Remark 3
Tag 0020, permanent. Cite it as [Bourbaki, Tag 0020].
Algebra, VIII, p. 28, § 2. The Structure of Modules of Finite Length
The assumption of assertion a) is satisfied if the A-module M is Noetherian; the assumption of assertion b) is satisfied if M is Artinian; by Proposition 1 of VIII, p. 2, the assumption of assertion c) is satisfied if M has finite length.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.