Example 2

Tag 06YX, permanent. Cite it as [Bourbaki, Tag 06YX].

Algebra, chapter VI, § 2. Ordered fields

A product of ordered rings, equipped with the product ordering, is an ordered ring. In particular the ring $\mathbf{A}^E$ of mappings from a set $E$ to an ordered ring $\mathbf{A}$ is an ordered ring.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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