Corollary 1
Tag 0ARJ, permanent. Cite it as [Bourbaki, Tag 0ARJ].
Lie Groups and Lie Algebras, chapter V, § 4. The geometric representation of a Coxeter group
The group W acts simply-transitively on the set of w(C) for w ∈ W.
This is clear.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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