I don't know if this will make sense to you, but it is easier to get stronger while losing fat, than gaining muscle while losing fat.
A lot of people find they can train their CNS to accept more strain and stimulation, then when their weight is down, they generally pack on decent muscle with a proper diet that requires constant adjustments or tweaks.
Keeping muscle while losing weight can be done and is easier than building muscle while losing weight. Both are possible, one is just much easier for most people.
As far as your belly band, I personally feel it's more of a tool to hide bf than it is to lose bf. However, I have no experience with one, so I may be incorrect.
There are 3 loves in my life: my wife, my English mastiffs, and my weightlifting....Man, my wife gets really pissed when I get the 3 confused...
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