Proposition 2

Tag 01AH, permanent. Cite it as [Bourbaki, Tag 01AH].

Lie Groups and Lie Algebras, chapter IX, § 2. Maximal tori of compact Lie groups

Let $f$ : G $\rightarrow G'$ be a surjective morphism of connected compact Lie groups whose kernel is central. The maps $H \rightarrow f(H)$ and $H' \rightarrow f^{-1}(H')$ are inverse bijections between the set of connected closed subgroups of G of maximal rank and the analogous set for $G'$ .

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.

Cited by

Proposition 3, § 2

Cites

Nothing.