reserve X for ARS, a,b,c,u,v,w,x,y,z for Element of X;
reserve i,j,k for Element of ARS_01;
reserve l,m,n for Element of ARS_02;
reserve A for set;

theorem Lem18:
  x <<01>> y implies x <<>> y
  proof
    given z such that
A2: x <=01= z & z =01=> y;
    take z;
    thus x <=*= z & z =*=> y by A2,Lem1;
  end;
