proof.scala

import scala.language.higherKinds

class Cartesian[F[_]] {
  trait Arbitrary1
  trait Arbitrary2
  implicit val fa1: F[Arbitrary1] = null.asInstanceOf
  implicit val fa2: F[Arbitrary2] = null.asInstanceOf
  class QED
  implicit def proof(implicit fa12: F[(Arbitrary1, Arbitrary2)]): QED = null
}

trait Foo[T]
object Foo {
  implicit def pair[A, B](implicit fa: Foo[A], fb: Foo[B]): Foo[(A, B)] = new Foo[(A, B)] {}
}

object Test {
  object FooIsCartesian extends Cartesian[Foo]
  def test(implicit fc: FooIsCartesian.QED): Unit = ()
  test
}