  The Hilbert symbol $(\cdot,\cdot )$ from characteristic $\neq 2$ has two
analogues in characteristic $2$, $[\cdot,\cdot )$ and $((\cdot,\cdot ))$.
  In characteristic $\neq 2$ we have a well known result called the common slot
lemma or the chain lemma. It involves the symbol $(\cdot,\cdot )$. This result
has three analogues in characteristic $2$. Two of these analogues involve the
symbol $[\cdot,\cdot )$ and one involves $((\cdot,\cdot ))$. So far only one of
these analogues has been considered. In this paper we state and prove the
remaining two analogues.
