Converting code from Eq.contramap example in fp-ts docs

import { contramap, Eq } from 'fp-ts/Eq'
import { pipe } from 'fp-ts/function'
import * as S from 'fp-ts/string'

type UUID = string

interface User {
  readonly key: UUID
  readonly firstName: string
  readonly lastName: string
}

const eqUUID: Eq<UUID> = S.Eq

const eqUserByKey: Eq<User> = pipe(
  eqUUID,
  contramap((user) => user.key)
)

assert.deepStrictEqual(
  eqUserByKey.equals({ key: 'k1', firstName: 'a1', lastName: 'b1' }, { key: 'k2', firstName: 'a1', lastName: 'b1' }),
  false
)
assert.deepStrictEqual(
  eqUserByKey.equals({ key: 'k1', firstName: 'a1', lastName: 'b1' }, { key: 'k1', firstName: 'a2', lastName: 'b1' }),
  true
)