1. ## Proof help

Theorem:
Suppose
m,n eN are such that

n >= m. Then n = m + b if and only if b = n - m.

The problem:
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?

2. Hi

You just have to use your theorem twice.

$y,z\leq x,$ so you know that $z=x-y\Leftrightarrow x=z+y.$ That was a first time, now, with the theorem and addition commutativity:

$x=z+y\Leftrightarrow ...?$

3. I'm still not seeing how to prove it?? Any more advice?

4. Do you agree with what I've done?

5. Nevermind...I figured it out. Thanks for all your help!

6. Originally Posted by jzellt
Nevermind...I figured it out. Thanks for all your help!
jzelt are you sure the problem is correct??

7. Yes, the problem is correct!