Theorem 1
Tag 05RI, permanent. Cite it as [Bourbaki, Tag 05RI].
Algebra, chapter II, § 7. Vector spaces
Every vector space over a field K is a free K-module.
It must be proved that every vector space admits a basis; this will follow from the following more precise theorem:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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