The vertical composition in $\mathsf{Rel}^{\mathsf{dbl}}$ is defined as follows: for each vertically composable pair
of $2$-morphisms of $\mathsf{Rel}^{\mathsf{dbl}}$, i.e. for each each pair of inclusions of relations, we define the vertical compositionof $\alpha $ and $\beta $ as the inclusion of relations
given by the pasting of inclusions[1]