```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 script implements `activeEmails` using array methods—`.filter()` for selection and `.map()` for transformation. It leverages TypeScript's duck typing to ensure the function behaves exactly as required without explicit checks for the presence of keys in object literals.

**Checklist Verification:**

- The function uses `.filter()` to select only active users.
  - This is a valid implementation when `active` properties do not count as active, which aligns with the problem constraints.
  - No deep nesting or complex conditional logic is required by the interface.