theorem Th47:
  for P being RedSequence of ==>.-relation(TS), k st k in dom P &
  k + 1 in dom P holds ex s, v, t, w st P.k = [s, v] & P.(k + 1) = [t, w]
proof
  let P be RedSequence of ==>.-relation(TS), k;
  assume k in dom P & k + 1 in dom P;
  then [P.k, P.(k + 1)] in ==>.-relation(TS) by REWRITE1:def 2;
  hence thesis by Th31;
end;
