# Poincare lemma on current

The Poincare lemma on current states that:

If $U$ is a star-shaped open set in $\mathbb R^n$ and $T$ is a $k$-current on $U$ such that $dT=0$, then there is a $k-1$-current $S$ on $U$ such that $dS = T$.

I wish to find a reference for this result. I know that a proof is given in Demailly's "Complex analytic and algebraic geometry", but it seems to me that this is an online note and is not published in book form. I wish to have a "more reliable" reference, such as a published book or some peer-reviewed journals. Thanks in advanced.