Remark 2
Tag 0AQA, permanent. Cite it as [Bourbaki, Tag 0AQA].
Lie Groups and Lie Algebras, chapter V, § 3. Groups of displacements generated by reflections
It follows from Props. 1 and 2 that, for any non-empty subset A of E, there exists a point such that ; moreover, the group is a Coxeter group (Th. 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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