“Greater than AND smaller than” condition in integer linear program with a binary variable

Question

I found this related question, but that's not quite it

Is it possible to model this with integer programming:

$$A = \begin{cases} 1 & \text{if } B \geq C \geq D \\ 0 & \text{otherwise}\end{cases}$$

where $A \in \{0,1\}$, $B, D \in \mathbb R$ and $C \in \mathbb N$. We have upper and lower bounds on $B$, $C$ and $D$.