It was showed by Donner in [Extension of positive operators and Korovkin theorems, Lecture Notes in Mathematics, vol. 904, Springer-Verlag, Berlin-New York, 1982] that every order complete vector lattice
X
X
may be embedded into a cone
X
s
X^s
, called the sup-completion of
X
X
. We show that if one represents the universal completion of
X
X
as
C
∞
(
K
)
C^\infty (K)
, then
X
s
X^s
is the set of all continuous functions from
K
K
to
[
−
∞
,
∞
]
[-\infty ,\infty ]
that dominate some element of
X
X
. This provides a functional representation of
X
s
X^s
, as well as an easy alternative proof of its existence.