In other words, $\smash {\lambda ^{\mathsf{Sets}_{*},\rhd }_{X}}$ acts on elements as
\[ \lambda ^{\mathsf{Sets}_{*},\rhd }_{X}\webleft (x\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft [\webleft (1,x\webright )\webright ] \]
i.e. by
\[ \lambda ^{\mathsf{Sets}_{*},\rhd }_{X}\webleft (x\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}1\rhd x \]
for each $x\in X$.
