Remark 1

Tag 07R6, permanent. Cite it as [Bourbaki, Tag 07R6].

Topological Vector Spaces, chapter IV, § 1. Duality

Formula (3) is a particular case of (4), corresponding to the linear mapping $\lambda \mapsto \lambda x$ from K into E.

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

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