(** ** Treeify *)
Notation ifpred p n := (if p then pred n else n%nat).
Definition treeify_invariant size (f:treeify_t) :=
forall acc,
size <= length acc ->
let (t,acc') := f acc in
cardinal t = size /\ acc = elements t ++ acc'.

Lemma treeify_aux_spec n (p:bool) :
treeify_invariant (ifpred p (Pos.to_nat n)) (treeify_aux p n).