theorem Th59:
  for P being RedSequence of ==>.-relation(TS) st P.1 = [x, v] & P
  .len P = [y, w] holds len v >= len w
proof
  let P be RedSequence of ==>.-relation(TS);
  assume P.1 = [x, v] & P.len P = [y, w];
  then ex u st v = u^w by Th53;
  hence thesis by Th9;
end;
