Fixpoint AbsList (l:list R) (x:R) : list R :=
  match l with
    | nil => nil
    | a :: l' => (Rabs (a - x) / 2) :: (AbsList l' x)
  end.

Lemma AbsList_P1 : forall (l:list R) (x y:R), In y l -> In (Rabs (y - x) / 2) (AbsList l x).