Example 1

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

Theory of Sets, chapter III, § 1. Order relations. Ordered sets

\* In the ordered set $E = \mathbf{R}$ of real numbers, consider the subset $F = \mathbf{Q}$ of rational numbers and the set $A \subset F$ of rational numbers $< \sqrt{2}$ ; $\sup_E A$ exists but $\sup_F A$ does not.

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.

Cited by

Example 2, § 1

Cites

Nothing.