Let $N\in\mathbb N$, let $M\subset\mathbb C^N$ be a real-analytic embedded generic CR submanifold, and let $T^{0,1}M\subset \mathbb C TM$ denote the induced antiholomorphic CR bundle. Let $f\in\mathcal D'(M)$ be a CR distribution, meaning that for every [open set](/page/Open%20Set) $U\subset M$ and every real-analytic local section $\bar L\in\Gamma(U,T^{0,1}M)$ one has $\bar L f=0$ in $\mathcal D'(U)$. Let $\operatorname{Char}(\bar\partial_b)\subset T^*M\setminus\{0\}$ be the set of nonzero covectors $\eta\in T_p^*M$ such that the principal symbol of every real-analytic local section of $T^{0,1}M$ vanishes at $(p,\eta)$. Then

\begin{align*} \operatorname{WF}_a(f)\subset \operatorname{Char}(\bar\partial_b). \end{align*}

Moreover, for every $p\in M$, the distribution $f$ is represented by a real-[analytic function](/page/Analytic%20Function) on some neighbourhood of $p$ in $M$ if and only if

\begin{align*} \operatorname{WF}_a(f)\cap \bigl(T_p^*M\setminus\{0\}\bigr)=\varnothing. \end{align*}