Example 3

Tag 00TM, permanent. Cite it as [Bourbaki, Tag 00TM].

Lie Groups and Lie Algebras, chapter VII, § 2. Cartan subalgebras and regular elements of a Lie algebra

Let $\mathfrak{h}$ be a Cartan subalgebra of $\mathfrak{g}$ and let $\mathfrak{g}_1$ be a subalgebra of $\mathfrak{g}$ containing $\mathfrak{h}$ . Then $\mathfrak{h}$ is a Cartan subalgebra of $\mathfrak{g}_1$ ; this follows immediately from Def. 1.

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 1, § 2

Cites

Def. 1