Remark 1

Tag 0AX9, permanent. Cite it as [Bourbaki, Tag 0AX9].

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

The map $\gamma \mapsto \gamma(0)$ is a bijection from $\Gamma_C$ to $\overline{C} \cap P(R^-)$ .

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

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