By the Helmholtz theorem a vector field is described completely by its divergence and curl. As the divergence was not defined, we are justified by choosing the Lorenz Gauge condition above provided that we consistently use this definition of the divergence of A in all subsequent analysis. However, other choices for ∇ ∇ ⋅ ⋅ A are just as valid and lead to other equations, which all describe the same phenomena, and the solutions of the equations for any choice of ∇ ∇ ⋅ ⋅ A lead to the same electromagnetic fields, and the same physical predictions about the fields and charges are accelerated by them.