```ts
export interface User {
  email: string;
  active: boolean;
}

/** The lowercased addresses of the active users, in order. */
export function activeEmails(users: readonly User[]): string[] {
  return users.filter(user => user.active).map(user => user.email.toLowerCase());
}
```

This solution introduces a pure function `activeEmails` that uses:
- `.filter()` to find only the active users.
- `.map()` to transform each active user's email into lowercase.