= Solution
For equal logarithmic width $d\log D$, the number of bodies is $n(D)D\,d\log D$. Their mass is therefore
$$
dM=\frac{\pi\rho K}{6}D^{4-\alpha}\,d\log D.
$$
The mass removed by <catastrophic planetesimal collisions> per logarithmic bin per unit time scales as
$$
\dot M_{\rm loss}(D)\propto D^{4-\alpha}R_{\rm cc}(D).
$$
Assume a steady <collisional cascade> with supply only at the large end, loss only at the small end, negligible reassembly or cratering contributions, and self-similar fragmentation that transfers mass through comparable logarithmic intervals. <Mass conservation> requires the downward mass flux across every intermediate size boundary to be the same; otherwise mass would accumulate or deplete there. Under the scale-invariant bin-transfer assumption, this is proportional by a size-independent factor to $\dot M_{\rm loss}$, so
$$
\boxed{D^{4-\alpha}R_{\rm cc}(D)=\mathrm{constant}.}
$$
This is <constant mass flux in a collisional cascade>. Steady state alone fixes the net flux, while the identification with the destruction rate of each bin additionally uses the stated fragmentation assumptions.
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