Corollary 2
Tag 06S8, permanent. Cite it as [Bourbaki, Tag 06S8].
Algebra, chapter V, § 14. Transcendental extensions
— Suppose that E = K(x_1, ..., x_m), then m ≥ n; if moreover m = n, then (x_1, ..., x_m) is a pure basis of E over K, and E is then a pure extension of K.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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