Help needed!

**Def.**
Let $F(x _ 1,\dots,x _ n),G(x _ 1,\dots,x _ n)$ be two polynomials in $K[x _ 1,\dots,x _ n].$ $F,G$ are indecomposable iff there are no $u(x)\in K[x]$ with $\operatorname{deg}(u)\ge 2$ satisfying $F=u(H)$ for any $H\in K[x _ 1,\dots,x _ n]$.

**Prop.** If $F,G$ are two indecomposable polynomial and exist one variable polynomials $U _ 1(x),U _ 2(x)$ s.t. $U _ 1(F)=U _ 2(G)$, then $G=aF+b$ for $a,b\in K$.

Is there an elementary proof to this proposition? Note that $F,G$ has at least two variables or this proposition is trivially satisfied. Thanks alot!