I've certainly heard that, to move with your hara. The observable effect is for better posture and more centered stances. More likely, in our school, we will hear to drive off the back leg. The observable effect that has is to create more power. From my perspective, I can see doing both at the same time. I think this Mental approach gives you better awareness of where you are, power and center.
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The older I get, the better I was!