Remark 1
Tag 0AQ9, permanent. Cite it as [Bourbaki, Tag 0AQ9].
Lie Groups and Lie Algebras, chapter V, § 3. Groups of displacements generated by reflections
It follows from Th. 2 that, if C is a chamber and F a facet, there exists a unique facet F' contained in that is transformed into F by an element of W.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.