A Tits System is defined to be a quadruple, $(G,B,N,S)$ consisting of $G$ a group, $B$ and $N$ subgroups of $G$, and $S$ a subset of $W:=N/(N\cap B)$ satisfying the following properties:
a) $B\cup N$ generates $G$ and $B\cap N$ is normal in $N$.
b) The group $W$ is generated by $S$ which consists of elements of order $2$.
c) We have $sBw\subset BwB\cup BswB$ for $s\in S$, $w\in W$.
Remark: $s$ and $w$ are really just classes modulo $N\cap B$ however as sets $sBw, BwB, BswB$ do not depend on the representatives chosen; so the above axiom does make sense.
d) For every $s\in S$ we must have that $sBs$ is not contained in $B$.
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My question is about axiom $c$. I'm confused about the remark. In the set containment claim, are we taking $s$ to be an element of $S$, or a representative of an element in $S$?