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This paper deals with the order of the graduate module $k[X_0,\mathrm{\cdots },X_n]/(f_1,\mathrm{\cdots },f_m)$ where $f_1,\mathrm{\cdots },f_m$ is a $k[X_0,\mathrm{\cdots },X_n]$-sequence of polynomials. The general form of Bézout's theorem is deduced from the calculation of this order. An alternative proof of this theorem is given, under the assumption that $n=m$.