Proposition 4
Tag 005V, permanent. Cite it as [Bourbaki, Tag 005V].
Algebra, VIII, p. 83, § 5. Commutation
A semisimple module with finitely generated countermodule is balanced.
This follows from Example 3 of VIII, p. 81 and the remark.
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.