(** ** 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 plength_aux_spec l p :
Pos.to_nat (plength_aux l p) = length l + Pos.to_nat p.