 The idea underlying the proof is that, because of its sufficiently low degree, can be divided by formula_16 to produce a quotient of degree strictly lower than , and a remainder of still lower degree, so that both will be orthogonal to formula_16, by the defining property of formula_16.Thus

Because of the choice of nodes , the corresponding relation

holds also.The exactness of the computed integral for formula_21 then follows from corresponding exactness for polynomials of degree only or less (as is formula_22).