This is what I've found when googling how cabbage leaves work for swelling and Mastitis: Cabbage releases various anti-inflammatory chemicals as well as phytohormones. Leaving the leaves in the bra will have a slow-release effect as the body warms them and draws out beneficial chemicals.
Hot cabbage poultices have also been used for sprains and strains and to draw out splinters. I used the above remedy to treat a breast abscess (a side-effect of mastitis) resistant to antibiotics. Greek women used vine leaves for the same purpose. It would be interesting to find out if the leaves have the same chemicals in them.
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