Paul gave you the answers. Let me put in simple terms for you.
If you have an aircraft traveling at 100kts, trimmed for level flight there are one of two ways to make it climb. Either use elevator, in which case airspeed will decrease, or add power (I should say thrust) and the airplane will climb at the same speed given no other changes. (Rate of climb dependent upon excessive thrust)
To slow down requires two actions. Same situation as above with the airplane in level flight. If all you do is reduce thrust with no trim change, then the airplane will descend at the same airspeed it was trimmed for in level flight.
Now if you and you buddy are talking about the area of flight below L/D Max, then you are opening a whole other can of worms of which I want no part!