theorem Th48:
  for P being RedSequence of ==>.-relation(TS), k st k in dom P &
k + 1 in dom P holds P.k = [(P.k)`1, (P.k)`2] & P.(k + 1) = [(P.(k + 1))`1, (P.
  (k + 1))`2]
proof
  let P be RedSequence of ==>.-relation(TS), k;
  assume k in dom P & k + 1 in dom P;
  then ex s, v, t, w st P.k = [s, v] & P.(k + 1) = [t, w] by Th47;
  hence thesis;
end;
