Occam bound on lowest complexity of elements

The combined universal probability M(D)M(D) of strings x in sets D   is close to maxx∈D⁡M({x})maxx∈D⁡M({x}): their ∼logs differ by at most D  's information j=I(D:H)j=I(D:H) about the halting sequence HH. Thus if all x   have complexity K(x)≥kK(x)≥k, D carries ≥i bits of information on each x   where i+j∼ki+j∼k. Note, there are no ways (whether natural or artificial) to generate D   with significant I(D:H)I(D:H).