Last Question of Assignment 2

For the last problem of A2, we have to prove if m >= n, then gcd(m,n) = gcd(n, m-n). I got stuck at first until being inspired by the project of CSC148.

For CSC148, we wrote bunch of methods such as __less_equal__(self, s2), and __equal__(self, s2). For __equal__, the comment says we can just use __less_equal__ by saying (self <= s2 and s2 <= self). That's smart and tricky then I realized a = b is equivalent to  a<= b and b <= a.
Based on what I found above, instead of proving the equation directly, which I found impossible, I can prove it indirectly by proving gcd(m,n) >= gcd(n, m-n) and gcd(m,n) <= gcd(n, m-n).
Here are the steps. Hope that make sense.