Remark 3

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

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

Elements of $\mathfrak{g}'$ regular in $\mathfrak{g}$ do not necessarily exist. If at least one does exist, the set of these elements is precisely the set denoted by S in the above proof.

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.

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