(CNN) Supreme Court Justice Ruth Bader Ginsburg's vocal support of the #MeToo movement demonstrates her belief in the continued fight for equality now being led by younger generations, Clara Spera, the granddaughter of the judge, told CNN.

My grandmother "understands that there are generational shifts when it comes to seeking certain rights and equality," Spera told Poppy Harlow and Jeffrey Toobin in the premiere episode of CNN's new podcast series, "RBG: Beyond Notorious," which was released Monday.

"What she may have been fighting [against] in the seventies -- actual black and white discrimination written into laws on paper -- while there may be less of that type of gender-based discrimination now, there are perhaps similarly insidious types of discrimination that appear in different ways," Spera told Harlow and Toobin, adding she believes that progress won in social movements must be codified in law to have a lasting impact.

The podcast series tells the story of the life and times of Ginsburg. The fifth episode revisits the 1970s, when Ginsburg worked as an attorney and the director of the American Civil Liberties Union's Women's Rights Project.

At that time, she took on clients who had experienced gender-based discrimination, arguing six such cases before the Supreme Court.

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