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36 of ), and so the rest of the proof amounts to a sequence of lengthy calculations which we will briefly summarize. 20) is given by N pr(2) v = v + ϕxj j=1 ∂ ∂ + ϕy + ∂uxj ∂uy N ϕxj xk j,k=1 ∂ ∂uxj xk N ϕxj y + j=1 ∂ ∂ + ϕyy ∂uxj y ∂uyy where the coefficients ϕxj , ϕy , etc. are calculated via a general formula and the expressions uxj , uy , etc. represent the coordinates in the higher order jet spaces. 19) depends only on y, uxj xj , uyy . 21) yields a polynomial in 1, u, Du, D2 u with coefficients that 39 depend on ξ, η, ϕ and their partial derivatives up to order two.