theorem Th58:
  x, v -->. y, TS iff <*[x, v^w], [y, w]*> is RedSequence of ==>.-relation(TS)
proof
  thus x, v -->. y, TS implies <*[x, v^w], [y, w]*> is RedSequence of
  ==>.-relation(TS)
  proof
    assume x, v -->. y, TS;
    then [[x, v^w], [y, w]] in ==>.-relation(TS) by Th38;
    hence thesis by REWRITE1:7;
  end;
  assume <*[x, v^w], [y, w]*> is RedSequence of ==>.-relation(TS);
  then [[x, v^w], [y, w]] in ==>.-relation(TS) by Th8;
  hence thesis by Th38;
end;
