val, treebox_rep t p_in -* treebox_rep (partial_tree_tree pt t) p_root.

Lemma emp_partial_treebox_rep_H: forall p,
emp |-- partial_treebox_rep SearchTree_ext.H p p.