Boolean in scala type

Boolean in scala type.scala

sealed trait BoolType {
  type Not <: BoolType
  type Or[That <: BoolType] <: BoolType
}
sealed trait TrueType extends BoolType {
  override type Not = FalseType
  override type Or[That <: BoolType] = TrueType
}
sealed trait FalseType extends BoolType {
  override type Not = TrueType
  override type Or[That <: BoolType] = That
}
object BoolType {
  type \/[A <: BoolType, B <: BoolType] = A#Or[B]
}


object BoolTypeSpecs {
  import BoolType._

  implicitly[TrueType =:= TrueType]
  implicitly[FalseType =:= FalseType]
  implicitly[TrueType#Not =:= FalseType]
  implicitly[FalseType#Not =:= TrueType]
  implicitly[TrueType#Or[TrueType] =:= TrueType]
  implicitly[TrueType#Or[FalseType] =:= TrueType]
  implicitly[FalseType#Or[TrueType] =:= TrueType]
  implicitly[FalseType#Or[FalseType] =:= FalseType]
  implicitly[\/[TrueType, TrueType] =:= (TrueType \/ TrueType)]
}