Corollary 4

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

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

Let B be a basis of R, $B'$ a subset of B, $V'$ the vector subspace of V generated by $B'$ , and $R' = R \cap V'$ . Then $B'$ is a basis of the root system $B'$ .

This follows immediately from Cor. 3 and the Cor. of Prop. 4.

We call $R'$ the root system generated by $B'$ .

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

Cited by

Corollary 5, § 1
Corollary 6, § 1
Proposition 28, § 1
§ 4. Classification of root systems

Cites

Cor. of Prop. 4
Cor. 3