theorem
  TS is deterministic implies ([x, [y1, z1]] in ==>.-relation(TS) & [x,
  [y2, z2]] in ==>.-relation(TS) implies y1 = y2 & z1 = z2)
proof
  assume
A1: TS is deterministic;
  assume
  [x, [y1, z1]] in ==>.-relation(TS) & [x, [y2, z2]] in ==>.-relation( TS);
  then [y1, z1] = [y2, z2] by A1,Th44;
  hence thesis by XTUPLE_0:1;
end;
