Remark 2
Tag 084B, permanent. Cite it as [Bourbaki, Tag 084B].
Functions of a Real Variable, chapter I, § 2. THE MEAN VALUE THEOREM
We shall show later how to identify the case of equality in (7), and also how to generalize th. 2 to the case where E is an arbitrary locally convex space, with the help of another method of proof which allows one to deduce th. 2 from th. 1.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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