theorem Th32:
  [[x1, x2], [y1, y2]] in ==>.-relation(TS) implies x1 in TS & y1
in TS & x2 in E^omega & y2 in E^omega & x1 in dom dom (the Tran of TS) & y1 in
  rng (the Tran of TS)
proof
  assume [[x1, x2], [y1, y2]] in ==>.-relation(TS);
  then x1, x2 ==>. y1, y2, TS by Def4;
  hence thesis by Th20;
end;
