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

theorem
  x <=+=> y & y =01=> z implies x <=+=> z
  proof
    assume
A1: x <=+=> y;
    assume
A2: y =01=> z;
A3: y <=01=> z by A2,Lem43;
    thus x <=+=> z by A1,A3,Lem18;
  end;
