We prove that every semilattice
(
L
,
∧
)
(L, \wedge )
admits an embedding
Q
Q
into the set
R
(
X
)
R(X)
of all partial orders on some set
X
X
such that for all
a
a
,
b
∈
L
b \in L
,
Q
(
a
∧
b
)
=
Q
(
a
)
∩
Q
(
b
)
Q(a \wedge b) = Q(a) \cap Q(b)
and if
a
∨
b
a \vee b
exists then also
Q
(
a
∨
b
)
=
Q
(
b
)
∘
Q
(
a
)
Q(a \vee b) = Q(b) \circ Q(a)
.