Remark 2

Tag 0AXA, permanent. Cite it as [Bourbaki, Tag 0AXA].

Lie Groups and Lie Algebras, chapter VI, § 2. Affine Weyl group

The group $G$ is also the normaliser of $W_a$ in the group of automorphisms of $E$ provided only with its affine structure (cf. Exerc. 3).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.