Let N represent the number of people in the line.

Basis step: Let N=2. If there are only two people in the line, then clearly a woman is directly in front of a man. Our base case is confirmed and we can continue.

Induction hypothesis: Suppose that in a line of k people, a woman is directly in front of a man.

Next, we need to show that in a line of k+1 people, a woman is directly in front of a man.

Look at the second to last person. If the second to last person is a woman, then clearly a woman is directly in front of a man, and we're done. On the other hand, if the second to last person is a man, then remove the last person and we have the exact same line as k, and therefore a woman is still directly in front of a man. Therefore, the statement is true for k + 1 people.