  Let $\tau\colon\tilde{\mathcal{E}}\to\mathcal{E}$ be a differential covering
of a PDE $\tilde{\mathcal{E}}$ over $\mathcal{E}$. We prove that if
$\mathcal{E}$ possesses infinite number of symmetries and/or conservation laws
then $\tilde{\mathcal{E}}$ has similar properties.
