Rumer Willis says mom Demi Moore shows 'courage,' 'vulnerability' in memoir

July 24 (UPI) -- Rumer Willis has nothing but praise for mom Demi Moore's forthcoming memoir.

The 30-year-old actress discussed the book, Inside Out, while attending the Los Angeles premiere of her movie Once Upon a Time in Hollywood on Monday.

Willis spoke to Entertainment Tonight on the red carpet in an interview published Wednesday.

"I actually finished it not too recently and I'm so incredibly proud of her," the star said. "It's so beautiful and she shows such courage and vulnerability."

"I think [it shows] a depth inside of herself that no one has really seen yet, which I'm really excited for people to get to know that side of her," she added.

Inside Out gives a candid look at the ups and downs of Moore's personal and professional life. She discusses her struggles with addiction and body image, and her marriages to Freddy Moore, Bruce Willis and Ashton Kutcher.

Willis attended the Once Upon a Time in Hollywood premiere with her sisters, Scout Willis, 28, and Tallulah Willis, 25. The trio are the daughters of Moore and actor Bruce Willis, who were married from 1987 to 2000.

The sisters posed for photos together on the red carpet. Scout and Tallulah Willis voiced their support for Rumer Willis, who plays Joanna Pettet in Once Upon a Time in Hollywood, on Instagram.

"SISTERS SUPPORTING SISTERS," Scout wrote.

"WE LOVE YOU SISTER," Tallulah added.

Once Upon a Time in Hollywood opens in theaters Friday. Inside Out will be published in September.