theorem Th57:
  x, y -->. z, TS iff <*[x, y], [z, <%>E]*> is RedSequence of ==>.-relation(TS)
proof
  thus x, y -->. z, TS implies <*[x, y], [z, <%>E]*> is RedSequence of
  ==>.-relation(TS)
  proof
    assume x, y -->. z, TS;
    then [[x, y], [z, <%>E]] in ==>.-relation(TS) by Th37;
    hence thesis by REWRITE1:7;
  end;
  assume <*[x, y], [z, <%>E]*> is RedSequence of ==>.-relation(TS);
  then [[x, y], [z, <%>E]] in ==>.-relation(TS) by Th8;
  hence thesis by Th37;
end;
