Corollary 1
Tag 03NF, permanent. Cite it as [Bourbaki, Tag 03NF].
Theory of Sets, chapter III, § 6. Infinite sets
A totally ordered set E is well-ordered if and only if every decreasing sequence of elements of E is stationary.
For to say that E is well-ordered is equivalent to saying that every non-empty subset of E has a minimal element (§ 1, no. 10, Proposition 10), and the assertion therefore follows from Proposition 6.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
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Nothing.