Corollary
Tag 0AX3, permanent. Cite it as [Bourbaki, Tag 0AX3].
Lie Groups and Lie Algebras, chapter VI, § 2. Affine Weyl group
(i) If \overline{\omega} \in P(R'), there exists an alcove C such that \overline{\omega} is an extremal point of \overline{C}. (ii) If C is an alcove, \overline{C} \cap Q(R') reduces to a single point and this is an extremal point of \overline{C}.
This follows from Prop. 3, in view of the Cor. of Prop. 11 of Chap. V, § 3, no. 10 and Prop. 12 of Chap. V, § 3, no. 10.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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