Overcoherence implies holonomicity

Let $\V$ be a mixed characteristic complete discrete valuation ring with perfect residue field. Let $\X$ be a smooth formal scheme over $\V$. We prove than a $\D ^†_{\X,\Q} $-module which is overcoherent after any change of basis is an holonomic $\D ^†_{\X,\Q} $-module. Furthermore, we check that this implies than a bounded complex $\E$ of $\D ^†_{\X,\,\Q}$-modules is overholonomic after any change of basis if and only if, for any integer $j$, $\mathcal{H} ^{j} (\E) $ is overholonomic after any change of basis.

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