Group type class with context bounds

PairGroup.scala

implicit def pairGroup[T1: Group, T2: Group]: Group[(T1, T2)] = {
  val t1Group = implicitly[Group[T1]]
  val t2Group = implicitly[Group[T2]]

  new Group[(T1, T2)] {
    val zero = (t1Group.zero, t2Group.zero)

    def plus(x: (T1, T2), y: (T1, T2)): (T1, T2) = (x, y) match {
      case ((x1, x2), (y1, y2)) =>
        (t1Group.plus(x1, y1), t2Group.plus(x2, y2))
    }

    def inverse(x: (T1, T2)) = x match {
      case (x1, x2) => (t1Group.inverse(x1), t2Group.inverse(x2))
    }
  }
}

pairGroupSig.scala

implicit def pairGroup[T1: Group, T2: Group]: Group[(T1, T2)] = ...

sum.scala

def sum[T: Group](elems: Seq[T]): T =
  elems.foldLeft(implicitly[Group[T]].zero)(implicitly[Group[T]].plus)
 
def sumNonEmpty[T: Group](elems: Seq[T]): Option[T] = 
  if (elems.isEmpty) None
  else Some(sum(elems))
 
def sumDifference[T: Group](elems1: Seq[T], elems2: Seq[T]): T = 
  implicitly[Group[T]].minus(sum(elems1), sum(elems2))

sumSig.scala

def sum[T: Group](elems: Seq[T]): T = ...
def sumNonEmpty[T: Group](elems: Seq[T]): Option[T] = ...
def sumDifference[T: Group](elems1: Seq[Int], elems2: Seq[Int]): Int = ...