```ts
/**
 * The lowercased addresses of the active users, in order.
 */
export function activeEmails(users: readonly User[]): string[] {
  const map = new Map();

  for (const user of users) {
    if (user.active) {
      map.set(user.email, user);
    }
  }

  return Array.from(map.values())
    .map(({ email }) => email.toLowerCase())
    .filter(Boolean);
}
```