 Using Solèr's theorem, the field "K" over which the vector space is defined can be proven, with additional hypotheses, to be either the real numbers, complex numbers, or the quaternions, as is needed for Gleason's theorem to hold.By invoking Gleason's theorem, the form of a probability function on lattice elements can be restricted.Assuming that the mapping from lattice elements to probabilities is noncontextual, Gleason's theorem establishes that it must be expressible with the Born rule.