Corollary
Tag 00XI, permanent. Cite it as [Bourbaki, Tag 00XI].
Lie Groups and Lie Algebras, chapter VII, Appendix 1. Polynomial maps and Zariski topology
If is algebraically closed and if satisfies the assumptions of Prop. 4, the image under of any dense open subset of V contains a dense open subset of W.
This follows from Props. 3 and 4.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
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Nothing.