$ADD = {x=y+z}$ with $x, y, z$ binary integers, and $x$ is the sum of $y$ and $z$. Pumping lemma to show that $ADD$ is not regular
Your answer has a slight omission: If perchance $y$ is of length $p$ (note: $x$ is permitted to be empty), then choosing $i=0$ leaves one with, not a false equation, but no equation (the string begins with '=').  But of course the conclusion is the same.  You can avoid that nit by choosing $i=2$ (say) instead of $i=0$.

And yes, I think yours is just another correct pick.