Let *X* be the set of all filters on *B*. Let *f*(*a*) be the subset of all filters that contain *a*. Let *N* be the ideal generated by subsets of *X* of the form (*f*(*a*))^{c}∩(*f*(~*a*))^{c}. One can check that *f*(*a*) is in *N* if and only if *a*=0 (this is pretty easy: if *f*(*a*) is a subset of an intersection of the sets of the form (*f*(*a*_{i}))^{c}∩(*f*(~*a*_{i}))^{c}, then *a* will have to be orthogonal to the meet of all the *a*_{i}. But swapping some of the *a*_{i} with their negations, we see that *a* is orthogonal to every boolean combination of the *a*_{i}, and hence is zero. Moreover, *f* preserves meets, so *f* embeds *B* into 2^{X}/*N*.

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