Definition 1
Tag 0AQW, permanent. Cite it as [Bourbaki, Tag 0AQW].
Lie Groups and Lie Algebras, chapter V, § 3. Groups of displacements generated by reflections
A point of is special for if it satisfies the equivalent conditions in Prop. 9.
It is clear that the set of special points of is stable under .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.