Proposition 4

Tag 013N, permanent. Cite it as [Bourbaki, Tag 013N].

Lie Groups and Lie Algebras, chapter VIII, § 7. Finite dimensional modules over a split semi-simple Lie algebra

Let V be a finite dimensional $\mathfrak{g}$ -module and $d$ an integer $\geq 1$ . The set of weights of V of multiplicity $\geq d$ is R-saturated.

This follows immediately from Prop. 3.

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.

Cited by

Proposition 5, § 7

Cites

Prop. 3