Corollary

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

Lie Groups and Lie Algebras, chapter III, § 4. Passage from Lie algebras to Lie groups

Let G be a Lie group germ and X a manifold of class $C^r$ . Consider two law chunks of left operation of class $C^r$ of G on X. Suppose that, for all $a \in L(G)$ , the corresponding vector field $D_a$ on X is the same for both law chunks. Then these two law chunks coincide on a neighbourhood of $\{e\} \times X$ .

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

Cited by

Theorem 6, § 4
Corollary 1, § 4
Proposition 16, § 6

Cites

Nothing.