Proposition 5

Tag 0AD2, permanent. Cite it as [Bourbaki, Tag 0AD2].

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

Let G be a Lie group, k a non-discrete closed subfield of K, G' the group G considered as a Lie group over k and $\phi$ (resp. $\phi'$ ) an exponential mapping of G (resp. G'). Then $\phi$ and $\phi'$ coincide on a neighbourhood of 0.

$\phi$ satisfies hypothesis (i) of Theorem 4 relative to G' and is therefore an exponential mapping of G'.

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

Cited by

Proposition 9, § 6

Cites

Theorem 4