Proposition 5

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

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

Let E be an ordered set and let A, B be two subsets of E, each of which has a least upper bound (resp. greatest lower bound) in E. If $A \subset B$ , then $\sup A \leqslant \sup B$ (resp. $\inf A \geqslant \inf B$ ).

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

Proposition 9, § 1

Cites

Nothing.