Corollary 1

Tag 03K4, permanent. Cite it as [Bourbaki, Tag 03K4].

Theory of Sets, chapter III, § 2. Well-ordered sets

Let E be an inductive ordered set and let a be an element of E. Then there exists a maximal element m of E such that $m\geq a$ .

For it follows from Definition 3 that the set F of elements $x\geq a$ in E is inductive, and a maximal element of F is also maximal in E.

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 3, § 3
Theorem 1, § 7

Cites

Definition 3