Remark 1

Tag 0ARE, permanent. Cite it as [Bourbaki, Tag 0ARE].

Lie Groups and Lie Algebras, chapter V, § 4. The geometric representation of a Coxeter group

We shall see in no. 4 that $\sigma$ is injective; the group W can thus be identified with the subgroup of $\mathbf{GL}(E)$ generated by the $\sigma_s$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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