I have these two definitions:
\documentclass[12pt]{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign*}
&\boldsymbol{R*^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')&\\
&\boldsymbol{R*_{weak}^\sigma} & \sigma_{superset}(F)&=\sigma_{superset}(F')\cap\mathcal{P}(A)&
\end{flalign*}
\end{document}
Compiled, it looks like this: 
I want the equations to be aligned by "=" as they are; but also that they are not centered but quite next to the bold symbols. Like, also aligned left.
It should look like this (done with MS Paint): 
