The proof of Gleason’s theorem is notoriously intricate.  It is notable, however, that this corollary of Gleason’s theorem can be obtained more directly via means much more elementary than those employed in Gleason’s proof.  Bell (1982: 994, 1987: 164) credits J. M. Jauch with drawing his attention (in 1963) to Gleason’s theorem, and with pointing out that it implies the strengthening of von Neumann’s result, with the additivity requirement only for commuting observables.  Bell then went on to prove the result in an elementary way, without use of Gleason’s proof (Bell 1966).  Unknown to Bell, Specker had already arrived at this result, alluded to (but not presented) in Specker (1960), as ein elementargeometrisches Argument.[5] The argument was presented in Kochen and Specker (1967).  Bell’s proof and the Kochen-Specker proof utilize similar constructions in 3-dimensional Hilbert space, though they differ in their details. Kochen and Specker go on to explicitly construct a finite set of projections that cannot be assigned values subject to the constraint that the additivity requirement (3) hold when A and B commute.  Though Bell does not do so, one can readily obtain from Bell’s construction also a finite set of observables that cannot be assigned values subject to the additivity constraint for commuting observables (see Mermin 1993).