Basic understanding of an injected engine and power conservation should be enough here. When you're downshifting you're braking with your engine. This means tw

Basic understanding of an injected engine and power conservation should be enough here. When you're downshifting you're braking with your engine. This means two things: 1. Less fuel is burned. The injectors are closed while the engine is braking. 2. Momentum, not fuel, is used to drive the alternator, AC etc. If you instead were to brake the car, it would need to use fuel just to keep the engine running. In the same way as it would if you were idling parked. Even more fuel is needed to combat the resistance from your AC and alternator.