How to prove to recipient that we are using public parameters correctly in lattice IBE

Question

Many lattice IBE scheme follow the scheme outlined in ABB10.

In ABB10, the ciphertext is

$c_0 = u^\top s + x$, where $u$ is a public parameter. (No consider message here.)

I want to ask:

Is it possible to make sure the ciphertext is generated following the scheme?

That is, can the sender provide a zero-knowledge proof that $c_1$ is generated from $us+x$, instead of $u's+x$?