theorem Th62:
  for S, n for q being Element of S^^n holds len decomp(S, n, q) = n
proof
  let S, n;
  reconsider n1 = n as Element of NAT by ORDINAL1:def 12;
  let q be Element of S^^n;
  set p = decomp(S, n, q);
  dom p = Seg n by Def32;
  then len p = n1 by FINSEQ_1:def 3;
  hence thesis;
end;
