Brooks Nader is keeping the heat on her ex, Gleb Savchenko -- and she's promising fans will see the proof of his promiscuity for themselves on her family's upcoming Hulu show.

We got the Sports Illustrated model out shopping on Rodeo Drive in Beverly Hills on Monday, and asked about the buzz surrounding her upcoming reality series with her sisters, "Love Thy Nader."

In the show's trailer, Brooks is seen addressing claims Gleb cheated during their relationship -- and she tells us she didn't exactly choose to share it ... 'cause she says he flat-out cheated. Gallery Launch Gallery

Brooks also shades Gleb for constantly speaking out about their fling, telling us he loves to give press interviews about the relationship.

When pressed on what receipts she has to back up her cl

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