You just have to use your theorem twice.
so you know that That was a first time, now, with the theorem and addition commutativity:
Supposem,n eN are such that
n >= m. Then n = m + b if and only if b = n - m.
Suppose x,y,z e N are such that y <= x and z <= x. THen, x - y = z if and only if x - z = y.
I must prove this problem as a consequence of the above theorem...any advice?