Definition 2
Tag 0AXG, permanent. Cite it as [Bourbaki, Tag 0AXG].
Lie Groups and Lie Algebras, chapter VI, § 2. Affine Weyl group
A group G satisfying the equivalent conditions of Prop. 9 is called a crystallographic group.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.