Let $\displaystyle \mathcal{V}_{ar}=\{+,.,0,1\}$ be the vocabulary of arithmetic. Let R be the structure that has universe $\displaystyle \mathbb{R}$ and interprets the vocabulary in the usual manner.

Define a $\displaystyle \mathcal{V}_{ar}$ formula $\displaystyle \beta(x,y)$ such that for any

$\displaystyle a,b\in\mathbb{R}, R\models\beta(a,b) $ if and only if $\displaystyle b\geq{a}$.

Is this correct (i think that it is but im just a little unsure)

$\displaystyle a=b\vee (\exists{y}(y\neq0\wedge\exists{x}(x.x=y))\wedge a+y=b)$

thanks for any help