Product of estimates: (âb̂ − ab)² ≤ 2F²((â − a)² + (b̂ − b)²) when |a|, |b̂| ≤ F

For all $\htmlData{mx=1}{a, b, \mathit{ahat}, \mathit{bhat}, F \in \htmlData{mx=0}{\mathbb{R}}}$, if $\htmlData{mx=1}{\left\lvert \htmlData{mx=0}{a} \right\rvert} \mathrel{\htmlData{mx=3}{\leq}} \htmlData{mx=2}{F}$ and $\htmlData{mx=1}{\left\lvert \htmlData{mx=0}{\mathit{bhat}} \right\rvert} \mathrel{\htmlData{mx=3}{\leq}} \htmlData{mx=2}{F}$, then