Cauchy-Davenport theorem

Statement
Suppose $$p$$ is a prime number. Denote by $$G = \mathbb{Z}/p\mathbb{Z}$$ the group of prime order $$p$$. Then, for any subsets $$A$$ and $$B$$ of $$G$$, we have the following lower bound on the size of the sumset $$A + B$$of $$A$$ and $$B$$:

$$|A + B| \ge \min \{ p, |A| + |B| - 1 \}$$

Related facts

 * Erdos-Heilbronn conjecture
 * Kneser's theorem
 * Kemperman's theorem