Definition 8
Tag 03QM, permanent. Cite it as [Bourbaki, Tag 03QM].
Theory of Sets, chapter III, § 1. Order relations. Ordered sets
An ordered set E is said to be a lattice if every subset consisting of two elements of E has a least upper bound and a greatest lower bound in E.
Every product of lattices is a lattice; this follows from the condition for the existence of a least upper bound in a product of ordered sets (no. 9, Proposition 8). The set of subsets of a set A, ordered by inclusion, is a lattice because the union and intersection of two subsets of A are again subsets of A.
Examples
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
Nothing.