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

Lemma loweqK h1 h2 t1 t2 :
def (h1 :+ t1) -> def (h2 :+ t2) ->
h1 =~ h2 -> h1 :+ t1 =~ h2 :+ t2 -> t1 =~ t2.