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 treebox_rep_partial_treebox_rep: forall t pt p q,
treebox_rep t p * partial_treebox_rep pt q p |-- treebox_rep (partial_tree_tree pt t) q.