  We establish that for any non-empty, compact set
$K\subset\mathbb{R}_{\mathrm{sym}}^{3\times 3}$ the $1$- and $\infty$-symmetric
div-quasiconvex hulls $K^{(1)}$ and $K^{(\infty)}$ coincide. This settles a
conjecture in a recent work of Conti, M\"{u}ller and Ortiz (Symmetric
Div-Quasiconvexity and the Relaxation of Static Problems. Arch. Ration. Mech.
Anal. 235(2):841-880) in the affirmative. As a key novelty, we construct an
$\mathrm{L}^{\infty}$-truncation that preserves both symmetry and solenoidality
of matrix-valued maps in $\mathrm{L}^{1}$.
