Module PartialTree_WandQFrame_Func_Hole.
Definition partialT (rep: tree val -> val -> mpred) (P: tree val -> tree val) (p_root p_in: val): mpred :=
ALL t: tree val, rep t p_in -* rep (P t) p_root.

(* Specifications: *)
Lemma partialT_rep_partialT_rep: forall rep pt12 pt23 p1 p2 p3,
partialT rep pt12 p2 p1 * partialT rep pt23 p3 p2 |-- partialT rep (Basics.compose pt23 pt12) p3 p1.
Lemma emp_partialT_rep_H: forall rep p,
emp |-- partialT rep (fun t => t) p p.
Lemma rep_partialT_rep: forall rep t P p q,
rep t p * partialT rep P q p |-- rep (P t) q.