Does one have a base change theorem in crystalline cohomology like in étale cohomology?

Suppose one has the following cartesian diagram

$$ \newcommand{\ra}[1]{\!\!\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!\!\!\!} \newcommand{\da}[1]{\left\downarrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.} % \begin{array}{lll} U & \to & V \\ \da{f} & & \da{g} \\ X & \ra{h} & Y \\ \end{array} $$

Where $U,V, X, Y$ are all smooth proper scheme over $\mathbb{Z}_p$ and $h$ is embedding. Assume $g$ is a good enough map (smooth, proper, etc..). Consier the map $$ h^* R^1(g_*)_{cry}(\mathcal{O}_{V})\to R^1 (f_{*})_{cry}(\mathcal{O}_U) $$ Is the above map an isomorphism (but not in the sense of derived categories)?