  Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of
quantum mechanics (QM). Within this theory dispersion free ensembles do not
exist. To accommodate a theory of quantum mechanics that allow dispersion free
ensemble some of the assumptions need be modified. An existing formulation of
QM, the phase space (PS) formulation allow dispersion free ensembles and thus
is qualifies as an hidden variable theory. Within the PS theory we identify the
violated assumption (dubbed I in the text) to be the one that requires that the
value r for the quantity $\mathbb{R}$ implies the value f(r) for the quantity
$f(\mathbb{R})$. We note that this violation arise due to tracking within
c-number hidden variable theory of the operator ordering involved in HS theory
as is required for a 1-1 correspondence between the theories.
