Remark 1
Tag 0AA6, permanent. Cite it as [Bourbaki, Tag 0AA6].
Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra
It is the action of G on itself by right translation which defines the fields of left invariant distributions.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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