Example 1

Tag 03T9, permanent. Cite it as [Bourbaki, Tag 03T9].

Theory of Sets, chapter III, § 4. Natural integers. Finite sets

The set of totally ordered subsets of an ordered set $E$ is of finite character. Indeed, a subset $X$ of $E$ is totally ordered if and only if every subset of $X$ consisting of two elements is totally ordered.

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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