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;
    consider u such that
A3: y <=*=> u & u <==> z by A2,Th8;
    thus x <=+=> z by A3,A1,Th7,Th8;
  end;
