Complex sentence: This proof does not provide a method for computing Bézout's coefficients, however, Bézout's lemma is also a corollary of the proof of the Extended Euclidean algorithm and this algorithm does provide an efficient method of computing these coefficients.
Split into simpler sentences: This proof does not provide a method for computing Bézout's coefficients. However, Bézout's lemma is also a corollary of the proof of the Extended Euclidean algorithm and this algorithm does provide an efficient method of computing these coefficients.