theorem Th37:
  x, y -->. z, TS iff [[x, y], [z, <%>E]] in ==>.-relation(TS)
proof
  thus x, y -->. z, TS implies [[x, y], [z, <%>E]] in ==>.-relation(TS)
  proof
    assume x, y -->. z, TS;
    then x, y ==>. z, <%>E, TS by Th23;
    hence thesis by Def4;
  end;
  assume [[x, y], [z, <%>E]] in ==>.-relation(TS);
  then x, y ==>. z, <%>E, TS by Def4;
  hence thesis;
end;
