  We establish the new main inequality as a minimizing criterion for minimal
maps to products of $\mathbb{R}$-trees, and the infinitesimal new main
inequality as a stability criterion for minimal maps to $\mathbb{R}^n$. Along
the way, we develop a new perspective on destabilizing minimal surfaces in
$\mathbb{R}^n$, and as a consequence we reprove the instability of some
classical minimal surfaces; for example, the Enneper surface.
