  Second, a failure of NC could be understood in two ways. Either the value of an observable might be context-dependent, although the observable itself is not; or the value of an observable might be context-dependent, because the observable itself is. In either case, the independence from context of an observable implies that there is a correspondence of observables and operators. This implication of NC is what we will use presently in the derivation of FUNC.  We will indeed assume that, if NC holds, this means that the observable — and thereby also its value — is independent of the measurement context, i.e. is independent of how it is measured. In particular, the independence from context of an observable implies that there is a 1:1 correspondence of observables and operators. This implication of NC is what we will use presently in the derivation of FUNC. Conversely, failure of NC will be construed solely as failure of the 1:1 correspondence.