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 MaxRlist_P2 : forall l:list R, (exists y : R, In y l) -> In (MaxRlist l) l.