theorem Th38:
  x, v -->. y, TS iff [[x, v^w], [y, w]] in ==>.-relation(TS)
proof
  thus x, v -->. y, TS implies [[x, v^w], [y, w]] in ==>.-relation(TS)
  proof
    assume x, v -->. y, TS;
    then x, v^w ==>. y, w, TS;
    hence thesis by Def4;
  end;
  assume [[x, v^w], [y, w]] in ==>.-relation(TS);
  then x, v^w ==>. y, w, TS by Def4;
  hence thesis by Th24;
end;
