As homework, I shall show that the retarded scalar potential satisfîes the Lorentz gauge condition as well as the inhomogenous wave equation. We saw in class how to do it. But I was thinking about this, and it seems to me that it's redundant to prove both of those things. For, if the scalar potential satisfies the Lorentz gauge condition, it will automatically lead to the inhomogenous wave equation. So if I show that the retarded scalar potential satisfies the inhomogenous wave equation, that automatically implies that it satisfies the Lorentz gauge condition. So why would I have to prove both assertions?