Corollary 2

Tag 06CA, permanent. Cite it as [Bourbaki, Tag 06CA].

— The derivation $D_i$ is the unique continuous derivation of the A-algebra $\mathbf{A}[[\mathbf{I}]]$ such that

D_i(X_i) = 1 , \quad D_i(X_j) = 0 \quad \text{for} \quad j \neq i .

This follows from Cor. 1.

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

Cited by

Nothing.