$L$ elliptic diff op $\implies$ singsupp$(u)\subseteq$singsupp$(Lu)$ for distributions $u$?

Question

If $L:D'(\mathbb{R}^n)\to D'(\mathbb{R}^n),n\in\mathbb{N}$ is a weakly elliptic, linear differential operator with constant coefficients then for every $\Omega\subseteq\mathbb{R}^n$, and for all $u\in D'(\Omega)$ one has $${\rm sing\,supp}(u)\subseteq{\rm sing\,supp}(Lu).$$

I think it's due to Malgrange but I'm not sure. I can't find it for the life of me. Is it a named theorem? Can anyone provide me with a source?

Thanks in advance.

Answer 1

Ahh found it. It's in Taylor's PDE volume I, chapter 3, or so it seems. I don't have the book in front of me.

EDIT: No, that's the one. And we have equality rather than just containment.