  We look at what type of arguments can rule out the joint reality (or value
definiteness) of two observables of a physical system, such as a qubit, and
give several strong yet simple no-go results based on assumptions typically
weaker than those considered previously. The first result uses simple geometry
combined with a locality assumption to derive device-independent steering
inequalities. These may also be regarded as "conditional" Bell inequalities,
are simpler in principle to test than standard Bell inequalities, and for
two-qubit systems are related to properties of the quantum steering ellipsoid.
We also derive a Bell inequality from locality and a one-sided reality
assumption, and demonstrate a close connection between device-independent
steering and Bell nonlocality. Moreover, we obtain a no-go result without the
use of locality or noncontextuality assumptions, based on similar geometry and
an assumption that we call "operational completeness". The latter is related
to, but strictly weaker than, preparation noncontextuality. All arguments are
given for finite statistics, without requiring any assumption that joint
relative frequencies converge to some (unobservable) joint probability
distribution. We also generalise a recent strong result of Pusey, for
preparation noncontextuality, to the scenarios of device-independent steering
and operational completeness.
