Example 4

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

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

The set $\mathfrak{F}(I,\mathbf{R})$ of all real-valued functions defined on an interval I of $\mathbf{R}$ is a lattice with respect to the order relation $f\leqslant g$ (no. 4), and as such is isomorphic to the product $\mathbf{R}^{I}$ . \*

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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