theorem Th125:
  k <= n implies doms(k,m) c= doms(n,m)
proof
  assume k <= n;
  then
A1: Seg k c= Seg n by FINSEQ_1:5;
  let y;
  assume y in doms(k,m);
  then consider p be Element of (Seg k)* such that
A2: y=p & len p = m;
  rng p c= Seg n by A1;
  then p is FinSequence of Seg n by FINSEQ_1:def 4;
  then p in (Seg n)* by FINSEQ_1:def 11;
  hence thesis by A2;
end;
