Definition 4
Tag 048Q, permanent. Cite it as [Bourbaki, Tag 048Q].
Commutative Algebra, chapter II, § 3. Local rings. Passage from the local to the global
A ring is called semi-local if it satisfies the equivalent conditions (a), (b) of Proposition 16.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Nothing.