  Suppose $X$ is a closed sub-scheme of $Y$ and $Y$ is a closed sub-scheme of
$Z$ that formally locally has an analog of a tubular neighborhood in a sense
that we define in the paper. In this setting, we prove a formula for
calculating the Segre class of $X$ in $Y$ in terms of the Segre class of $X$ in
$Z$ and the Chern class of the normal bundle of $Y$ in $Z$. Intuitively, this
means that we can obtain the Segre class of $X$ in $Y$ by first calculating the
Segre class of $X$ in $Z$, and then "cancelling out" the contribution of the
embedding of $Y$ in $Z$. It is important to note that the tubular neighborhood
condition may be verified formally locally. As an application, we obtain a
generalization of the Riemann Kempf formula to arbitrary integral curves.
