It is needed to prove that $K(x, K(x))=K(x) + O(1)$ where $K$ means Kolmogorov complexity.
I think the equality is true because when we find Kolmogorov complexity of $x$ we already knows $K(x)$ and all that we need for printing also $K(x)$ is only to say that we also must print Kolmogorov complexity of $x$. To say it we need some bytes(O(1)). Could you tell me if my proof is true? If it is not true please help me to find true proof. Thank you in advance.