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

theorem
  x <=+=> y & y <=+=> z implies x <=*=> z
  proof
    assume
A1: x <=+=> y;
    assume
A2: y <=+=> z;
A3: x <=*=> y by A1,Lem2A;
A4: y <=*=> z by A2,Lem2A;
    thus x <=*=> z by A3,A4,Th7;
  end;
