Stone prime filter theorem (source code)

= Stone prime filter theorem
{c}
{wiki=Boolean_prime_ideal_theorem#Prime_ideal_theorems_for_distributive_lattices}

If a <lattice filter> $F$ and <lattice ideal> $I$ in a <distributive lattice> are disjoint, there is a <prime filter of a distributive lattice> containing $F$ and disjoint from $I$.