Proposition 5

Tag 0A6Y, permanent. Cite it as [Bourbaki, Tag 0A6Y].

For x, y in G,

\exp_A \cdot \exp_A y = \exp_A h(x, y).

e^{U e^V} = e^{H(U, V)}

and hence

m \circ (1 + \tilde{\epsilon}, 1 + \tilde{\epsilon}) = (1 + \tilde{\epsilon}) \circ \tilde{H}

\tilde{H}(A \times A; A)

(where m denotes multiplication on A). The proposition then follows from Proposition 2, Lemma 3 and Differentiable and Analytic Manifolds, R, 4.1.5.

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

Cited by

Nothing.