Let g1, g2, ..., gm be linear functionals on ℜn.

Let g1, g2, ..., gm be linear functionals on â„œn. For fixed numbers c1, c2,..., cm, the system of inequalities
gj(x) ≥ cj, j = 1, 2,..., m (31)
is consistent for some x ∈ ℜn if and only if
Let g1, g2, ..., gm be linear functionals on ℜn.

implies that

Let g1, g2, ..., gm be linear functionals on â„œn.

for every set of nonnegative numbers λ1, λ2,..., λm.

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