Is KNO scaling proved or postulated?

Assuming Feynman's scaling law, Koba, Nielson and Olesen had shown that as s → ∞, (i) 〈n^q〉/〈n〉^q → d_q where d_q is independent of s and $\text{(ii)}\text{σ}{}_{\mathrm{n}}\text{(s)/σ}{}^{\mathrm{(s)}}{}_{\mathrm{<mtext>incl</mtext>}}\text{→ (}\text{1}\text{〈n〉)}\text{Ψ(n/〈n〉)}$. The derivation of the latter result is, however, not rigorous and it does not follow, as a necessary consequence, from the scaling law.