Corollary 1

Tag 05RY, permanent. Cite it as [Bourbaki, Tag 05RY].

If $E, F, G$ are vector spaces over a field $K$ , every exact sequence of linear mappings $0 \to E \to F \to G \to 0$ splits.

This is another way of expressing Proposition 4 (§ 1, no. 9).

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

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Nothing.