The problem mentions that I must prove this by induction.

I did the base case k = 0: If m+0 = n+0, by identity m=n.

Then I attempt to show that m+1 = n+1 implies m=n, but I am stuck, I don't see how induction can be used to prove this and then next predicate that m+k = n+k implies m=n.

Any help would be greatly appreciated, and thanks in advance.