Definition 1
Tag 0AI4, permanent. Cite it as [Bourbaki, Tag 0AI4].
Lie Groups and Lie Algebras, chapter III, § 8. Lie groups over R or Qp
A topological group G is called a real (resp. p-adic) Lie group if there exists on G a real (resp. p-adic) Lie group structure compatible with its topology.
That structure is then unique and we can speak of the dimension of such a group. If G and H are two such groups, every continuous morphism of G into H is analytic.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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