theorem
  not <%>E in rng dom (the Tran of TS) implies (==>.-relation(TS)
  reduces [x, u], [y, u] implies x = y)
proof
  assume
A1: not <%>E in rng dom (the Tran of TS);
  assume ==>.-relation(TS) reduces [x, u], [y, u];
  then len u > len u or x = y by A1,Th77;
  hence thesis;
end;
