Corollary
Tag 0ASV, permanent. Cite it as [Bourbaki, Tag 0ASV].
Lie Groups and Lie Algebras, chapter V, § 5. Invariants in the symmetric algebra
With the assumptions and notation of Th. 3, the product of the characteristic degrees of R is Card(G).
Indeed, (formula (6), no. 2). The characteristic degrees of S are equal to 1. Then the corollary follows from no. 1, Prop. 2 (iii).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.