Definition 2

Tag 04W5, permanent. Cite it as [Bourbaki, Tag 04W5].

Commutative Algebra, chapter VI, § 8. Extensions of a valuation to an algebraic extension

The degree $[\kappa(\mathbf{A}') : \kappa(\mathbf{A})]$ is called the residue class degree of $v'$ over $v$ (or over $\mathbf{K}$ *) and denoted by* $f(v'/v)$ (or $f(A'/A)$ , or sometimes $f(L/K)$ *).

This degree is a natural number or $+\infty$ .

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

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