Corollary 2

Tag 0DW2, permanent. Cite it as [Bourbaki, Tag 0DW2].

Let

0\longrightarrow E_n\longrightarrow E_{n-1}\longrightarrow\cdots\longrightarrow E_1\longrightarrow0

be an exact sequence of right $A$ -modules. If $E_i$ is flat for $i=1,\ldots,n-1$ , then $E_n$ is flat.

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

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