Proposition 6

Tag 0DU4, permanent. Cite it as [Bourbaki, Tag 0DU4].

When $A$ is left noetherian, every finitely generated $A$ -module $M$ possesses a free resolution $p : L \to M$ such that $L_n$ is finitely generated for every integer n. More generally:

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.