In Sophocles' The Oedipus Cycle what are some examples that show that a woman's role is to help men get further in life?
First, although Sophocles' plays about Thebes are on related subjects, they are not actually a cycle; they were not written as a trilogy nor were they intended by Sophocles to be performed together.
Next, the notion of a woman's role being "to help men get further in life" is phrased in a way that is somewhat anachronistic. In ancient Greece, the spheres of men and women were completely separate. Women were not involved in politics nor did respectable women (as opposed to prostitutes) attend social events with men, or otherwise help them in their careers. Instead, their role was to stay home, bear children, and take care of two important elements of the household economy, food preparation and weaving. Women also had gender specific religious duties including ones associated with funerals.
Instead, therefore, rather than talking about getting ahead in life, the speeches we find about women's roles in Antigone, for example, emphasize that a woman's role should involve proper subordination to men. Ismene was generally considered an example of how a traditional woman in ancient Greece should behave, and she makes a clear statement about the proper role of women:
Rather, consider that we were born women, proving we should not fight with men, and that we are ruled by more powerful people and must obey them. (61-63)