Remark

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

Lie Groups and Lie Algebras, chapter V, § 3. Groups of displacements generated by reflections

Formula (4) is actually valid for all $i, j \in I$ : in fact, $\pi / m_{ij} = 0$ if $m_{ij} = \infty$ , and if $i = j$ then $m_{ij} = 1$ and $(e_i|e_j) = 1$ .

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

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