immunication target rate of return

This is from curriculum, anyone can help me understand the relationship here? Thanks “For an upward-sloping curve, the immunization target rate of return will be less than the yield to maturity because of the lower reinvestment return. Conversely, a negative or downward sloping yield curve will result in an immunization target rate of return greater than the yied to maturity because of the higher reinvestment return.”

For upward sloping curve the payments you reinvest are going to be reinvested at lower rates in the beginning for downward sloping your reinvested payments are higher yields in the beginning. I think?