How to prove this TM problem?

U= {m| m is a Turing machine that computes a decision problem }

size(m)::= Length of TM description (standardized) of the TM m.

Prop: Let S(n)={m| m∈U, size(m)=n }.
          Q(n)={q| q is problem that can be computed by a TM in S(n) }
      Q(a)⊂Q(b) iff a<b

I.e. The set of problems that larger TM solve cannot be (all) solved by smaller ones.

Prop is easy to comprehend, but how to prove it?
I have many problems hinge on this proposition.