Definition lfresh h := (last null (get_lows h)) .+ 2.
Definition hfresh h := (last (null .+ 1) (get_highs h)) .+ 2.

Lemma highPtUn A h1 h2 (x : ptr) (v : A) :
def (x :-> v :+ h1) -> high x ->
(x :-> v :+ h1 =~ h2) = (h1 =~ h2).