A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation

We display three equivalent conditions for a sublattice, isomorphic to a P {Mathematical expression}, of the propositional system P(ℋ) of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim {Mathematical expression}≥3. We prove that one of them is still necessary and sufficient if dim {Mathematical expression}<3. A physical interpretation of this condition is given.