  The daseinisation is a mapping from an orthomodular lattice in ordinary
quantum theory into a Heyting algebra in topos quantum theory. While
distributivity does not always hold in orthomodular lattices, it does in
Heyting algebras. We investigate the conditions under which negations and meets
are preserved by daseinisation, and the condition that any element in the
Heyting algebra transformed through daseinisation corresponds to an element in
the original orthomodular lattice. We show that these conditions are
equivalent, and that, not only in the case of non-distributive orthomodular
lattices but also in the case of Boolean algebras containing more than four
elements, the Heyting algebra transformed from the orthomodular lattice through
daseinisation will contain an element that does not correspond to any element
of the original orthomodular lattice.
