 5.1 Theorem:  Let \(L\) be a complete, atomic, irreducible orthomodular lattice satisfying the atomic covering law. If \(L\) contains at least 4 orthogonal atoms, then there exists an involutive division ring \(D\) and a generalized Hilbert space \(\mathbf{V}\) over \(D\) such that \(L\) is isomorphic to \(L(\mathbf{V})\). 