Remark 1
Tag 01AF, permanent. Cite it as [Bourbaki, Tag 01AF].
Lie Groups and Lie Algebras, chapter IX, § 2. Maximal tori of compact Lie groups
Proposition 1 generalizes immediately to connected groups with compact Lie algebras. In particular, if G is a connected Lie group whose Lie algebra is compact, the Cartan subgroups of G (cf. Remark 3, no. 2) are exactly the inverse images of the maximal tori of the connected compact Lie group Ad(G) (under the canonical homomorphism from G to Ad(G)).
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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