Hi folks,
I'd like to prove for all natural numbers a,b that a +a=b+b implies
a=b.

My ideas so far: Having shown that a<b, a=b, b<a are mutually
exclusive, it should be possible to deduce from a+a=b+b that a<b, b<a
resp. is impossible, so equality must hold.

Or is there an easier way?

Thanks,

Thomas