```typescript
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 uses array methods `filter` and `map` to achieve the desired functionality without the use of explicit loops or manual index manipulation, adhering to the constraints provided.