Corollary 2

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

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

Every regular element of $\mathfrak{g}$ is semi-simple.

Indeed, such an element belongs to a Cartan subalgebra (no. 3, Th. 1 (i)).

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

Nothing.

Cites

no. 3, Th. 1