Cauchy-davenport

The Cauchy-Davenport Theorem states that for all nonempty sets $A,B \subseteq \mathbb{Z}/p\mathbb{Z}$ , we have that $|A+B| \geq \min\{|A|+|B|-1,p\},$ where $A+B$ is defined as the set of all $c \in \mathbb{Z}/p\mathbb{Z}$ that can be expressed as $a+b$ for $a \in A$ and $b \in B$ .