In this proof, we will show that the equation ∇ ∇ ⋅ ⋅ E = ρ ρ ε ε 0 is equivalent to the equation ∇ ∇ ⋅ ⋅ D = ρ ρ f r e e Note that we are only dealing with the differential forms, not the integral forms, but that is sufficient since the differential and integral forms are equivalent in each case, by the divergence theorem.