Minimum-energy active-constraint conjecture for EAST+ optimization

Let $E_j$ denote the harvested energy of node $j$ and let $c_4$ denote its consumed energy. Assume that harvested energy is less than consumed energy for every node, so that

$$\forall_j:\ E_j<c_4.$$

The derivative in the displayed expression defining the monotonicity of the measurement constraint is greater than $0$.

Minimum-energy active-constraint conjecture. Under this assumption, the optimal solution requires only the constraint corresponding to the node with minimum energy, $E_1$, to be active; equivalently, the node with minimum energy operates at exact energy-neutral operation.

If true, this would reduce the number of constraints in the EAST+ optimization problem to one. The supplied text does not establish the sign of the derivative or otherwise provide evidence resolving the conjecture.