I have asked this question yesterday, and my friend told me, to rememeber to "prove it" also from the other side e.g. Let x $\in$ Conv($M+u$).....then $x$ $\in$ Conv($M$)+ $u$.
Why would somebody care for proving it from the other side, when using only equalities in the first place? If I had used something like
$X$ $\subseteq$ $B$ // one side
$B$ $\subseteq$ $X$ // other side
and from that conclude that $X = B$, I would agree. But why write out the other side when using only equalities?
I think that if using equalities, the other side is useless, am I right?
If not, please give me some examples.