reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;

theorem Th8:
  x <=+=> y iff ex z st x <=*=> z & z <==> y
  proof
    x <=+=> y iff ex z st y <==> z & z <=*=> x by Def8;
    hence thesis;
  end;
