If $D \neq B$, $D \isin L$. By No Replay of $D$ in $L$, $D \le L$.
Thus by Foreign Contents of $L$, $\patchof{D} = \bot$. OK.
If $D \neq B$, $D \isin L$. By No Replay of $D$ in $L$, $D \le L$.
Thus by Foreign Contents of $L$, $\patchof{D} = \bot$. OK.