theorem
  for P being RedSequence of ==>.-relation(TS), k st k in dom P & k + 1
in dom P & P.k = [x, u] & P.(k + 1) = [y, v] holds ex w st x, w -->. y, TS & u
  = w^v
proof
  let P be RedSequence of ==>.-relation(TS), k;
  assume k in dom P & k + 1 in dom P & P.k = [x, u] & P.(k + 1) = [y, v];
  then [[x, u], [y, v]] in ==>.-relation(TS) by REWRITE1:def 2;
  hence thesis by Th36;
end;
