I am looking for a reference for the following admittedly imprecise statement:
Any projective invariant of n points in the projective plane may be expressed as a function of well-chosen cross-ratios.
By projective invariant I mean a rational function defined on the set of $n$-tuple of distinct points in the projective plane on an arbitrary field $K$, invariant under the action of the projective group of transformations. This is a folklore result that is often stated without proof (e.g. in Efimov, higher geometry) but I can't find a reference providing a precise statement and a proof.