Let S be the image of D under H. That ∬ ∬ S ∇ ∇ × × F d S = ∮ ∮ Γ Γ F d Γ Γ follows immediately from Stokes' theorem. F is lamellar, so the left side vanishes, i.e. 0 = ∮ ∮ Γ Γ F d Γ Γ = ∑ ∑ i = 1 4 ∮ ∮ Γ Γ i F d Γ Γ