Fixpoint MaxRlist (l:list R) : R :=
  match l with
    | nil => 0
    | a :: l1 =>
      match l1 with
        | nil => a
        | a' :: l2 => Rmax a (MaxRlist l1)
      end
  end.Fixpoint MinRlist (l:list R) : R :=
  match l with
    | nil => 1
    | a :: l1 =>
      match l1 with
        | nil => a
        | a' :: l2 => Rmin a (MinRlist l1)
      end
  end.

(* Specifications: *)
Lemma MaxRlist_P1 : forall (l:list R) (x:R), In x l -> x <= MaxRlist l.