Corollary

Tag 0A83, permanent. Cite it as [Bourbaki, Tag 0A83].

Lie Groups and Lie Algebras, chapter III, § 1. Lie groups

If τ is a vector functor of class C^r for isomorphisms, τ(TX) is a vector G-bundle of class C^{r-1}.

This follows from Propositions 15 and 16.

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

Cited by

Nothing.