Definition 1

Tag 0C3Z, permanent. Cite it as [Bourbaki, Tag 0C3Z].

A metric $d$ on a group $G$ (written multiplicatively) is said to be left-invariant (resp. right-invariant) if we have

d(zx, zy) = d(x, y) \quad [\text{resp. } d(xz, yz) = d(x, y)]

for all $x, y, z$ in $G$ .

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

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