I'm supposed to prove that:

If 0<y(1)<x(1) and x(n+1)=(x(n)+y(n))/2 and y(n+1)=sqrt(x(n)y(n)

then 0<y(n)<x(n).

I can't figure out how to get started on this proof. I can see that it should be an induction proof...but I can't figure out how to prove it. Any help would be great.