Problem

Prove that any function $f(x_1,x_2,$dots,$x_n)$ can be expressed in a

complement$-$free form as follows:

$f(x_1,x_2,$dots,$x_n)=d_{0}o+d_1{x}_{1}o+d_2{x}_{2}o+$cdotso$+d_n{x}_n$

$o+d_{n+1}{x}_1{x}_{2}o+d_{n+2}{x}_1{x}_{3}o+$cdotso$+d_{n\frac{n+1}{2}}{x}_{n-1}{x}_n$

$o+d_{[n\frac{n+1}{2}]+1}{x}_1{x}_2{x}_{3}o+cdots{d}_{2^{n-1}}{x}_1{x}_{2}cdots{x}_n,$

where $d_0,d_1,$dots,$d_{2^{n-1}}$ are two$-$valued variables.