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 partial_treebox_rep_partial_treebox_rep: forall pt12 pt23 p1 p2 p3,
partial_treebox_rep pt12 p2 p1 * partial_treebox_rep pt23 p3 p2 |-- partial_treebox_rep (partial_tree_partial_tree pt23 pt12) p3 p1.