In other words, $\smash {\lambda ^{\mathsf{Sets}_{*},\lhd }_{X}}$ acts on elements as
\begin{align*} \lambda ^{\mathsf{Sets}_{*},\lhd }_{X}\webleft (0\lhd x\webright ) & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}x_{0},\\ \lambda ^{\mathsf{Sets}_{*},\lhd }_{X}\webleft (1\lhd x\webright ) & \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}x\end{align*}
for each $1\lhd x\in S^{0}\lhd X$.
