theorem Th27:
  x, u^w ==>* y, v^w, TS implies x, u ==>* y, v, TS
proof
  assume x, u^w ==>* y, v^w, TS;
  then ==>.-relation(TS) reduces [x, u^w], [y, v^w] by REWRITE3:def 6;
  then ==>.-relation(TS) reduces [x, u], [y, v] by Th26;
  hence thesis by REWRITE3:def 6;
end;
