theorem Th42:
  s ==>* t, {}(E^omega, E^omega) implies s = t
proof
  assume s ==>* t, {}(E^omega, E^omega);
  then ==>.-relation({}(E^omega, E^omega)) reduces s, t;
  then {}(E^omega, E^omega) reduces s, t by Th29;
  then {} reduces s, t by PARTIT_2:def 1;
  hence thesis by REWRITE1:13;
end;
