theorem
  not <%>E in rng dom (the Tran of TS) implies ([[x, u], [y, v]] in
  ==>.-relation(TS) implies len u > len v)
proof
  assume
A1: not <%>E in rng dom (the Tran of TS);
  assume [[x, u], [y, v]] in ==>.-relation(TS);
  then x, u ==>. y, v, TS by Def4;
  hence thesis by A1,Th29;
end;
