Remark 2

Tag 0AU9, permanent. Cite it as [Bourbaki, Tag 0AU9].

Lie Groups and Lie Algebras, chapter VI, § 1. Root systems

Proposition 1 reduces the study of root systems to the case $k = \mathbf{Q}$ . Remark 1 reduces it further to the study of root systems in the real vector space $V_{\mathbf{R}} = V_{\mathbf{Q}} \otimes_{\mathbf{Q}} \mathbf{R}$ . The Weyl groups associated to these different systems are canonically identified.

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

Cited by

§ 1. Root systems
Proposition 4, § 1

Cites

Remark 1
Proposition 1